diff --git a/.github/workflows/gh-pages.yml b/.github/workflows/gh-pages.yml index 66a9694..939d25e 100644 --- a/.github/workflows/gh-pages.yml +++ b/.github/workflows/gh-pages.yml @@ -28,9 +28,8 @@ jobs: - name: Build api with pdoc3 run: uv run pdoc --html -c latex_math=True --output-dir docs --force heavytail - #- name: Build static HTML for notebooks - # run: | - # uv run jupyter nbconvert --to html --execute --allow-errors docs/*.ipynb + - name: Build static HTML pages for Jupyter notebooks + run: uv run jupyter nbconvert --to html --execute --allow-errors docs/*.ipynb - name: Deploy uses: JamesIves/github-pages-deploy-action@4.1.4 # Source: https://github.com/marketplace/actions/deploy-to-github-pages diff --git a/docs/TylerCovariance.ipynb b/docs/TylerCovariance.ipynb new file mode 100644 index 0000000..d5c900e --- /dev/null +++ b/docs/TylerCovariance.ipynb @@ -0,0 +1,156 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "875794b5", + "metadata": {}, + "source": [ + "# Tyler Covariance Estimator\n", + "\n", + "\n", + "In this example, we will compare the Tyler covariance estimator with the standard sample covariance estimator in the presence of outliers and fat tails. \n", + "This example demonstrates that the Tyler estimator is robust to outliers, while the standard sample covariance can be heavily influenced by them." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6797d3c3", + "metadata": {}, + "outputs": [], + "source": [ + "# Copyright (c) 2025 Mohammadjavad Vakili\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from doc_utils import generate_2d_data_with_outliers, generate_2d_student_t_data, plot_2d_data, plot_covariance_contour\n", + "\n", + "from heavytail.tyler import tyler_covariance\n" + ] + }, + { + "cell_type": "markdown", + "id": "15bc8e0e", + "metadata": {}, + "source": [ + "## Comparison between Tyler and Standard Sample Covariance Estimators in the presence of Outliers" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "80e40698", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'Tyler Covariance Contour')" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "\n", + "true_cov = np.array([[1, 0.5], [0.5, 1]])\n", + "data = generate_2d_data_with_outliers(cov=true_cov, n_outliers=50, n_samples=1000)\n", + "mean = np.mean(data, axis=0)\n", + "fig, ax = plt.subplots(figsize=(8, 8))\n", + "plot_2d_data(data, ax=ax)\n", + "tyler_cov = tyler_covariance(data)\n", + "sample_cov = np.cov(data, rowvar=False)\n", + "\n", + "plot_covariance_contour(mean=mean, cov=true_cov, ax=ax, n_std=2., color='k', alpha=1, label='True Covariance')\n", + "plot_covariance_contour(mean=mean, cov=tyler_cov, ax=ax, n_std=2., color='C1', alpha=1, label='Tyler Covariance')\n", + "plot_covariance_contour(mean=mean, cov=sample_cov, ax=ax, n_std=2., color='C3', alpha=1, label='Sample Covariance')\n", + "plt.legend(frameon=False)\n", + "plt.title(\"Tyler Covariance Contour\")" + ] + }, + { + "cell_type": "markdown", + "id": "09e69d1f", + "metadata": {}, + "source": [ + "## Comparison between Tyler and Standard Sample Covariance Estimators with fat-tailed distribution" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "46af3f49", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "true_cov = np.array([[1, 0.5], [0.5, 1]])\n", + "nu = 4 # Degrees of freedom for the Student's t-distribution\n", + "data = generate_2d_student_t_data(nu=4, cov=true_cov, n_samples=1000)\n", + "mean = np.mean(data, axis=0)\n", + "fig, ax = plt.subplots(figsize=(8, 8))\n", + "plot_2d_data(data, ax=ax)\n", + "tyler_cov = tyler_covariance(data)\n", + "sample_cov = np.cov(data, rowvar=False)\n", + "plot_covariance_contour(mean=mean, cov=true_cov, ax=ax, n_std=2., color='k', alpha=1, label='True Covariance')\n", + "plot_covariance_contour(mean=mean, cov=tyler_cov, ax=ax, n_std=2., color='C1', alpha=1, label='Tyler Covariance')\n", + "plot_covariance_contour(mean=mean, cov=sample_cov, ax=ax, n_std=2., color='C3', alpha=1, label='Sample Covariance')\n", + "plt.legend(frameon=False)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "heavy-tail (3.13.5)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/doc_utils.py b/docs/doc_utils.py new file mode 100644 index 0000000..7cb70ae --- /dev/null +++ b/docs/doc_utils.py @@ -0,0 +1,144 @@ +# Copyright (c) 2024 Mohammadjavad Vakili. All rights reserved. +"""Utility functions for generating 2D data with outliers and plotting covariance contours.""" + +from typing import Any + +import matplotlib.pyplot as plt +import numpy as np +from matplotlib.axes import Axes +from matplotlib.patches import Ellipse +from scipy.stats import multivariate_t + + +def generate_2d_data_with_outliers( + n_samples: int = 100, + n_outliers: int = 10, + mean: tuple = (0, 0), + cov: list | None = None, + outlier_range: float = 8, +) -> np.ndarray: + """ + Generate synthetic 2D data with outliers. + + Parameters + ---------- + n_samples : int + Number of normal data samples to generate. + n_outliers : int + Number of outlier samples to generate. + mean : tuple + Mean of the normal data distribution. + cov : list or np.ndarray + Covariance matrix for the normal data. + outlier_range : float + Range for generating outlier values. + + Returns + ------- + np.ndarray + Combined array of normal data and outliers, shape (n_samples + n_outliers, 2). + """ + if cov is None: + cov = [[1, 0.5], [0.5, 1]] + # Generate normal data + rng = np.random.default_rng() + data = rng.multivariate_normal(mean, cov, n_samples) + # Generate outliers + outliers = rng.uniform(low=-outlier_range, high=outlier_range, size=(n_outliers, 2)) + # Combine data and outliers + return np.vstack([data, outliers]) + + +def generate_2d_student_t_data( + n_samples: int = 100, + cov: list | None = None, + nu: float = 4.0, +) -> np.ndarray: + """ + Generate synthetic 2D data from a multivariate Student's t-distribution. + + Parameters + ---------- + n_samples : int + Number of samples to generate. + cov : list or np.ndarray + Covariance matrix for the data. + nu : float + Degrees of freedom for the Student's t-distribution. + + Returns + ------- + np.ndarray + Generated data of shape (n_samples, 2). + """ + if cov is None: + cov = [[1, 0], [0, 1]] + scatter = (nu / (nu - 2)) * np.array(cov) + return multivariate_t.rvs(loc=[0, 0], shape=scatter, df=nu, size=n_samples) + + +def plot_covariance_contour( + mean: tuple[float, float], + cov: np.ndarray, + ax: Axes | None = None, + n_std: float = 2.0, + **kwargs: dict[str, Any], +) -> Axes: + """Plot covariance ellipse for 2D data. + + Parameters + ---------- + mean: tuple[float, float] + Mean vector (2D). + cov: np.ndarray + Covariance matrix (2x2). + ax: Optional[plt.Axes] + Matplotlib axis to plot on. If None, uses current axis. + n_std: float + Factor for scaling the standard deviations for ellipse size. + **kwargs: dict[str, Any] + Additional keyword arguments for Ellipse. + + Returns + ------- + plt.axes.Axes + The matplotlib axis with the covariance ellipse and data plotted. + """ + if ax is None: + ax = plt.gca() + # Eigenvalue decomposition + evals, evecs = np.linalg.eigh(cov) + order = evals.argsort()[::-1] + evals, evecs = evals[order], evecs[:, order] + theta = np.degrees(np.arctan2(*evecs[:, 0][::-1])) + width, height = 2 * n_std * np.sqrt(evals) + ellip = Ellipse(xy=mean, width=width, height=height, angle=theta, edgecolor="red", fc="None", lw=2, **kwargs) + ax.add_patch(ellip) + ax.set_aspect("equal") + ax.set_xlabel("X") + ax.set_ylabel("Y") + return ax + + +def plot_2d_data(data: np.ndarray, ax: Axes | None = None) -> Axes: + """Plot 2D data points. + + Parameters + ---------- + data: np.ndarray + 2D data points of shape (n_samples, 2). + ax: Optional[plt.Axes] + Matplotlib axis to plot on. If None, uses current axis. + + Returns + ------- + plt.axes.Axes + The matplotlib axis with the 2D data points plotted. + """ + if ax is None: + ax = plt.gca() + ax.scatter(data[:, 0], data[:, 1], s=10) + ax.set_aspect("equal") + ax.set_xlabel("X") + ax.set_ylabel("Y") + return ax diff --git a/docs/index.md b/docs/index.md index 11e3a48..09a764f 100644 --- a/docs/index.md +++ b/docs/index.md @@ -1 +1,29 @@ -Hi. \ No newline at end of file +# [heavytail] + + +[🌐 **GitHub**](https://github.com/quantfinlib/heavy-tail) +    [🔗 **API**](heavytail) +    [📖 **Docs**](https://quantfinlib.github.io/heavy-tail/) + + +## Getting Started + +* [Tyler Covariance Estimator](TylerCovariance.html) + + +## Documentation + +The documentation is available at [githubpages](https://quantfinlib.github.io/heavy-tail/). +The [🔗 API documentation](heavytail) is generated using [pdoc3](https://pdoc3.github.io/pdoc/). + +To manually generate the documentation, first, install the heavytail package with the doc dependencies using `uv`: + +```bash +$ uv pip install -e .[docs] +``` + +Then + +```bash +$ uv run pdoc --html -c latex_math=True --output-dir docs --force heavytail +``` \ No newline at end of file