# Questions tagged [gaussian-mixture]

A type of mixed distribution or model which assumes subpopulations follow Gaussian distributions.

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### Bayesian mixture model joint posterior

I am just starting to learn about bayesian mixture models. There is a few clarifications that I want to make which I am not sure myself. The graphical model below describes a gaussian mixture model ...
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### Why does the smallest eigenvalue of the covariance matrix of a GMM equal the common variance?

I've been reading a paper "Introduction to Tensor Decompositions and Their Applications in Machine Learning". In it, the author describes an algorithm for estimating the means of the ...
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### What distribution best describes multiple, sequential normal distributions: What is the sum of more than two normal distributions?

I am curious as to what describes the following distribution. If we were to record some data which are all from a normal distribution, but the standard-deviation changes for blocks of points recorded. ...
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### Given two normal populations,, classifying a given data point

I have two normal populations S1 and S2, where S1 ~ N (μ1, σ1) and S2 ~ N (μ2, σ2) respectively. The populations are independent of each other and a data point X has to be either from S1 or from S2. ...
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### Derive cauchy distribution as a scale mixture of normal distributions

I doing Bayesian modelling these days. I found that cauchy distribution can be written as a scale mixture of normal based on following source. Link So I started to derive this. Somehow, I am not ...
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### Probabilistic generative models for clustering and classification

I have a question regarding the probabilistic setting of clustering and classification. More specifically regarding Gaussian Mixture Models and probabilistic generative models for classification. In ...
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### Is 0 the unique center for the mixture density of $N(-a,\sigma^2)$ and $N(a,\sigma^2)$, each with weight 0.5? [duplicate]

Suppose $f_{-a}(x)$ is the pdf for $N(-a,\sigma^2)$ and $f_{a}(x)$ is the pdf for $N(a,\sigma^2)$. Let $f(x)=0.5f_{-a}(x)+0.5f_{a}(x)$ be the mixture density. Is $c=0$ the unique center for $f(x)$ in ...
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### In cluster analysis, how does Gaussian mixture model differ from K Means when we know the clusters are spherical?

I understand how main difference between K-mean and Gaussian mixture model (GMM) is that K-Mean only detects spherical clusters and GMM can adjust its self to elliptic shape cluster. However, how do ...
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### How to get number of iterations in EM-algorithm using R mclust gaussian mixture model

I am clustering data using the mclust function from the R mclust package. I am struggling to get the number of iterations the EM ...
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### How to calculate log likelihood for gaussian mixture model

I'm trying to check the calculation of the log likelihood of a 2 component Gaussian Mixture Model using optim, but I get the wrong answer (it should return mu, sigma, alpha actual). The log ...
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### Fitting a mixture model distribution to kurtotic data

I need to fit a parametric distribution to data that has non-zero (unknown) kurtosis. First I tried to fit a Pearson type VII / Student's t, but the fitting is especially poor in the two tails, ...
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### Building a mixture model that fits well to the tail of a kurtotic distribution

I need to fit a distribution to data that has non-zero (unknown) kurtosis. I tried to fit a Pearson type VII / Student's t, but the fitting is especially poor in the two tails, possibly due to less ...
80 views

### Are Neural Networks Mixture Models?

To my understanding, Gaussian Mixture models are a set of parameterized gaussian distributions that collectively describe an entire, aggregate distribution. ^ from McGonagle et al Also to my ...
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### Can a variational autoencoder be interpreted as a mixture of Gaussians?

In a variational autoencoder (VAE) we have an encoder network $E_{\phi}$ that maps inputs $x$ to the distribution parameters of the approximate posterior $q_{\phi}(z \vert x)$. Most commonly we model ...
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### M step EM algorithm in Mixture Models. Expected value of the indicator variable under the posterior [closed]

I am not able to solve the following expectation. In the EM algorithm, the first step in the M step is to compute the expected value of $\log p(x,z)$ where $x$ are observations and $z$ indicator ...
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### Mixture or Convolution

tl;dr is final paragraph at the bottom. I have read the posts explaining the differences between mixture distributions and convolutions of distributions, but am having a hard time understanding which ...
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### Initialisation strategies for learning Hidden Markov Models

I used hmmlearn library to initialize an HMM (Hidden Markov Model). sampled observations from the HMM, and used the sampled data to re-estimate the parameters of ...
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### Gaussian mixture models for image matrix not determining E step

I want to calculate responsibility for each of the data points, for the given MU, SIGMA and PI. ...
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### Compute membership probabilities in E-step of EM algorithm with log-densities instead of densities

As an exercise I have implemented the EM algorithm for Gaussian mixtures, however, I have the problem that in high dimensions the densities of data points become so small that I get a numerical ...
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### Multinomial Likelihood function with conditional probabilities drawn from Gaussian Mixtures

I have a Likelihood function that is a multinomial distribution: $p(X | \alpha, \beta) = \prod_{n=1}^N [p(x_n | \alpha)]^{I_n} [p(x_n | \beta)]^{1-I_n}$ where $I_n$ is an indicator function and both \$...