{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "(factor_analysis)=\n", "# Factor analysis\n", "\n", ":::{post} 19 Mar, 2022\n", ":tags: factor analysis, matrix factorization, PCA \n", ":category: advanced, how-to\n", ":author: Chris Hartl, Christopher Krapu, Oriol Abril-Pla, Erik Werner\n", ":::" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Factor analysis is a widely used probabilistic model for identifying low-rank structure in multivariate data as encoded in latent variables. It is very closely related to principal components analysis, and differs only in the prior distributions assumed for these latent variables. It is also a good example of a linear Gaussian model as it can be described entirely as a linear transformation of underlying Gaussian variates. For a high-level view of how factor analysis relates to other models, you can check out [this diagram](https://www.cs.ubc.ca/~murphyk/Bayes/Figures/gmka.gif) originally published by Ghahramani and Roweis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ":::{include} ../extra_installs.md\n", ":::" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running on PyMC v5.10.2\n" ] } ], "source": [ "import arviz as az\n", "import numpy as np\n", "import pymc as pm\n", "import pytensor.tensor as pt\n", "import scipy as sp\n", "import seaborn as sns\n", "import xarray as xr\n", "\n", "from matplotlib import pyplot as plt\n", "from matplotlib.lines import Line2D\n", "from numpy.random import default_rng\n", "from xarray_einstats import linalg\n", "from xarray_einstats.stats import XrContinuousRV\n", "\n", "print(f\"Running on PyMC v{pm.__version__}\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%config InlineBackend.figure_format = 'retina'\n", "az.style.use(\"arviz-darkgrid\")\n", "\n", "np.set_printoptions(precision=3, suppress=True)\n", "RANDOM_SEED = 31415\n", "rng = default_rng(RANDOM_SEED)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulated data generation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To work through a few examples, we'll first generate some data. The data will not follow the exact generative process assumed by the factor analysis model, as the latent variates will not be Gaussian. We'll assume that we have an observed data set with $N$ rows and $d$ columns which are actually a noisy linear function of $k_{true}$ latent variables." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": true }, "outputs": [], "source": [ "n = 250\n", "k_true = 4\n", "d = 10" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next code cell generates the data via creating latent variable arrays M and linear transformation Q. Then, the matrix product $QM$ is perturbed with additive Gaussian noise controlled by the variance parameter err_sd." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "err_sd = 2\n", "M = rng.binomial(1, 0.25, size=(k_true, n))\n", "Q = np.hstack([rng.exponential(2 * k_true - k, size=(d, 1)) for k in range(k_true)]) * rng.binomial(\n", " 1, 0.75, size=(d, k_true)\n", ")\n", "Y = np.round(1000 * Q @ M + rng.standard_normal(size=(d, n)) * err_sd) / 1000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because of the way we have generated the data, the covariance matrix expressing correlations between columns of $Y$ will be equal to $QQ^T$. The fundamental assumption of PCA and factor analysis is that $QQ^T$ is not full rank. We can see hints of this if we plot the covariance matrix:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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