robust_pdf_plot.ipynb

Kernel: pyprobml

Understanding Effect of Outliers on diffrent PDF

import jax.numpy as jnp
from jax import random
import matplotlib.pyplot as plt
from scipy.stats import t, laplace, norm
import seaborn as sns
import numpy as np

try:
    from probml_utils import savefig, latexify
except ModuleNotFoundError:
    %pip install -qq git+https://github.com/probml/probml-utils.git
    from probml_utils import savefig, latexify

latexify(width_scale_factor=2, fig_height=2.0)

C:\Users\NITISH SHARMA\.pyenv\pyenv-win\versions\3.9.10\lib\site-packages\probml_utils\plotting.py:26: UserWarning: LATEXIFY environment variable not set, not latexifying
  warnings.warn("LATEXIFY environment variable not set, not latexifying")

def plot_outlier_effect(
    save_name,
    outlier_pos=0,
    outliers=[],
    bins=7,
    samples_norm_dist=30,
    samples_graph_xaxis=500,
    range_xaxis=[-5, 10],
    range_yaxis=[0, 0.60],
    fig=None,
    ax=None,
):
    """
    Sample from a normal distribution and plot the PDF for
    normal distribution, laplacian distribution, and the student T
    distribution. The function plots/saves data for distributions.
    If outliers are provided, we see the robustness of the student
    T distribution compared to the normal distribution.


    Args:
    ----------
    save_name : string
        The filenames to save the graphs

    outlier_pos : int, default=0
        Changes position of outliers

    outliers :  list, default=[]
        A list of outlier values

    bins : int, default=7
        Value of bin size for normal distribution histogram

    samples_norm_dist : int, default=30
        Number of samples to be taken from the normal distribution

    samples_graph_xaxis : int, default=500
        Number of values for the x-axis i.e the values the
        random variable can take

    range_xaxis : list, default=[-5, 10]
        The range of values for the x-axis

    range_yaxis : list, default=[0, 0.6]
        The range of values for the y-axis

    fig : None
        Will be used to store matplotlib figure

    ax : None
        Will be used to store matplotlib axes

    Returns:
    ----------
    fig : matplotlib figure object
        Stores the graph data displayed

    ax : matplotlib axis object
        Stores the axes data of the graph displayed
    """

    # Generate Samples from normal distribution
    norm_dist_sample = random.normal(random.PRNGKey(42), shape=(samples_norm_dist,))

    # Generate values for x axis i.e. the values your random variable can take
    x_axis = jnp.linspace(range_xaxis[0], range_xaxis[1], samples_graph_xaxis)

    # Set figure
    fig, ax = plt.subplots()

    if outliers:
        samples = jnp.hstack((norm_dist_sample, jnp.array(outliers) + outlier_pos))

        # Plot the data from normal distribution
        ax.hist(
            np.array(norm_dist_sample),
            bins,
            color="steelblue",
            ec="steelblue",
            weights=[1 / (norm_dist_sample.shape[0] + len(outliers))] * norm_dist_sample.shape[0],
            rwidth=0.8,
        )

        # Plot outlier data
        ax.hist(
            np.array(outliers) + outlier_pos,
            len(outliers),
            color="steelblue",
            ec="steelblue",
            weights=[1 / (norm_dist_sample.shape[0] + len(outliers))] * len(outliers),
            rwidth=0.8,
        )
    else:
        samples = norm_dist_sample

        # Plot the data from normal distribution
        ax.hist(
            np.array(norm_dist_sample),
            bins,
            color="steelblue",
            ec="steelblue",
            weights=[1 / norm_dist_sample.shape[0]] * norm_dist_sample.shape[0],
            rwidth=0.8,
        )

    # Calculate mean and standard deviation for different distributions and then
    # find the PDF for each distribution
    loc, scale = norm.fit(samples)
    norm_pdf = norm.pdf(x_axis, loc=loc, scale=scale)

    loc, scale = laplace.fit(samples)
    laplace_pdf = laplace.pdf(x_axis, loc=loc, scale=scale)

    fd, loc, scale = t.fit(samples)
    studentT_pdf = t.pdf(x_axis, fd, loc=loc, scale=scale)

    # Find range of values for PDF i.e y-axis
    y_range = range_yaxis

    # Update tick intervals for x-axis
    ax.set_xticks(jnp.arange(range_xaxis[0], range_xaxis[1] + 1, 5))

    # Update the tick intervals and limit for y-axis
    ax.set_ylim(y_range)
    ax.set_yticks(jnp.linspace(y_range[0], y_range[1], 5))

    # Plot the different PDF's obtained
    ax.plot(x_axis, norm_pdf, "k-", linewidth=2.0)
    ax.plot(x_axis, studentT_pdf, "r-.", linewidth=2.0)
    ax.plot(x_axis, laplace_pdf, "b:", linewidth=2.0)

    # Update the Legend and the axis labels
    ax.legend(("gaussian", "student T", "laplace", "data"))
    ax.set_xlabel("$x$")
    ax.set_ylabel("$p(x)$")

    sns.despine()

    # Save figure to files
    if len(save_name) > 0:
        savefig(save_name)

    return fig, ax

plot_outlier_effect(save_name="robust_pdf_plot")

WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)
C:\Users\NITISH SHARMA\.pyenv\pyenv-win\versions\3.9.10\lib\site-packages\probml_utils\plotting.py:79: UserWarning: set FIG_DIR environment variable to save figures
  warnings.warn("set FIG_DIR environment variable to save figures")

(<Figure size 432x288 with 1 Axes>,
 <AxesSubplot:xlabel='$x$', ylabel='$p(x)$'>)

plot_outlier_effect(save_name="robust_pdf_plot_outliers", outliers=[8, 8.75, 9.5])

C:\Users\NITISH SHARMA\.pyenv\pyenv-win\versions\3.9.10\lib\site-packages\probml_utils\plotting.py:79: UserWarning: set FIG_DIR environment variable to save figures
  warnings.warn("set FIG_DIR environment variable to save figures")

(<Figure size 432x288 with 1 Axes>,
 <AxesSubplot:xlabel='$x$', ylabel='$p(x)$'>)

from ipywidgets import interact


@interact(outlier_pos=(-5, 5))
def interactive_plot(outlier_pos):
    fig, ax = plot_outlier_effect(save_name="", outlier_pos=outlier_pos, outliers=[8, 8.75, 9.5])

interactive(children=(IntSlider(value=0, description='outlier_pos', max=5, min=-5), Output()), _dom_classes=('…