# Questions tagged [gaussian-mixture-distribution]

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

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### Question about Gaussian Mixture model [duplicate]

suppose I have two parameters: $(\mu_{1},\Sigma_{1},\alpha_{1},\mu_{2},\Sigma_{2})$ and $(\mu_{1},\Sigma_{1},\alpha_{1},\mu_{2},\Sigma_{2})$ and suppose I mapped them to PDF using the gaussian mixture ...
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### Derivation of EM algorithm for Gaussian mixture

I am going through Expectation Maximization (EM) algorithm derivation for Gaussian Mixture models. I understand it except for a small detail. So, the general idea of EM is to maximize the expectation ...
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### Derive ELBO for Mixture of Gaussian

I am working through "Variational Inference: A Review for Statisticians" by Blei et al. (see https://arxiv.org/abs/1601.00670) and they illustrate Variational Inference using a Bayesian ...
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### Understanding of Gamma distribution as precision prior in Bayesian inference for Gaussian

Christopher M. Bishop in his book "Pattern Recognition and Machine Learning" nicely explains where does Student t-distribution $St(x|\mu,\lambda,\upsilon)$ originate into. In Chapter 2, it ...
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### Identify outliers in testing data based on trained Gaussian mixture model

I use Gaussian mixture model (GMM) to infer probability density of multidimensional data written as: $p(x) = \sum_{j=1}^{K}\pi_j*N(x|\bf \mu_j, \Sigma_j)$, where $K$ is a number of mixtures, $\pi_j$ ...
1 vote
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### Evaluate CDF and outliers of multidimensional Gaussian mixture [closed]

I use Gaussian mixture model (GMM) to infer probability density of multidimensional data written as: $p(x) = \sum_{j=1}^{K}\pi_j*N(x|\bf \mu_j, \Sigma_j)$, where $K$ is a number of mixtures, $\pi_j$ ...
1 vote
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### Gaussian Mixture Model with Minkowski distance

Gaussian Mixture Models assume Mahalanobis distance (essentially L2). Is it possible to use Lp distance in a GMM? Intuitively, in 1-space, distance is clear. In 2-space, the relation between the two ...
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### Are combinations of variables a problem in multinomial mixture models?

I am quite new to cluster analysis and I am currently using Gaussian-multinomial mixture models. I have a sample size of 10000 people with some continuous variables and about 14 categorical variables (...
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### MAP estimation for a Gaussian mixture using EM. Concerns with the covariance update formula

I am implementing the EM algorithm for a Gaussian mixture model with prior; that is, I am using the EM algorithm to find the MAP estimate, rather than the ML estimate. As briefly discussed in section ...
1 vote
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### Linear Discriminant Analysis with unlabeled data

In section 4.4.5 "Logistic regression or LDA?" of Elements of Statistical Learning by Friedman, Tibshirani and Hastie, it is claimed the following: From the mixture formulation [that is, ...
1 vote
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### Generate marginally dependent (with predetermined covariance) but conditionally independent data from a Mixture of Gaussians

Suppose you have three variables $y\in\{0,1\}$ and $x_1\in\mathbb{R}$ and $x_2\in\mathbb{R}$. I want to produce data with the following generative process which corresponds to a Mixture of Gaussians (...
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### Mixture Model: Data Consist of Continuous and Binary Features

I have a features like below id x1 x2 x3 x4 x5 id1 0.4 1.4 5.6 1 0 id2 -0.01 0.5 -3.4 0 1 where x1, x2, x3 are continuous features and x4 and x5 are binary. The goal is to find $k$ clusters using ...
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### Supervised classifier for nested interval data and ordinal classes

I'm having trouble formalizing the following classification problem: Let $x_i$ denote univariate (scalar), continuous, real data points Let $y_i \in \mathbb{N}$ be their corresponding labels Classes ...
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### Jacobian and proposal ratio of Birth/death step in RJMCMC of Gaussian mixture model

I am asking questions regarding RJMCMC several times in this site. Some of my questions are answered and some are unanswered. It didn't clarify all of my unclear points but I am glad that I have ...
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### Assumptions and setting for bayesian mixture model (for RJMCMC)

I want to understand about Bayesian mixture model discussed in RJMCMC paper (Richardson and Green, 1997) (https://academic.oup.com/jrsssb/article/59/4/731/7083042) I also posted similar question ...
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### EM algorithm get new parameters by optimizing the Q function (lower bound of likelihood function) or optimizing the likelihood function

We know that in the EM (Expectation-Maximization) algorithm, the E-step determines the $Q$ function by calculating expectations, which is a lower bound of the likelihood function. In the M-step, by ...
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### Why gaussian mixture model is sensitive to cluster size?

I did an experiment where I generated 3 well separated clusters with a different multivariate gaussian distribution for each cluster. One of the clusters contains 1000 points and the other two ...
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### Flexmix maxima are not where they are expected to be

For my dataset I have plotted the density with ggplot. As the data's density is multimodal (a total of 6 destinct modi) I tried to gain insight on the normal distributions associated to each modus. ...
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### Decomposing into Gaussian components using Bhattacharya from topFishR

I am working with fishery data. I have a data vector called SFL that contains the sizes of the fish caught. Here is some sample data: ...
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### Confidence interval for unsymmetrical Gaussian Mixure Model PDFs?

Let Y be a vector of observations. A Gaussian Mixure Model (GMM) is fit to the dataset. The distribution can appear unsymmetrical, with different thickness of tails in both sides. What is the best way ...
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### Fitting a Gaussian Mixture Model with known share of noise/outliers

A Gaussian Mixture model is fitted by the Expectation-Maximization algorithm. This fairly simple iterative algorithm consists of two steps and the initialization. Initialization (for ...
1 vote
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### What does mixture refer to in LCMM and HLME in R

I am trying to use the HLME and LCMM functions to fit latent class mixed models to my data. Here are the documentations to both of them: https://www.rdocumentation.org/packages/lcmm/versions/1.8.1.1/...
1 vote
164 views

### Gaussian mixture model probabilities

I'm using scipy's optimize to fit two Gaussian distributions to my data. I expected the posterior likelihood of belonging to the rightmost class to start from 0 ...
1 vote
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### How to solve gamma from GMM

GMM refers to the Gaussian mixture model, cf. here. Suppose we have $N$ data points (or observations in Statistics) and $K$ Gaussian models to mix. After going through Maximum Likelihood Estimation, ...
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### Mixture of Gaussian is not log-concave

I've encountered the statement: For $p\in(0,1),$ the location mixture of standard univariate normal densities $f(x)=p\phi(x)+(1-p)\phi(x-\mu)$ is log-concave if and only if $\Vert\mu\Vert \leq 2.$ ...
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### Mixture of Two Normals

Suppose we have a data which consists of two normals, x = rnorm(50,mean=1,sd=2) y = rnorm(50,mean=2,sd=3) z = sample( c(x,y) , size = 100, replace=FALSE ) The goal ...
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### Metric to check the number of clusters in one dimentional data

I have a set of 1D data as shown below. I want to find a metric that represents the number of clusters in data. Is there any suitable metric that matches my criteria? Example 1D data list: [68, 3, 3, ...
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### Is there methods for splitting a Guassian Mixture model into separate unimodal distributions?

I want to apply an algorithm which usually works on unimodal distributions on multimodal distributions, I'm considering doing this by splitting the multimodal distributions into multiple unimodal ...
1 vote
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### How do I make a table that prints the Mean and its corresponding weight of a Gaussian Mixture model?

I am successfully generating weights and means for a GMM, but I'm trying to get the results to print in a way that shows the corresponding mean for a weight. Here's what I have now: ...
1 vote