Plotting and Theoretical Overview

Gaussian Assumption for Normality

The Gaussian (normal) distribution is a key assumption in many statistical methods. It is mathematically represented by the probability density function (PDF):

\[f(x) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)\]

where:

\(\mu\) is the mean
\(\sigma^2\) is the variance

In a normally distributed dataset:

68% of data falls within \(\mu \pm \sigma\)
95% within \(\mu \pm 2\sigma\)
99.7% within \(\mu \pm 3\sigma\)

Histograms and Kernel Density Estimation (KDE)

Histograms:

Visualize data distribution by binning values and counting frequencies.
If data is Gaussian, the histogram approximates a bell curve.

KDE:

A non-parametric way to estimate the PDF by smoothing individual data points with a kernel function.
The KDE for a dataset \(X = \{x_1, x_2, \ldots, x_n\}\) is given by:

\[\hat{f}(x) = \frac{1}{nh} \sum_{i=1}^{n} K\left(\frac{x - x_i}{h}\right)\]

where:

\(K\) is the kernel function (often Gaussian)
\(h\) is the bandwidth (smoothing parameter)

Combined Use of Histograms and KDE

Histograms offer a discrete, binned view of the data.
KDE provides a smooth, continuous estimate of the underlying distribution.
Together, they effectively illustrate how well the data aligns with the Gaussian assumption, highlighting any deviations from normality.

Pearson Correlation Coefficient

The Pearson correlation coefficient, often denoted as \(r\), is a measure of the linear relationship between two variables. It quantifies the degree to which a change in one variable is associated with a change in another variable. The Pearson correlation ranges from \(-1\) to \(1\), where:

\(r = 1\) indicates a perfect positive linear relationship.
\(r = -1\) indicates a perfect negative linear relationship.
\(r = 0\) indicates no linear relationship.

The Pearson correlation coefficient between two variables \(X\) and \(Y\) is defined as:

\[r_{XY} = \frac{\text{Cov}(X, Y)}{\sigma_X \sigma_Y}\]

where:

\(\text{Cov}(X, Y)\) is the covariance of \(X\) and \(Y\).
\(\sigma_X\) is the standard deviation of \(X\).
\(\sigma_Y\) is the standard deviation of \(Y\).

Covariance measures how much two variables change together. It is defined as:

\[\text{Cov}(X, Y) = \frac{1}{n} \sum_{i=1}^{n} (X_i - \mu_X)(Y_i - \mu_Y)\]

where:

\(n\) is the number of data points.
\(X_i\) and \(Y_i\) are the individual data points.
\(\mu_X\) and \(\mu_Y\) are the means of \(X\) and \(Y\).

The standard deviation measures the dispersion or spread of a set of values. For a variable \(X\), the standard deviation \(\sigma_X\) is:

\[\sigma_X = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (X_i - \mu_X)^2}\]

Substituting the covariance and standard deviation into the Pearson correlation formula:

\[r_{XY} = \frac{\sum_{i=1}^{n} (X_i - \mu_X)(Y_i - \mu_Y)}{\sqrt{\sum_{i=1}^{n} (X_i - \mu_X)^2} \sqrt{\sum_{i=1}^{n} (Y_i - \mu_Y)^2}}\]

This formula normalizes the covariance by the product of the standard deviations of the two variables, resulting in a dimensionless coefficient that indicates the strength and direction of the linear relationship between \(X\) and \(Y\).

\(r > 0\): Positive correlation. As \(X\) increases, \(Y\) tends to increase.
\(r < 0\): Negative correlation. As \(X\) increases, \(Y\) tends to decrease.
\(r = 0\): No linear correlation. There is no consistent linear relationship between \(X\) and \(Y\).

The closer the value of \(r\) is to \(\pm 1\), the stronger the linear relationship between the two variables.

Partial Dependence Foundations

Let \(\mathbf{X}\) represent the complete set of input features for a machine learning model, where \(\mathbf{X} = \{X_1, X_2, \dots, X_p\}\). Suppose we’re particularly interested in a subset of these features, denoted by \(\mathbf{X}_S\). The complementary set, \(\mathbf{X}_C\), contains all the features in \(\mathbf{X}\) that are not in \(\mathbf{X}_S\). Mathematically, this relationship is expressed as:

\[\mathbf{X}_C = \mathbf{X} \setminus \mathbf{X}_S\]

where \(\mathbf{X}_C\) is the set of features in \(\mathbf{X}\) after removing the features in \(\mathbf{X}_S\).

Partial Dependence Plots (PDPs) are used to illustrate the effect of the features in \(\mathbf{X}_S\) on the model’s predictions, while averaging out the influence of the features in \(\mathbf{X}_C\). This is mathematically defined as:

\[\begin{split}\begin{align*} \text{PD}_{\mathbf{X}_S}(x_S) &= \mathbb{E}_{\mathbf{X}_C} \left[ f(x_S, \mathbf{X}_C) \right] \\ &= \int f(x_S, x_C) \, p(x_C) \, dx_C \\ &= \int \left( \int f(x_S, x_C) \, p(x_C \mid x_S) \, dx_C \right) p(x_S) \, dx_S \end{align*}\end{split}\]

where:

\(\mathbb{E}_{\mathbf{X}_C} \left[ \cdot \right]\) indicates that we are taking the expected value over the possible values of the features in the set \(\mathbf{X}_C\).
\(p(x_C)\) represents the probability density function of the features in \(\mathbf{X}_C\).

This operation effectively summarizes the model’s output over all potential values of the complementary features, providing a clear view of how the features in \(\mathbf{X}_S\) alone impact the model’s predictions.

2D Partial Dependence Plots

Consider a trained machine learning model 2D Partial Dependence Plots \(f(\mathbf{X})\), where \(\mathbf{X} = (X_1, X_2, \dots, X_p)\) represents the vector of input features. The partial dependence of the predicted response \(\hat{y}\) on a single feature \(X_j\) is defined as:

\[\text{PD}(X_j) = \frac{1}{n} \sum_{i=1}^{n} f(X_j, \mathbf{X}_{C_i})\]

where:

\(X_j\) is the feature of interest.
\(\mathbf{X}_{C_i}\) represents the complement set of \(X_j\), meaning the remaining features in \(\mathbf{X}\) not included in \(X_j\) for the \(i\)-th instance.
\(n\) is the number of observations in the dataset.

For two features, \(X_j\) and \(X_k\), the partial dependence is given by:

\[\text{PD}(X_j, X_k) = \frac{1}{n} \sum_{i=1}^{n} f(X_j, X_k, \mathbf{X}_{C_i})\]

This results in a 2D surface plot (or contour plot) that shows how the predicted outcome changes as the values of \(X_j\) and \(X_k\) vary, while the effects of the other features are averaged out.

Single Feature PDP: When plotting \(\text{PD}(X_j)\), the result is a 2D line plot showing the marginal effect of feature \(X_j\) on the predicted outcome, averaged over all possible values of the other features.
Two Features PDP: When plotting \(\text{PD}(X_j, X_k)\), the result is a 3D surface plot (or a contour plot) that shows the combined marginal effect of \(X_j\) and \(X_k\) on the predicted outcome. The surface represents the expected value of the prediction as \(X_j\) and \(X_k\) vary, while all other features are averaged out.

3D Partial Dependence Plots

For a more comprehensive analysis, especially when exploring interactions between two features, 3D Partial Dependence Plots are invaluable. The partial dependence function for two features in a 3D context is:

\[\text{PD}(X_j, X_k) = \frac{1}{n} \sum_{i=1}^{n} f(X_j, X_k, \mathbf{X}_{C_i})\]

Here, the function \(f(X_j, X_k, \mathbf{X}_{C_i})\) is evaluated across a grid of values for \(X_j\) and \(X_k\). The resulting 3D surface plot represents how the model’s prediction changes over the joint range of these two features.

The 3D plot offers a more intuitive visualization of feature interactions compared to 2D contour plots, allowing for a better understanding of the combined effects of features on the model’s predictions. The surface plot is particularly useful when you need to capture complex relationships that might not be apparent in 2D.

Feature Interaction Visualization: The 3D PDP provides a comprehensive view of the interaction between two features. The resulting surface plot allows for the visualization of how the model’s output changes when the values of two features are varied simultaneously, making it easier to understand complex interactions.
Enhanced Interpretation: 3D PDPs offer enhanced interpretability in scenarios where feature interactions are not linear or where the effect of one feature depends on the value of another. The 3D visualization makes these dependencies more apparent.

KDE and Histogram Distribution Plots

KDE Distribution Function

Generate KDE or histogram distribution plots for specified columns in a DataFrame.

The kde_distributions function is a versatile tool designed for generating Kernel Density Estimate (KDE) plots, histograms, or a combination of both for specified columns within a DataFrame. This function is particularly useful for visualizing the distribution of numerical data across various categories or groups. It leverages the powerful seaborn library [2] for plotting, which is built on top of matplotlib [3] and provides a high-level interface for drawing attractive and informative statistical graphics.

Key Features and Parameters

Flexible Plotting: The function supports creating histograms, KDE plots, or a combination of both for specified columns, allowing users to visualize data distributions effectively.
Leverages Seaborn Library: The function is built on the seaborn library, which provides high-level, attractive visualizations, making it easy to create complex plots with minimal code.
Customization: Users have control over plot aesthetics, such as colors, fill options, grid sizes, axis labels, tick marks, and more, allowing them to tailor the visualizations to their needs.
Scientific Notation Control: The function allows disabling scientific notation on the axes, providing better readability for certain types of data.
Log Scaling: The function includes an option to apply logarithmic scaling to specific variables, which is useful when dealing with data that spans several orders of magnitude.
Output Options: The function supports saving plots as PNG or SVG files, with customizable filenames and output directories, making it easy to integrate the plots into reports or presentations.

kde_distributions(df, vars_of_interest=None, figsize=(5, 5), grid_figsize=None, hist_color='#0000FF', kde_color='#FF0000', mean_color='#000000', median_color='#000000', hist_edgecolor='#000000', hue=None, fill=True, fill_alpha=1, n_rows=None, n_cols=None, w_pad=1.0, h_pad=1.0, image_path_png=None, image_path_svg=None, image_filename=None, bbox_inches=None, single_var_image_filename=None, y_axis_label='Density', plot_type='both', log_scale_vars=None, bins='auto', binwidth=None, label_fontsize=10, tick_fontsize=10, text_wrap=50, disable_sci_notation=False, stat='density', xlim=None, ylim=None, plot_mean=False, plot_median=False, std_dev_levels=None, std_color='#808080', label_names=None, show_legend=True, **kwargs)

Parameters:

df (pandas.DataFrame) – The DataFrame containing the data to plot.
vars_of_interest (list of str, optional) – List of column names for which to generate distribution plots. If ‘all’, plots will be generated for all numeric columns.
figsize (tuple of int, optional) – Size of each individual plot, default is (5, 5). Used when only one plot is being generated or when saving individual plots.
grid_figsize (tuple of int, optional) – Size of the overall grid of plots when multiple plots are generated in a grid. Ignored when only one plot is being generated or when saving individual plots. If not specified, it is calculated based on figsize, n_rows, and n_cols.
hist_color (str, optional) – Color of the histogram bars, default is '#0000FF'.
kde_color (str, optional) – Color of the KDE plot, default is '#FF0000'.
mean_color (str, optional) – Color of the mean line if plot_mean is True, default is '#000000'.
median_color (str, optional) – Color of the median line if plot_median is True, default is '#000000'.
hist_edgecolor (str, optional) – Color of the histogram bar edges, default is '#000000'.
hue (str, optional) – Column name to group data by, adding different colors for each group.
fill (bool, optional) – Whether to fill the histogram bars with color, default is True.
fill_alpha (float, optional) – Alpha transparency for the fill color of the histogram bars, where 0 is fully transparent and 1 is fully opaque. Default is 1.
n_rows (int, optional) – Number of rows in the subplot grid. If not provided, it will be calculated automatically.
n_cols (int, optional) – Number of columns in the subplot grid. If not provided, it will be calculated automatically.
w_pad (float, optional) – Width padding between subplots, default is 1.0.
h_pad (float, optional) – Height padding between subplots, default is 1.0.
image_path_png (str, optional) – Directory path to save the PNG image of the overall distribution plots.
image_path_svg (str, optional) – Directory path to save the SVG image of the overall distribution plots.
image_filename (str, optional) – Filename to use when saving the overall distribution plots.
bbox_inches (str, optional) – Bounding box to use when saving the figure. For example, 'tight'.
single_var_image_filename (str, optional) – Filename to use when saving the separate distribution plots. The variable name will be appended to this filename. This parameter uses figsize for determining the plot size, ignoring grid_figsize.
y_axis_label (str, optional) – The label to display on the y-axis, default is 'Density'.
plot_type (str, optional) – The type of plot to generate, options are 'hist', 'kde', or 'both'. Default is 'both'.
log_scale_vars (str or list of str, optional) – Variable name(s) to apply log scaling. Can be a single string or a list of strings.
bins (int or sequence, optional) – Specification of histogram bins, default is 'auto'.
binwidth (float, optional) – Width of each bin, overrides bins but can be used with binrange.
label_fontsize (int, optional) – Font size for axis labels, including xlabel, ylabel, and tick marks, default is 10.
tick_fontsize (int, optional) – Font size for tick labels on the axes, default is 10.
text_wrap (int, optional) – Maximum width of the title text before wrapping, default is 50.
disable_sci_notation (bool, optional) – Toggle to disable scientific notation on axes, default is False.
stat (str, optional) – Aggregate statistic to compute in each bin (e.g., 'count', 'frequency', 'probability', 'percent', 'density'), default is 'density'.
xlim (tuple or list, optional) – Limits for the x-axis as a tuple or list of (min, max).
ylim (tuple or list, optional) – Limits for the y-axis as a tuple or list of (min, max).
plot_mean (bool, optional) – Whether to plot the mean as a vertical line, default is False.
plot_median (bool, optional) – Whether to plot the median as a vertical line, default is False.
std_dev_levels (list of int, optional) – Levels of standard deviation to plot around the mean.
std_color (str or list of str, optional) – Color(s) for the standard deviation lines, default is '#808080'.
label_names (dict, optional) – Custom labels for the variables of interest. Keys should be column names, and values should be the corresponding labels to display.
show_legend (bool, optional) – Whether to show the legend on the plots, default is True.
kwargs (additional keyword arguments) – Additional keyword arguments passed to the Seaborn plotting function.

Raises:

ValueError –
- If plot_type is not one of 'hist', 'kde', or 'both'.
- If stat is not one of 'count', 'density', 'frequency', 'probability', 'proportion', 'percent'.
- If log_scale_vars contains variables that are not present in the DataFrame.
- If fill is set to False and hist_edgecolor is not the default.
- If grid_figsize is provided when only one plot is being created.
UserWarning –
- If both bins and binwidth are specified, which may affect performance.

Returns:

None

KDE and Histograms Example

In the below example, the kde_distributions function is used to generate histograms for several variables of interest: "age", "education-num", and "hours-per-week". These variables represent different demographic and financial attributes from the dataset. The plot_type="both" parameter ensures that a Kernel Density Estimate (KDE) plot is overlaid on the histograms, providing a smoothed representation of the data’s probability density.

The visualizations are arranged in a single row of four columns, as specified by n_rows=1 and n_cols=3, respectively. The overall size of the grid figure is set to 14 inches wide and 4 inches tall (grid_figsize=(14, 4)), while each individual plot is configured to be 4 inches by 4 inches (single_figsize=(4, 4)). The fill=True parameter fills the histogram bars with color, and the spacing between the subplots is managed using w_pad=1 and h_pad=1, which add 1 inch of padding both horizontally and vertically.

Note

If you do not set n_rows or n_cols to any values, the function will automatically calculate and create a grid based on the number of variables being plotted, ensuring an optimal arrangement of the plots.

To handle longer titles, the text_wrap=50 parameter ensures that the title text wraps to a new line after 50 characters. The bbox_inches="tight" setting is used when saving the figure, ensuring that it is cropped to remove any excess whitespace around the edges. The variables specified in vars_of_interest are passed directly to the function for visualization.

Each plot is saved individually with filenames that are prefixed by "kde_density_single_distribution", followed by the variable name. The `y-axis` for all plots is labeled as “Density” (y_axis_label="Density"), reflecting that the height of the bars or KDE line represents the data’s density. The histograms are divided into 10 bins (bins=10), offering a clear view of the distribution of each variable.

Additionally, the font sizes for the axis labels and tick labels are set to 16 points (label_fontsize=16) and 14 points (tick_fontsize=14), respectively, ensuring that all text within the plots is legible and well-formatted.

from eda_toolkit import kde_distributions

vars_of_interest = [
    "age",
    "education-num",
    "hours-per-week",
]

kde_distributions(
    df=df,
    n_rows=1,
    n_cols=3,
    grid_figsize=(14, 4),  # Size of the overall grid figure
    fill=True,
    fill_alpha=0.60,
    text_wrap=50,
    bbox_inches="tight",
    vars_of_interest=vars_of_interest,
    y_axis_label="Density",
    bins=10,
    plot_type="both", # Can also just plot KDE by itself by passing "kde"
    label_fontsize=16,  # Font size for axis labels
    tick_fontsize=14,  # Font size for tick labels
)

Histogram Example (Density)

In this example, the kde_distributions() function is used to generate histograms for the variables "age", "education-num", and "hours-per-week" but with plot_type="hist", meaning no KDE plots are included—only histograms are displayed. The plots are arranged in a single row of four columns (n_rows=1, n_cols=3), with a grid size of 14x4 inches (grid_figsize=(14, 4)). The histograms are divided into 10 bins (bins=10), and the y-axis is labeled “Density” (y_axis_label="Density"). Font sizes for the axis labels and tick labels are set to 16 and 14 points, respectively, ensuring clarity in the visualizations. This setup focuses on the histogram representation without the KDE overlay.

from eda_toolkit import kde_distributions

vars_of_interest = [
    "age",
    "education-num",
    "hours-per-week",
]

kde_distributions(
    df=df,
    n_rows=1,
    n_cols=3,
    grid_figsize=(14, 4),  # Size of the overall grid figure
    fill=True,
    text_wrap=50,
    bbox_inches="tight",
    vars_of_interest=vars_of_interest,
    y_axis_label="Density",
    bins=10,
    plot_type="hist",
    label_fontsize=16,  # Font size for axis labels
    tick_fontsize=14,  # Font size for tick labels
)

KDE Distributions - Histograms (Density)

Histogram Example (Count)

In this example, the kde_distributions() function is modified to generate histograms with a few key changes. The hist_color is set to “orange”, changing the color of the histogram bars. The y-axis label is updated to “Count” (y_axis_label="Count"), reflecting that the histograms display the count of observations within each bin. Additionally, the stat parameter is set to "Count" to show the actual counts instead of densities. The rest of the parameters remain the same as in the previous example, with the plots arranged in a single row of four columns (n_rows=1, n_cols=3), a grid size of 14x4 inches, and a bin count of 10. This setup focuses on visualizing the raw counts in the dataset using orange-colored histograms.

from eda_toolkit import kde_distributions

vars_of_interest = [
    "age",
    "education-num",
    "hours-per-week",
]

kde_distributions(
    df=df,
    n_rows=1,
    n_cols=3,
    grid_figsize=(14, 4),  # Size of the overall grid figure
    text_wrap=50,
    hist_color="orange",
    bbox_inches="tight",
    vars_of_interest=vars_of_interest,
    y_axis_label="Count",
    bins=10,
    plot_type="hist",
    stat="Count",
    label_fontsize=16,  # Font size for axis labels
    tick_fontsize=14,  # Font size for tick labels
)

Histogram Example - (Mean and Median)

In this example, the kde_distributions() function is customized to generate histograms that include mean and median lines. The mean_color is set to "blue" and the median_color is set to "black", allowing for a clear distinction between the two statistical measures. The function parameters are adjusted to ensure that both the mean and median lines are plotted (plot_mean=True, plot_median=True). The y_axis_label remains "Density", indicating that the histograms represent the density of observations within each bin. The histogram bars are colored using hist_color="brown", with a fill_alpha=0.60 while the s tatistical overlays enhance the interpretability of the data. The layout is configured with a single row and multiple columns (n_rows=1, n_cols=3), and the grid size is set to 15x5 inches. This example highlights how to visualize central tendencies within the data using a histogram that prominently displays the mean and median.

from eda_toolkit import kde_distributions

vars_of_interest = [
    "age",
    "education-num",
    "hours-per-week",
]

kde_distributions(
    df=df,
    n_rows=1,
    n_cols=3,
    grid_figsize=(14, 4),  # Size of the overall grid figure
    text_wrap=50,
    hist_color="brown",
    bbox_inches="tight",
    vars_of_interest=vars_of_interest,
    y_axis_label="Density",
    bins=10,
    fill_alpha=0.60,
    plot_type="hist",
    stat="Density",
    label_fontsize=16,  # Font size for axis labels
    tick_fontsize=14,  # Font size for tick labels
    plot_mean=True,
    plot_median=True,
    mean_color="blue",
)

Histogram Example - (Mean, Median, and Std. Deviation)

In this example, the kde_distributions() function is customized to generate a histogram that include mean, median, and 3 standard deviation lines. The mean_color is set to "blue" and the median_color is set to "black", allowing for a clear distinction between these two central tendency measures. The function parameters are adjusted to ensure that both the mean and median lines are plotted (plot_mean=True, plot_median=True). The y_axis_label remains "Density", indicating that the histograms represent the density of observations within each bin. The histogram bars are colored using hist_color="brown", with a fill_alpha=0.40, which adjusts the transparency of the fill color. Additionally, standard deviation bands are plotted using colors "purple", "green", and "silver" for one, two, and three standard deviations, respectively.

The layout is configured with a single row and multiple columns (n_rows=1, n_cols=3), and the grid size is set to 15x5 inches. This setup is particularly useful for visualizing the central tendencies within the data while also providing a clear view of the distribution and spread through the standard deviation bands. The configuration used in this example showcases how histograms can be enhanced with statistical overlays to provide deeper insights into the data.

Note

You have the freedom to choose whether to plot the mean, median, and standard deviation lines. You can display one, none, or all of these simultaneously.

from eda_toolkit import kde_distributions

vars_of_interest = [
    "age",
]

kde_distributions(
    df=df,
    figsize=(10, 6),
    text_wrap=50,
    hist_color="brown",
    bbox_inches="tight",
    vars_of_interest=vars_of_interest,
    y_axis_label="Density",
    bins=10,
    fill_alpha=0.40,
    plot_type="both",
    stat="Density",
    label_fontsize=16,  # Font size for axis labels
    tick_fontsize=14,  # Font size for tick labels
    plot_mean=True,
    plot_median=True,
    mean_color="blue",
    image_path_svg=image_path_svg,
    image_path_png=image_path_png,
    std_dev_levels=[
        1,
        2,
        3,
    ],
    std_color=[
        "purple",
        "green",
        "silver",
    ],
)

Stacked Crosstab Plots

Generates stacked bar plots and crosstabs for specified columns in a DataFrame.

The stacked_crosstab_plot function is a versatile tool for generating stacked bar plots and contingency tables (crosstabs) from a pandas DataFrame. This function is particularly useful for visualizing categorical data across multiple columns, allowing users to easily compare distributions and relationships between variables. It offers extensive customization options, including control over plot appearance, color schemes, and the ability to save plots in multiple formats.

The function also supports generating both regular and normalized stacked bar plots, with the option to return the generated crosstabs as a dictionary for further analysis.

stacked_crosstab_plot(df, col, func_col, legend_labels_list, title, kind='bar', width=0.9, rot=0, custom_order=None, image_path_png=None, image_path_svg=None, save_formats=None, color=None, output='both', return_dict=False, x=None, y=None, p=None, file_prefix=None, logscale=False, plot_type='both', show_legend=True, label_fontsize=12, tick_fontsize=10, text_wrap=50, remove_stacks=False)

Generates stacked or regular bar plots and crosstabs for specified columns.

This function allows users to create stacked bar plots (or regular bar plots if stacks are removed) and corresponding crosstabs for specific columns in a DataFrame. It provides options to customize the appearance, including font sizes for axis labels, tick labels, and title text wrapping, and to choose between regular or normalized plots.

Parameters:

df (pandas.DataFrame) – The DataFrame containing the data to plot.
col (str) – The name of the column in the DataFrame to be analyzed.
func_col (list) – List of ground truth columns to be analyzed.
legend_labels_list (list) – List of legend labels for each ground truth column.
title (list) – List of titles for the plots.
kind (str, optional) – The kind of plot to generate ('bar' or 'barh' for horizontal bars), default is 'bar'.
width (float, optional) – The width of the bars in the bar plot, default is 0.9.
rot (int, optional) – The rotation angle of the x-axis labels, default is 0.
custom_order (list, optional) – Specifies a custom order for the categories in the col.
image_path_png (str, optional) – Directory path where generated PNG plot images will be saved.
image_path_svg (str, optional) – Directory path where generated SVG plot images will be saved.
save_formats (list, optional) – List of file formats to save the plot images in.
color (list, optional) – List of colors to use for the plots. If not provided, a default color scheme is used.
output (str, optional) – Specify the output type: "plots_only", "crosstabs_only", or "both". Default is "both".
return_dict (bool, optional) – Specify whether to return the crosstabs dictionary, default is False.
x (int, optional) – The width of the figure.
y (int, optional) – The height of the figure.
p (int, optional) – The padding between the subplots.
file_prefix (str, optional) – Prefix for the filename when output includes plots.
logscale (bool, optional) – Apply log scale to the y-axis, default is False.
plot_type (str, optional) – Specify the type of plot to generate: "both", "regular", "normalized". Default is "both".
show_legend (bool, optional) – Specify whether to show the legend, default is True.
label_fontsize (int, optional) – Font size for axis labels, default is 12.
tick_fontsize (int, optional) – Font size for tick labels on the axes, default is 10.
text_wrap (int, optional) – The maximum width of the title text before wrapping, default is 50.
remove_stacks (bool, optional) – If True, removes stacks and creates a regular bar plot using only the col parameter. Only works when plot_type is set to 'regular'. Default is False.
xlim (tuple or list, optional) – Limits for the x-axis as a tuple or list of (min, max).
ylim (tuple or list, optional) – Limits for the y-axis as a tuple or list of (min, max).

Raises:

ValueError –
- If output is not one of "both", "plots_only", or "crosstabs_only".
- If plot_type is not one of "both", "regular", "normalized".
- If remove_stacks is set to True and plot_type is not "regular".
- If the lengths of title, func_col, and legend_labels_list are not equal.
KeyError – If any columns specified in col or func_col are missing in the DataFrame.

Returns:

Dictionary of crosstabs DataFrames if return_dict is True. Otherwise, returns None.

Return type:

dict or None

Stacked Bar Plots With Crosstabs Example

The provided code snippet demonstrates how to use the stacked_crosstab_plot function to generate stacked bar plots and corresponding crosstabs for different columns in a DataFrame. Here’s a detailed breakdown of the code using the census dataset as an example [1].

First, the func_col list is defined, specifying the columns ["sex", "income"] to be analyzed. These columns will be used in the loop to generate separate plots. The legend_labels_list is then defined, with each entry corresponding to a column in func_col. In this case, the labels for the sex column are ["Male", "Female"], and for the income column, they are ["<=50K", ">50K"]. These labels will be used to annotate the legends of the plots.

Next, the title list is defined, providing titles for each plot corresponding to the columns in func_col. The titles are set to ["Sex", "Income"], which will be displayed on top of each respective plot.

Note

The legend_labels_list parameter should be a list of lists, where each inner list corresponds to the ground truth labels for the respective item in the func_col list. Each element in the func_col list represents a column in your DataFrame that you wish to analyze, and the corresponding inner list in legend_labels_list should contain the labels that will be used in the legend of your plots.

For example:

# Define the func_col to use in the loop in order of usage
func_col = ["sex", "income"]

# Define the legend_labels to use in the loop
legend_labels_list = [
    ["Male", "Female"],  # Corresponds to "sex"
    ["<=50K", ">50K"],   # Corresponds to "income"
]

# Define titles for the plots
title = [
    "Sex",
    "Income",
]

Important

Ensure that the number of elements in func_col, legend_labels_list, and title are the same. Each item in func_col must have a corresponding list of labels in legend_labels_list and a title in title. This consistency is essential for the function to correctly generate the plots with the appropriate labels and titles.

In this example:

func_col contains two elements: "sex" and "income". Each corresponds to a specific column in your DataFrame.
legend_labels_list is a nested list containing two inner lists:
- The first inner list, ["Male", "Female"], corresponds to the "sex" column in func_col.
- The second inner list, ["<=50K", ">50K"], corresponds to the "income" column in func_col.
title contains two elements: "Sex" and "Income", which will be used as the titles for the respective plots.

Note

If you assign the function to a variable, the dictionary returned when return_dict=True will be suppressed in the output. However, the dictionary is still available within the assigned variable for further use.

from eda_toolkit import stacked_crosstab_plot

# Call the stacked_crosstab_plot function
stacked_crosstabs = stacked_crosstab_plot(
    df=df,
    col="age_group",
    func_col=func_col,
    legend_labels_list=legend_labels_list,
    title=title,
    kind="bar",
    width=0.8,
    rot=45, # axis rotation angle
    custom_order=None,
    color=["#00BFC4", "#F8766D"], # default color schema
    output="both",
    return_dict=True,
    x=14,
    y=8,
    p=10,
    logscale=False,
    plot_type="both",
    show_legend=True,
    label_fontsize=14,
    tick_fontsize=12,
)

The above example generates stacked bar plots for "sex" and "income" grouped by "education". The plots are executed with legends, labels, and tick sizes customized for clarity. The function returns a dictionary of crosstabs for further analysis or export.

Important

Importance of Correctly Aligning Labels

It is crucial to properly align the elements in the legend_labels_list, title, and func_col parameters when using the stacked_crosstab_plot function. Each of these lists must be ordered consistently because the function relies on their alignment to correctly assign labels and titles to the corresponding plots and legends.

For instance, in the example above:

The first element in func_col is "sex", and it is aligned with the first set of labels ["Male", "Female"] in legend_labels_list and the first title "Sex" in the title list.
Similarly, the second element in func_col, "income", aligns with the labels ["<=50K", ">50K"] and the title "Income".

Misalignment between these lists would result in incorrect labels or titles being applied to the plots, potentially leading to confusion or misinterpretation of the data. Therefore, it’s important to ensure that each list is ordered appropriately and consistently to accurately reflect the data being visualized.

Proper Setup of Lists

When setting up the legend_labels_list, title, and func_col, ensure that each element in the lists corresponds to the correct variable in the DataFrame. This involves:

Ordering: Maintaining the same order across all three lists to ensure that labels and titles correspond correctly to the data being plotted.
Consistency: Double-checking that each label in legend_labels_list matches the categories present in the corresponding func_col, and that the title accurately describes the plot.

By adhering to these guidelines, you can ensure that the stacked_crosstab_plot function produces accurate and meaningful visualizations that are easy to interpret and analyze.

Output

Note

When you set return_dict=True, you are able to see the crosstabs printed out as shown below.

Crosstab for sex

sex	Female	Male	Total	Female_%	Male_%
age_group
< 18	295	300	595	49.58	50.42
18-29	5707	8213	13920	41	59
30-39	3853	9076	12929	29.8	70.2
40-49	3188	7536	10724	29.73	70.27
50-59	1873	4746	6619	28.3	71.7
60-69	939	2115	3054	30.75	69.25
70-79	280	535	815	34.36	65.64
80-89	40	91	131	30.53	69.47
90-99	17	38	55	30.91	69.09
Total	16192	32650	48842	33.15	66.85

Crosstab for income

income	<=50K	>50K	Total	<=50K_%	>50K_%
age_group
< 18	595	0	595	100	0
18-29	13174	746	13920	94.64	5.36
30-39	9468	3461	12929	73.23	26.77
40-49	6738	3986	10724	62.83	37.17
50-59	4110	2509	6619	62.09	37.91
60-69	2245	809	3054	73.51	26.49
70-79	668	147	815	81.96	18.04
80-89	115	16	131	87.79	12.21
90-99	42	13	55	76.36	23.64
Total	37155	11687	48842	76.07	23.93

When you set return_dict=True, you can access these crosstabs as DataFrames by assigning them to their own vriables. For example:

crosstab_age_sex = crosstabs_dict["sex"]
crosstab_age_income = crosstabs_dict["income"]

Pivoted Stacked Bar Plots Example

Using the census dataset [1], to create horizontal stacked bar plots, set the kind parameter to "barh" in the stacked_crosstab_plot function. This option pivots the standard vertical stacked bar plot into a horizontal orientation, making it easier to compare categories when there are many labels on the y-axis.

Stacked Bar Plot Age vs. Income (Pivoted)

Non-Normalized Stacked Bar Plots Example

In the census data [1], to create stacked bar plots without the normalized versions, set the plot_type parameter to "regular" in the stacked_crosstab_plot function. This option removes the display of normalized plots beneath the regular versions. Alternatively, setting the plot_type to "normalized" will display only the normalized plots. The example below demonstrates regular stacked bar plots for income by age.

Stacked Bar Plot Age vs. Income (Regular)

Regular Non-Stacked Bar Plots Example

In the census data [1], to generate regular (non-stacked) bar plots without displaying their normalized versions, set the plot_type parameter to "regular" in the stacked_crosstab_plot function and enable remove_stacks by setting it to True. This configuration removes any stacked elements and prevents the display of normalized plots beneath the regular versions. Alternatively, setting plot_type to "normalized" will display only the normalized plots.

When unstacking bar plots in this fashion, the distribution is aligned in descending order, making it easier to visualize the most prevalent categories.

In the example below, the color of the bars has been set to a dark grey (#333333), and the legend has been removed by setting show_legend=False. This illustrates regular bar plots for income by age, without stacking.

Box and Violin Plots

Create and save individual boxplots or violin plots, an entire grid of plots, or both for given metrics and comparisons.

The box_violin_plot function is designed to generate both individual and grid plots of boxplots or violin plots for a set of specified metrics against comparison categories within a DataFrame. This function offers flexibility in how the plots are presented and saved, allowing users to create detailed visualizations that highlight the distribution of metrics across different categories.

With options to customize the plot type (boxplot or violinplot), axis label rotation, figure size, and whether to display or save the plots, this function can be adapted for a wide range of data visualization needs. Users can choose to display individual plots, a grid of plots, or both, depending on the requirements of their analysis.

Additionally, the function includes features for rotating the plots, adjusting the font sizes of labels, and selectively showing or hiding legends. It also supports the automatic saving of plots in either PNG or SVG format, depending on the specified paths, making it a powerful tool for producing publication-quality figures.

The function is particularly useful in scenarios where the user needs to compare the distribution of multiple metrics across different categories, enabling a clear visual analysis of how these metrics vary within the dataset.

box_violin_plot(df, metrics_list, metrics_comp, n_rows=None, n_cols=None, image_path_png=None, image_path_svg=None, save_plots=None, show_legend=True, plot_type='boxplot', xlabel_rot=0, show_plot='both', rotate_plot=False, individual_figsize=(6, 4), grid_figsize=None, label_fontsize=12, tick_fontsize=10, text_wrap=50, xlim=None, ylim=None, label_names=None, **kwargs)

Parameters:

df (pandas.DataFrame) – The DataFrame containing the data to plot.
metrics_list (list of str) – List of metric names (columns in df) to plot.
metrics_comp (list of str) – List of comparison categories (columns in df).
n_rows (int, optional) – Number of rows in the subplot grid. Calculated automatically if not provided.
n_cols (int, optional) – Number of columns in the subplot grid. Calculated automatically if not provided.
image_path_png (str, optional) – Optional directory path to save .png images.
image_path_svg (str, optional) – Optional directory path to save .svg images.
save_plots (str, optional) – String, "all", "individual", or "grid" to control saving plots.
show_legend (bool, optional) – Boolean, True if showing the legend in the plots. Default is True.
plot_type (str, optional) – Specify the type of plot, either "boxplot" or "violinplot". Default is "boxplot".
xlabel_rot (int, optional) – Rotation angle for x-axis labels. Default is 0.
show_plot (str, optional) – Specify the plot display mode: "individual", "grid", or "both". Default is "both".
rotate_plot (bool, optional) – Boolean, True if rotating (pivoting) the plots. Default is False.
individual_figsize (tuple or list, optional) – Width and height of the figure for individual plots. Default is (6, 4).
grid_figsize (tuple or list, optional) – Width and height of the figure for grid plots.
label_fontsize (int, optional) – Font size for axis labels. Default is 12.
tick_fontsize (int, optional) – Font size for axis tick labels. Default is 10.
text_wrap (int, optional) – The maximum width of the title text before wrapping. Default is 50.
xlim (tuple or list, optional) – Limits for the x-axis as a tuple or list of (min, max).
ylim (tuple or list, optional) – Limits for the y-axis as a tuple or list of (min, max).
label_names (dict, optional) – Dictionary mapping original column names to custom labels. Default is None.
kwargs (additional keyword arguments) – Additional keyword arguments passed to the Seaborn plotting function.

Raises:

ValueError –

If show_plot is not one of "individual", "grid", or "both".
If save_plots is not one of None, "all", "individual", or "grid".
If save_plots is set without specifying image_path_png or image_path_svg.
If rotate_plot is not a boolean value.
If individual_figsize is not a tuple or list of two numbers.
If grid_figsize is provided and is not a tuple or list of two numbers.

Returns:

None

This function provides the ability to create and save boxplots or violin plots for specified metrics and comparison categories. It supports the generation of individual plots, a grid of plots, or both. Users can customize the appearance, save the plots to specified directories, and control the display of legends and labels.

Box Plots Grid Example

In this example with the US census data [1], the box_violin_plot function is employed to create a grid of boxplots, comparing different metrics against the "age_group" column in the DataFrame. The metrics_comp parameter is set to ["age_group"], meaning that the comparison will be based on different age groups. The metrics_list is provided as age_boxplot_list, which contains the specific metrics to be visualized. The function is configured to arrange the plots in a grid formatThe image_path_png and image_path_svg parameters are specified to save the plots in both PNG and SVG formats, and the save_plots option is set to "all", ensuring that both individual and grid plots are saved.

The plots are displayed in a grid format, as indicated by the show_plot="grid" parameter. The plot_type is set to "boxplot", so the function will generate boxplots for each metric in the list. Additionally, the `x-axis` labels are rotated by 90 degrees (xlabel_rot=90) to ensure that the labels are legible. The legend is hidden by setting show_legend=False, keeping the plots clean and focused on the data. This configuration provides a comprehensive visual comparison of the specified metrics across different age groups, with all plots saved for future reference or publication.

age_boxplot_list = df[
    [
        "education-num",
        "hours-per-week",
    ]
].columns.to_list()

from eda_toolkit import box_violin_plot

metrics_comp = ["age_group"]

box_violin_plot(
    df=df,
    metrics_list=age_boxplot_list,
    metrics_boxplot_comp=metrics_comp,
    image_path_png=image_path_png,
    image_path_svg=image_path_svg,
    save_plots="all",
    show_plot="both",
    show_legend=False,
    plot_type="boxplot",
    xlabel_rot=90,
)

Violin Plots Grid Example

In this example with the US census data [1], we keep everything the same as the prior example, but change the plot_type to violinplot. This adjustment will generate violin plots instead of boxplots while maintaining all other settings.

from eda_toolkit import box_violin_plot

metrics_comp = ["age_group"]

box_violin_plot(
    df=df,
    metrics_list=age_boxplot_list,
    metrics_comp=metrics_comp,
    image_path_png=image_path_png,
    image_path_svg=image_path_svg,
    save_plots="all",
    show_plot="both",
    show_legend=False,
    plot_type="violinplot",
    xlabel_rot=90,
)

Pivoted Violin Plots Grid Example

In this example with the US census data [1], we set xlabel_rot=0 and rotate_plot=True to pivot the plot, changing the orientation of the axes while keeping the x-axis labels upright. This adjustment flips the axes, providing a different perspective on the data distribution.

from eda_toolkit import box_violin_plot

metrics_comp = ["age_group"]

box_violin_plot(
    df=df,
    metrics_list=age_boxplot_list,
    metrics_boxplot_comp=metrics_comp,
    show_plot="both",
    rotate_plot=True,
    show_legend=False,
    plot_type="violinplot",
    xlabel_rot=0,
)

Scatter Plots and Best Fit Lines

Scatter Fit Plot

Create and Save Scatter Plots or a Grid of Scatter Plots

This function, scatter_fit_plot, is designed to generate scatter plots for one or more pairs of variables (x_vars and y_vars) from a given DataFrame. The function can produce either individual scatter plots or organize multiple scatter plots into a grid layout, making it easy to visualize relationships between different pairs of variables in one cohesive view.

Optional Best Fit Line

An optional feature of this function is the ability to add a best fit line to the scatter plots. This line, often called a regression line, is calculated using a linear regression model and represents the trend in the data. By adding this line, you can visually assess the linear relationship between the variables, and the function can also display the equation of this line in the plot’s legend.s

Customizable Plot Aesthetics

The function offers a wide range of customization options to tailor the appearance of the scatter plots:

Point Color: You can specify a default color for the scatter points or use a hue parameter to color the points based on a categorical variable. This allows for easy comparison across different groups within the data.
Point Size: The size of the scatter points can be controlled and scaled based on another variable, which can help highlight differences or patterns related to that variable.
Markers: The shape or style of the scatter points can also be customized. Whether you prefer circles, squares, or other marker types, the function allows you to choose the best representation for your data.

Axis and Label Configuration

The function also provides flexibility in setting axis labels, tick marks, and grid sizes. You can rotate axis labels for better readability, adjust font sizes, and even specify limits for the x and y axes to focus on particular data ranges.

Plot Display and Saving Options

The function allows you to display plots individually, as a grid, or both. Additionally, you can save the generated plots as PNG or SVG files, making it easy to include them in reports or presentations.

Correlation Coefficient Display

For users interested in understanding the strength of the relationship between variables, the function can also display the Pearson correlation coefficient directly in the plot title. This numeric value provides a quick reference to the linear correlation between the variables, offering further insight into their relationship.

scatter_fit_plot(df, x_vars=None, y_vars=None, n_rows=None, n_cols=None, max_cols=4, image_path_png=None, image_path_svg=None, save_plots=None, show_legend=True, xlabel_rot=0, show_plot='both', rotate_plot=False, individual_figsize=(6, 4), grid_figsize=None, label_fontsize=12, tick_fontsize=10, text_wrap=50, add_best_fit_line=False, scatter_color='C0', best_fit_linecolor='red', best_fit_linestyle='-', hue=None, hue_palette=None, size=None, sizes=None, marker='o', show_correlation=True, xlim=None, ylim=None, all_vars=None, label_names=None, **kwargs)

Create and save scatter plots or a grid of scatter plots for given x_vars and y_vars, with an optional best fit line and customizable point color, size, and markers.

Parameters:

df (pandas.DataFrame) – The DataFrame containing the data.
x_vars (list of str, optional) – List of variable names to plot on the x-axis.
y_vars (list of str, optional) – List of variable names to plot on the y-axis.
n_rows (int, optional) – Number of rows in the subplot grid. Calculated based on the number of plots and n_cols if not specified.
n_cols (int, optional) – Number of columns in the subplot grid. Calculated based on the number of plots and max_cols if not specified.
max_cols (int, optional) – Maximum number of columns in the subplot grid. Default is 4.
image_path_png (str, optional) – Directory path to save PNG images of the scatter plots.
image_path_svg (str, optional) – Directory path to save SVG images of the scatter plots.
save_plots (str, optional) – Controls which plots to save: "all", "individual", or "grid". If None, plots will not be saved.
show_legend (bool, optional) – Whether to display the legend on the plots. Default is True.
xlabel_rot (int, optional) – Rotation angle for x-axis labels. Default is 0.
show_plot (str, optional) – Controls plot display: "individual", "grid", or "both". Default is "both".
rotate_plot (bool, optional) – Whether to rotate (pivot) the plots. Default is False.
individual_figsize (tuple or list, optional) – Width and height of the figure for individual plots. Default is (6, 4).
grid_figsize (tuple or list, optional) – Width and height of the figure for grid plots. Calculated based on the number of rows and columns if not specified.
label_fontsize (int, optional) – Font size for axis labels. Default is 12.
tick_fontsize (int, optional) – Font size for axis tick labels. Default is 10.
text_wrap (int, optional) – The maximum width of the title text before wrapping. Default is 50.
add_best_fit_line (bool, optional) – Whether to add a best fit line to the scatter plots. Default is False.
scatter_color (str, optional) – Color code for the scattered points. Default is "C0".
best_fit_linecolor (str, optional) – Color code for the best fit line. Default is "red".
best_fit_linestyle (str, optional) – Linestyle for the best fit line. Default is "-".
hue (str, optional) – Column name for the grouping variable that will produce points with different colors.
hue_palette (dict, list, or str, optional) – Specifies colors for each hue level. Can be a dictionary mapping hue levels to colors, a list of colors, or the name of a seaborn color palette. This parameter requires the hue parameter to be set.
size (str, optional) – Column name for the grouping variable that will produce points with different sizes.
sizes (dict, optional) – Dictionary mapping sizes (smallest and largest) to min and max values.
marker (str, optional) – Marker style used for the scatter points. Default is "o".
show_correlation (bool, optional) – Whether to display the Pearson correlation coefficient in the plot title. Default is True.
xlim (tuple or list, optional) – Limits for the x-axis as a tuple or list of (min, max).
ylim (tuple or list, optional) – Limits for the y-axis as a tuple or list of (min, max).
all_vars (list of str, optional) – If provided, automatically generates scatter plots for all combinations of variables in this list, overriding x_vars and y_vars.
label_names (dict, optional) – A dictionary to rename columns for display in the plot titles and labels.
kwargs (dict, optional) – Additional keyword arguments to pass to sns.scatterplot.

Raises:

ValueError –

If all_vars is provided and either x_vars or y_vars is also provided.
If neither all_vars nor both x_vars and y_vars are provided.
If hue_palette is specified without hue.
If show_plot is not one of "individual", "grid", or "both".
If save_plots is not one of None, "all", "individual", or "grid".
If save_plots is set but no image paths are provided.
If rotate_plot is not a boolean value.
If individual_figsize or grid_figsize are not tuples/lists with two numeric values.

Returns:

None. This function does not return any value but generates and optionally saves scatter plots for the specified x_vars and y_vars, or for all combinations of variables in all_vars if it is provided.

Regression-Centric Scatter Plots Example

In this US census data [1] example, the scatter_fit_plot function is configured to display the Pearson correlation coefficient and a best fit line on each scatter plot. The correlation coefficient is shown in the plot title, controlled by the show_correlation=True parameter, which provides a measure of the strength and direction of the linear relationship between the variables. Additionally, the add_best_fit_line=True parameter adds a best fit line to each plot, with the equation for the line displayed in the legend. This equation, along with the best fit line, helps to visually assess the relationship between the variables, making it easier to identify trends and patterns in the data. The combination of the correlation coefficient and the best fit line offers both a quantitative and visual representation of the relationships, enhancing the interpretability of the scatter plots.

from eda_toolkit import scatter_fit_plot

scatter_fit_plot(
    df=df,
    x_vars=["age", "education-num"],
    y_vars=["hours-per-week"],
    show_legend=True,
    show_plot="grid",
    grid_figsize=None,
    label_fontsize=14,
    tick_fontsize=12,
    add_best_fit_line=True,
    scatter_color="#808080",
    show_correlation=True,
)

Scatter Plot Comparisons (with Best Fit Lines)

Scatter Plots Grouped by Category Example

In this example, the scatter_fit_plot function is used to generate a grid of scatter plots that examine the relationships between age and hours-per-week as well as education-num and hours-per-week. Compared to the previous example, a few key inputs have been changed to adjust the appearance and functionality of the plots:

Hue and Hue Palette: The hue parameter is set to "income", meaning that the data points in the scatter plots are colored according to the values in the income column. A custom color mapping is provided via the hue_palette parameter, where the income categories "<=50K" and ">50K" are assigned the colors "brown" and "green", respectively. This change visually distinguishes the data points based on income levels.
Scatter Color: The scatter_color parameter is set to "#808080", which applies a grey color to the scatter points when no hue is provided. However, since a hue is specified in this example, the hue_palette takes precedence and overrides this color setting.
Best Fit Line: The add_best_fit_line parameter is set to False, meaning that no best fit line is added to the scatter plots. This differs from the previous example where a best fit line was included.
Correlation Coefficient: The show_correlation parameter is set to False, so the Pearson correlation coefficient will not be displayed in the plot titles. This is another change from the previous example where the correlation coefficient was included.
Hue Legend: The show_legend parameter remains set to True, ensuring that the legend displaying the hue categories ("<=50K" and ">50K") appears on the plots, helping to interpret the color coding of the data points.

These changes allow for the creation of scatter plots that highlight the income levels of individuals, with custom color coding and without additional elements like a best fit line or correlation coefficient. The resulting grid of plots is then saved as images in the specified paths.

from eda_toolkit import scatter_fit_plot

hue_dict = {"<=50K": "brown", ">50K": "green"}

scatter_fit_plot(
    df=df,
    x_vars=["age", "education-num"],
    y_vars=["hours-per-week"],
    show_legend=True,
    show_plot="grid",
    label_fontsize=14,
    tick_fontsize=12,
    add_best_fit_line=False,
    scatter_color="#808080",
    hue="income",
    hue_palette=hue_dict,
    show_correlation=False,
)

Scatter Plots (All Combinations Example)

In this example, the scatter_fit_plot function is used to generate a grid of scatter plots that explore the relationships between all numeric variables in the df DataFrame. The function automatically identifies and plots all possible combinations of these variables. Below are key aspects of this example:

All Variables Combination: The all_vars parameter is used to automatically generate scatter plots for all possible combinations of numerical variables in the DataFrame. This means you don’t need to manually specify x_vars and y_vars, as the function will iterate through each possible pair.
Grid Display: The show_plot parameter is set to "grid", so the scatter plots are displayed in a grid format. This is useful for comparing multiple relationships simultaneously.
Font Sizes: The label_fontsize and tick_fontsize parameters are set to 14 and 12, respectively. This increases the readability of axis labels and tick marks, making the plots more visually accessible.
Best Fit Line: The add_best_fit_line parameter is set to True, meaning that a best fit line is added to each scatter plot. This helps in visualizing the linear relationship between variables.
Scatter Color: The scatter_color parameter is set to "#808080", applying a grey color to the scatter points. This provides a neutral color that does not distract from the data itself.
Correlation Coefficient: The show_correlation parameter is set to True, so the Pearson correlation coefficient will be displayed in the plot titles. This helps to quantify the strength of the relationship between the variables.

These settings allow for the creation of scatter plots that comprehensively explore the relationships between all numeric variables in the DataFrame. The plots are saved in a grid format, with added best fit lines and correlation coefficients for deeper analysis. The resulting images can be stored in the specified directory for future reference.

from eda_toolkit import scatter_fit_plot

scatter_fit_plot(
    df=df,
    all_vars=df.select_dtypes(np.number).columns.to_list(),
    show_legend=True,
    show_plot="grid",
    label_fontsize=14,
    tick_fontsize=12,
    add_best_fit_line=True,
    scatter_color="#808080",
    show_correlation=True,
)

Correlation Matrices

Generate and Save Customizable Correlation Heatmaps

The flex_corr_matrix function is designed to create highly customizable correlation heatmaps for visualizing the relationships between variables in a DataFrame. This function allows users to generate either a full or triangular correlation matrix, with options for annotation, color mapping, and saving the plot in multiple formats.

Customizable Plot Appearance

The function provides extensive customization options for the heatmap’s appearance:

Colormap Selection: Choose from a variety of colormaps to represent the strength of correlations. The default is "coolwarm", but this can be adjusted to fit the needs of the analysis.
Annotation: Optionally annotate the heatmap with correlation coefficients, making it easier to interpret the strength of relationships at a glance.
Figure Size and Layout: Customize the dimensions of the heatmap to ensure it fits well within reports, presentations, or dashboards.

Triangular vs. Full Correlation Matrix

A key feature of the flex_corr_matrix function is the ability to generate either a full correlation matrix or only the upper triangle. This option is particularly useful when the matrix is large, as it reduces visual clutter and focuses attention on the unique correlations.

Label and Axis Configuration

The function offers flexibility in configuring axis labels and titles:

Label Rotation: Rotate x-axis and y-axis labels for better readability, especially when working with long variable names.
Font Sizes: Adjust the font sizes of labels and tick marks to ensure the plot is clear and readable.
Title Wrapping: Control the wrapping of long titles to fit within the plot without overlapping other elements.

Plot Display and Saving Options

The flex_corr_matrix function allows you to display the heatmap directly or save it as PNG or SVG files for use in reports or presentations. If saving is enabled, you can specify file paths and names for the images.

flex_corr_matrix(df, cols=None, annot=True, cmap='coolwarm', save_plots=False, image_path_png=None, image_path_svg=None, figsize=(10, 10), title='Cervical Cancer Data: Correlation Matrix', label_fontsize=12, tick_fontsize=10, xlabel_rot=45, ylabel_rot=0, xlabel_alignment='right', ylabel_alignment='center_baseline', text_wrap=50, vmin=-1, vmax=1, cbar_label='Correlation Index', triangular=True, **kwargs)

Create a customizable correlation heatmap with options for annotation, color mapping, figure size, and saving the plot.

Parameters:

df (pandas.DataFrame) – The DataFrame containing the data.
cols (list of str, optional) – List of column names to include in the correlation matrix. If None, all columns are included.
annot (bool, optional) – Whether to annotate the heatmap with correlation coefficients. Default is True.
cmap (str, optional) – The colormap to use for the heatmap. Default is "coolwarm".
save_plots (bool, optional) – Controls whether to save the plots. Default is False.
image_path_png (str, optional) – Directory path to save PNG images of the heatmap.
image_path_svg (str, optional) – Directory path to save SVG images of the heatmap.
figsize (tuple, optional) – Width and height of the figure for the heatmap. Default is (10, 10).
title (str, optional) – Title of the heatmap. Default is "Cervical Cancer Data: Correlation Matrix".
label_fontsize (int, optional) – Font size for tick labels and colorbar label. Default is 12.
tick_fontsize (int, optional) – Font size for axis tick labels. Default is 10.
xlabel_rot (int, optional) – Rotation angle for x-axis labels. Default is 45.
ylabel_rot (int, optional) – Rotation angle for y-axis labels. Default is 0.
xlabel_alignment (str, optional) – Horizontal alignment for x-axis labels. Default is "right".
ylabel_alignment (str, optional) – Vertical alignment for y-axis labels. Default is "center_baseline".
text_wrap (int, optional) – The maximum width of the title text before wrapping. Default is 50.
vmin (float, optional) – Minimum value for the heatmap color scale. Default is -1.
vmax (float, optional) – Maximum value for the heatmap color scale. Default is 1.
cbar_label (str, optional) – Label for the colorbar. Default is "Correlation Index".
triangular (bool, optional) – Whether to show only the upper triangle of the correlation matrix. Default is True.
kwargs (dict, optional) – Additional keyword arguments to pass to seaborn.heatmap().

Raises:

ValueError –

If annot is not a boolean.
If cols is not a list.
If save_plots is not a boolean.
If triangular is not a boolean.
If save_plots is True but no image paths are provided.

Returns:

None This function does not return any value but generates and optionally saves a correlation heatmap.

Triangular Correlation Matrix Example

The provided code filters the census [1] DataFrame df to include only numeric columns using select_dtypes(np.number). It then utilizes the flex_corr_matrix() function to generate a right triangular correlation matrix, which only displays the upper half of the correlation matrix. The heatmap is customized with specific colormap settings, title, label sizes, axis label rotations, and other formatting options.

Note

This triangular matrix format is particularly useful for avoiding redundancy in correlation matrices, as it excludes the lower half, making it easier to focus on unique pairwise correlations.

The function also includes a labeled color bar, helping users quickly interpret the strength and direction of the correlations.

# Select only numeric data to pass into the function
df_num = df.select_dtypes(np.number)

from eda_toolkit import flex_corr_matrix

flex_corr_matrix(
    df=df,
    cols=df_num.columns.to_list(),
    annot=True,
    cmap="coolwarm",
    figsize=(10, 8),
    title="US Census Correlation Matrix",
    xlabel_alignment="right",
    label_fontsize=14,
    tick_fontsize=12,
    xlabel_rot=45,
    ylabel_rot=0,
    text_wrap=50,
    vmin=-1,
    vmax=1,
    cbar_label="Correlation Index",
    triangular=True,
)

Full Correlation Matrix Example

In this modified census [1] example, the key changes are the use of the viridis colormap and the decision to plot the full correlation matrix instead of just the upper triangle. By setting cmap="viridis", the heatmap will use a different color scheme, which can provide better visual contrast or align with specific aesthetic preferences. Additionally, by setting triangular=False, the full correlation matrix is displayed, allowing users to view all pairwise correlations, including both upper and lower halves of the matrix. This approach is beneficial when you want a comprehensive view of all correlations in the dataset.

from eda_toolkit import flex_corr_matrix

flex_corr_matrix(
    df=df,
    cols=df_num.columns.to_list(),
    annot=True,
    cmap="viridis",
    figsize=(10, 8),
    title="US Census Correlation Matrix",
    xlabel_alignment="right",
    label_fontsize=14,
    tick_fontsize=12,
    xlabel_rot=45,
    ylabel_rot=0,
    text_wrap=50,
    vmin=-1,
    vmax=1,
    cbar_label="Correlation Index",
    triangular=False,
)

Partial Dependence Plots

Partial Dependence Plots (PDPs) are a powerful tool in machine learning interpretability, providing insights into how features influence the predicted outcome of a model. PDPs can be generated in both 2D and 3D, depending on whether you want to analyze the effect of one feature or the interaction between two features on the model’s predictions.

2D Partial Dependence Plots

The plot_2d_pdp function generates 2D partial dependence plots for individual features or pairs of features. These plots are essential for examining the marginal effect of features on the predicted outcome.

Grid and Individual Plots: Generate all 2D partial dependence plots in a grid layout or as separate individual plots, offering flexibility in presentation.
Customization Options: Control the figure size, font sizes for labels and ticks, and the wrapping of long titles to ensure the plots are clear and informative.
Saving Plots: The function provides options to save the plots in PNG or SVG formats, and you can specify whether to save all plots, only individual plots, or just the grid plot.

plot_2d_pdp(model, X_train, feature_names, features, title='PDP of house value on CA non-location features', grid_resolution=50, plot_type='grid', grid_figsize=(12, 8), individual_figsize=(6, 4), label_fontsize=12, tick_fontsize=10, text_wrap=50, image_path_png=None, image_path_svg=None, save_plots=None, file_prefix='partial_dependence')

Generate 2D partial dependence plots for specified features using the given machine learning model. The function allows for plotting in grid or individual layouts, with various customization options for figure size, font sizes, and title wrapping. Additionally, the plots can be saved in PNG or SVG formats with a customizable filename prefix.

Parameters:

model (estimator object) – The trained machine learning model used to generate partial dependence plots.
X_train (pandas.DataFrame or numpy.ndarray) – The training data used to compute partial dependence. Should correspond to the features used to train the model.
feature_names (list of str) – A list of feature names corresponding to the columns in X_train.
features (list of int or tuple of int) – A list of feature indices or tuples of feature indices for which to generate partial dependence plots.
title (str, optional) – The title for the entire plot. Default is "PDP of house value on CA non-location features".
grid_resolution (int, optional) – The number of grid points to use for plotting the partial dependence. Higher values provide smoother curves but may increase computation time. Default is 50.
plot_type (str, optional) – The type of plot to generate. Choose "grid" for a grid layout, "individual" for separate plots, or "both" to generate both layouts. Default is "grid".
grid_figsize (tuple, optional) – Tuple specifying the width and height of the figure for the grid layout. Default is (12, 8).
individual_figsize (tuple, optional) – Tuple specifying the width and height of the figure for individual plots. Default is (6, 4).
label_fontsize (int, optional) – Font size for the axis labels and titles. Default is 12.
tick_fontsize (int, optional) – Font size for the axis tick labels. Default is 10.
text_wrap (int, optional) – The maximum width of the title text before wrapping. Useful for managing long titles. Default is 50.
image_path_png (str, optional) – The directory path where PNG images of the plots will be saved, if saving is enabled.
image_path_svg (str, optional) – The directory path where SVG images of the plots will be saved, if saving is enabled.
save_plots (str, optional) – Controls whether to save the plots. Options include "all", "individual", "grid", or None (default). If saving is enabled, ensure image_path_png or image_path_svg are provided.
file_prefix (str, optional) – Prefix for the filenames of the saved grid plots. Default is "partial_dependence".

Raises:

ValueError –

If plot_type is not one of "grid", "individual", or "both".
If save_plots is enabled but neither image_path_png nor image_path_svg is provided.

Returns:

None This function generates partial dependence plots and displays them. It does not return any values.

2D Plots - CA Housing Example

Consider a scenario where you have a machine learning model predicting median house values in California. [4] Suppose you want to understand how non-location features like the average number of occupants per household (AveOccup) and the age of the house (HouseAge) jointly influence house values. A 2D partial dependence plot allows you to visualize this relationship in two ways: either as individual plots for each feature or as a combined plot showing the interaction between two features.

For instance, the 2D partial dependence plot can help you analyze how the age of the house impacts house values while holding the number of occupants constant, or vice versa. This is particularly useful for identifying the most influential features and understanding how changes in these features might affect the predicted house value.

If you extend this to two interacting features, such as AveOccup and HouseAge, you can explore their combined effect on house prices. The plot can reveal how different combinations of occupancy levels and house age influence the value, potentially uncovering non-linear relationships or interactions that might not be immediately obvious from a simple 1D analysis.

Here’s how you can generate and visualize these 2D partial dependence plots using the California housing dataset:

Fetch The CA Housing Dataset and Prepare The DataFrame

from sklearn.datasets import fetch_california_housing
from sklearn.model_selection import train_test_split
from sklearn.ensemble import GradientBoostingRegressor
import pandas as pd

# Load the dataset
data = fetch_california_housing()
df = pd.DataFrame(data.data, columns=data.feature_names)

Split The Data Into Training and Testing Sets

X_train, X_test, y_train, y_test = train_test_split(
    df, data.target, test_size=0.2, random_state=42
)

Train a GradientBoostingRegressor Model

model = GradientBoostingRegressor(
    n_estimators=100,
    max_depth=4,
    learning_rate=0.1,
    loss="huber",
    random_state=42,
)
model.fit(X_train, y_train)

Create 2D Partial Dependence Plot Grid

# import the plot_2d_pdp function from
# the eda_toolkit library
from eda_toolkit import plot_2d_pdp

# Feature names
names = data.feature_names

# Generate 2D partial dependence plots
plot_2d_pdp(
    model=model,
    X_train=X_train,
    feature_names=names,
    features=[
        "MedInc",
        "AveOccup",
        "HouseAge",
        "AveRooms",
        "Population",
        ("AveOccup", "HouseAge"),
    ],
    title="PDP of house value on CA non-location features",
    grid_figsize=(14, 10),
    individual_figsize=(12, 4),
    label_fontsize=14,
    tick_fontsize=12,
    text_wrap=120,
    plot_type="grid",
    image_path_png="path/to/save/png",
    save_plots="all",
)

3D Partial Dependence Plots

The plot_3d_pdp function extends the concept of partial dependence to three dimensions, allowing you to visualize the interaction between two features and their combined effect on the model’s predictions.

Interactive and Static 3D Plots: Generate static 3D plots using Matplotlib or interactive 3D plots using Plotly. The function also allows for generating both types simultaneously.
Colormap and Layout Customization: Customize the colormaps for both Matplotlib and Plotly plots. Adjust figure size, camera angles, and zoom levels to create plots that fit perfectly within your presentation or report.
Axis and Title Configuration: Customize axis labels for both Matplotlib and Plotly plots. Adjust font sizes and control the wrapping of long titles to maintain readability.

plot_3d_pdp(model, dataframe, feature_names_list, x_label=None, y_label=None, z_label=None, title, html_file_path=None, html_file_name=None, image_filename=None, plot_type="both", matplotlib_colormap=None, plotly_colormap="Viridis", zoom_out_factor=None, wireframe_color=None, view_angle=(22, 70), figsize=(7, 4.5), text_wrap=50, horizontal=-1.25, depth=1.25, vertical=1.25, cbar_x=1.05, cbar_thickness=25, title_x=0.5, title_y=0.95, top_margin=100, image_path_png=None, image_path_svg=None, show_cbar=True, grid_resolution=20, left_margin=20, right_margin=65, label_fontsize=8, tick_fontsize=6, enable_zoom=True, show_modebar=True)

Generate 3D partial dependence plots for two features of a machine learning model.

This function supports both static (Matplotlib) and interactive (Plotly) visualizations, allowing for flexible and comprehensive analysis of the relationship between two features and the target variable in a model.

Parameters:

model (estimator object) – The trained machine learning model used to generate partial dependence plots.
dataframe (pandas.DataFrame or numpy.ndarray) – The dataset on which the model was trained or a representative sample. If a DataFrame is provided, feature_names_list should correspond to the column names. If a NumPy array is provided, feature_names_list should correspond to the indices of the columns.
feature_names_list (list of str) – A list of two feature names or indices corresponding to the features for which partial dependence plots are generated.
x_label (str, optional) – Label for the x-axis in the plots. Default is None.
y_label (str, optional) – Label for the y-axis in the plots. Default is None.
z_label (str, optional) – Label for the z-axis in the plots. Default is None.
title (str) – The title for the plots.
html_file_path (str, optional) – Path to save the interactive Plotly HTML file. Required if plot_type is "interactive" or "both". Default is None.
html_file_name (str, optional) – Name of the HTML file to save the interactive Plotly plot. Required if plot_type is "interactive" or "both". Default is None.
image_filename (str, optional) – Base filename for saving static Matplotlib plots as PNG and/or SVG. Default is None.
plot_type (str, optional) – The type of plots to generate. Options are: - "static": Generate only static Matplotlib plots. - "interactive": Generate only interactive Plotly plots. - "both": Generate both static and interactive plots. Default is "both".
matplotlib_colormap (matplotlib.colors.Colormap, optional) – Custom colormap for the Matplotlib plot. If not provided, a default colormap is used.
plotly_colormap (str, optional) – Colormap for the Plotly plot. Default is "Viridis".
zoom_out_factor (float, optional) – Factor to adjust the zoom level of the Plotly plot. Default is None.
wireframe_color (str, optional) – Color for the wireframe in the Matplotlib plot. If None, no wireframe is plotted. Default is None.
view_angle (tuple, optional) – Elevation and azimuthal angles for the Matplotlib plot view. Default is (22, 70).
figsize (tuple, optional) – Figure size for the Matplotlib plot. Default is (7, 4.5).
text_wrap (int, optional) – Maximum width of the title text before wrapping. Useful for managing long titles. Default is 50.
horizontal (float, optional) – Horizontal camera position for the Plotly plot. Default is -1.25.
depth (float, optional) – Depth camera position for the Plotly plot. Default is 1.25.
vertical (float, optional) – Vertical camera position for the Plotly plot. Default is 1.25.
cbar_x (float, optional) – Position of the color bar along the x-axis in the Plotly plot. Default is 1.05.
cbar_thickness (int, optional) – Thickness of the color bar in the Plotly plot. Default is 25.
title_x (float, optional) – Horizontal position of the title in the Plotly plot. Default is 0.5.
title_y (float, optional) – Vertical position of the title in the Plotly plot. Default is 0.95.
top_margin (int, optional) – Top margin for the Plotly plot layout. Default is 100.
image_path_png (str, optional) – Directory path to save the PNG file of the Matplotlib plot. Default is None.
image_path_svg (str, optional) – Directory path to save the SVG file of the Matplotlib plot. Default is None.
show_cbar (bool, optional) – Whether to display the color bar in the Matplotlib plot. Default is True.
grid_resolution (int, optional) – The resolution of the grid for computing partial dependence. Default is 20.
left_margin (int, optional) – Left margin for the Plotly plot layout. Default is 20.
right_margin (int, optional) – Right margin for the Plotly plot layout. Default is 65.
label_fontsize (int, optional) – Font size for axis labels in the Matplotlib plot. Default is 8.
tick_fontsize (int, optional) – Font size for tick labels in the Matplotlib plot. Default is 6.
enable_zoom (bool, optional) – Whether to enable zooming in the Plotly plot. Default is True.
show_modebar (bool, optional) – Whether to display the mode bar in the Plotly plot. Default is True.

Raises:

ValueError –

If plot_type is not one of "static", "interactive", or "both".
If plot_type is "interactive" or "both" and html_file_path or html_file_name are not provided.

Returns:

None This function generates 3D partial dependence plots and displays or saves them. It does not return any values.

Notes:

This function handles warnings related to scikit-learn’s partial_dependence function, specifically a FutureWarning related to non-tuple sequences for multidimensional indexing. This warning is suppressed as it stems from the internal workings of scikit-learn in Python versions like 3.7.4.
To maintain compatibility with different versions of scikit-learn, the function attempts to use "values" for grid extraction in newer versions and falls back to "grid_values" for older versions.

3D Plots - CA Housing Example

Consider a scenario where you have a machine learning model predicting median house values in California.[4]_ Suppose you want to understand how non-location features like the average number of occupants per household (AveOccup) and the age of the house (HouseAge) jointly influence house values. A 3D partial dependence plot allows you to visualize this relationship in a more comprehensive manner, providing a detailed view of how these two features interact to affect the predicted house value.

For instance, the 3D partial dependence plot can help you explore how different combinations of house age and occupancy levels influence house values. By visualizing the interaction between AveOccup and HouseAge in a 3D space, you can uncover complex, non-linear relationships that might not be immediately apparent in 2D plots.

This type of plot is particularly useful when you need to understand the joint effect of two features on the target variable, as it provides a more intuitive and detailed view of how changes in both features impact predictions simultaneously.

Here’s how you can generate and visualize these 3D partial dependence plots using the California housing dataset:

Static Plot

Fetch The CA Housing Dataset and Prepare The DataFrame

from sklearn.ensemble import GradientBoostingRegressor
from sklearn.datasets import fetch_california_housing
from sklearn.model_selection import train_test_split
import pandas as pd

# Load the dataset
data = fetch_california_housing()
df = pd.DataFrame(data.data, columns=data.feature_names)

Split The Data Into Training and Testing Sets

X_train, X_test, y_train, y_test = train_test_split(
    df, data.target, test_size=0.2, random_state=42
)

Train a GradientBoostingRegressor Model

model = GradientBoostingRegressor(
    n_estimators=100,
    max_depth=4,
    learning_rate=0.1,
    loss="huber",
    random_state=1,
)
model.fit(X_train, y_train)

Create Static 3D Partial Dependence Plot

# import the plot_3d_pdp function from
# the eda_toolkit library
from eda_toolkit import plot_3d_pdp

# Call the function to generate the plot
plot_3d_pdp(
    model=model,
    dataframe=X_test,  # Use the test dataset
    feature_names_list=["HouseAge", "AveOccup"],
    x_label="House Age",
    y_label="Average Occupancy",
    z_label="Partial Dependence",
    title="3D Partial Dependence Plot of House Age vs. Average Occupancy",
    image_filename="3d_pdp",
    plot_type="static",
    figsize=[8, 5],
    text_wrap=40,
    wireframe_color="black",
    image_path_png=image_path_png,
    grid_resolution=30,
)

Interactive Plot

# import the plot_3d_pdp function from
# the eda_toolkit library
from eda_toolkit import plot_3d_pdp

# Call the function to generate the plot
plot_3d_pdp(
    model=model,
    dataframe=X_test,  # Use the test dataset
    feature_names_list=["HouseAge", "AveOccup"],
    x_label="House Age",
    y_label="Average Occupancy",
    z_label="Partial Dependence",
    title="3D Partial Dependence Plot of House Age vs. Average Occupancy",
    html_file_path=image_path_png,
    image_filename="3d_pdp",
    html_file_name="3d_pdp.html",
    plot_type="interactive",
    text_wrap=40,
    zoom_out_factor=0.5,
    image_path_png=image_path_png,
    image_path_svg=image_path_svg,
    grid_resolution=30,
    label_fontsize=8,
    tick_fontsize=6,
    title_x=0.38,
    top_margin=10,
    right_margin=250,
    cbar_x=0.9,
    cbar_thickness=25,
    show_modebar=False,
    enable_zoom=True,
)

Warning

Scrolling Notice:

While interacting with the interactive Plotly plot below, scrolling down the page using the mouse wheel may be blocked when the mouse pointer is hovering over the plot. To continue scrolling, either move the mouse pointer outside the plot area or use the keyboard arrow keys to navigate down the page.

This interactive plot was generated using Plotly, which allows for rich, interactive visualizations directly in the browser. The plot above is an example of an interactive 3D Partial Dependence Plot. Here’s how it differs from generating a static plot using Matplotlib.

Key Differences

Plot Type:

The plot_type is set to "interactive" for the Plotly plot and "static" for the Matplotlib plot.

Interactive-Specific Parameters:

HTML File Path and Name: The html_file_path and html_file_name parameters are required to save the interactive Plotly plot as an HTML file. These parameters are not needed for static plots.
Zoom and Positioning: The interactive plot includes parameters like zoom_out_factor, title_x, cbar_x, and cbar_thickness to control the zoom level, title position, and color bar position in the Plotly plot. These parameters do not affect the static plot.
Mode Bar and Zoom: The show_modebar and enable_zoom parameters are specific to the interactive Plotly plot, allowing you to toggle the visibility of the mode bar and enable or disable zoom functionality.

Static-Specific Parameters:

Figure Size and Wireframe Color: The static plot uses parameters like figsize to control the size of the Matplotlib plot and wireframe_color to define the color of the wireframe in the plot. These parameters are not applicable to the interactive Plotly plot.

By adjusting these parameters, you can customize the behavior and appearance of your 3D Partial Dependence Plots according to your needs, whether for static or interactive visualization.