{ "cells": [ { "cell_type": "markdown", "id": "e2d6a8f5-e30f-47e8-8cba-c579b6abddfa", "metadata": {}, "source": [ "(gaussian_mixture_model)=\n", "# Gaussian Mixture Model\n", "\n", ":::{post} April, 2022\n", ":tags: mixture model, classification \n", ":category: beginner\n", ":author: Abe Flaxman\n", ":::\n", "\n", "A [mixture model](https://en.wikipedia.org/wiki/Mixture_model) allows us to make inferences about the component contributors to a distribution of data. More specifically, a Gaussian Mixture Model allows us to make inferences about the means and standard deviations of a specified number of underlying component Gaussian distributions.\n", "\n", "This could be useful in a number of ways. For example, we may be interested in simply describing a complex distribution parametrically (i.e. a [mixture distribution](https://en.wikipedia.org/wiki/Mixture_distribution)). Alternatively, we may be interested in [classification](https://en.wikipedia.org/wiki/Classification) where we seek to probabilistically classify which of a number of classes a particular observation is from." ] }, { "cell_type": "code", "execution_count": 1, "id": "a0b1403f-3cec-4237-a1c7-27f1c8681cb9", "metadata": {}, "outputs": [], "source": [ "import arviz as az\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import pymc as pm\n", "\n", "from scipy.stats import norm\n", "from xarray_einstats.stats import XrContinuousRV" ] }, { "cell_type": "code", "execution_count": 2, "id": "54c04faa-5c80-4b91-af3f-a57a2c927029", "metadata": {}, "outputs": [], "source": [ "%config InlineBackend.figure_format = 'retina'\n", "RANDOM_SEED = 8927\n", "rng = np.random.default_rng(RANDOM_SEED)\n", "az.style.use(\"arviz-darkgrid\")" ] }, { "cell_type": "markdown", "id": "1a506223-1cf2-4c1a-ab75-6a3e8684329e", "metadata": {}, "source": [ "First we generate some simulated observations." ] }, { "cell_type": "code", "execution_count": 3, "id": "9ad9800b-52ae-4d4c-9e7e-36b741480a50", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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