# Questions tagged [gaussian-mixture-distribution]

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

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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/...
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### 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 ...
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### Ask for help understanding a sentence in Bishop's PRML book on soft weight sharing

It's about section 5.5.7 of Christopher M. Bishop's "Pattern Recognition and Machine Learning" on soft weight sharing. The sentence is the first three lines of page 271. First the author ...
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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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### Do the Mixing Coefficients in a Gaussian Mixture Model Depend on the Datapoint?

Given a Gaussian mixture model with $K$ clusters, the probability of sampling a point $x\in\mathbb{R}^d$ is given by $$p(x) = \sum_{k=1}^K\pi_k\mathcal{N}(x;\boldsymbol\mu_k,\boldsymbol\sigma_k)$$ ...
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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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### Likelihood in mixture models

As per my understanding, normally, when we talk about Bayes rule, we write: p(z|x) = [p(x|z) * p(z)] / p(x) where, p(z|x) is called posterior p(x|z) is called likelihood p(z) is called prior p(x) is ...
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### What is the average bias in MLE of 2-component univariate Gaussian mixture model?

Imagine that you have a standard 2-component univariate Gaussian mixture model: $$p(x_i∣θ)=(1-λ)N(x_i|μ_1,σ_1^2 )+λN(x_i|μ_2,σ_2^2 )$$ $$θ=\{μ_1,μ_2,σ_1,σ_2,λ\}$$ $$L(θ;x)=∏_{i=1}^N p(x_i |θ)$$ The ...
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### AIC vs BIC for time series clustering and descriptive purposes

I'm in the process of fitting a hidden markov model with gaussian mixtures to time series health data. The primary purpose of this is descriptive, not predictive – I'm using the fitted model to give a ...
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### Test for gaussian mixture fit when component assignment is known?

I have a process 𝑃 generating random variables X_1, ... X_n. From each of these I've sampled a set of samples ...
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### MLE for Two component mixture model

Chapter 8 section 8.5.1 of the Elements of Statistical Learning book describes a simple mixture model for density estimation and the associated EM algorithm for carrying out maximum likelihood ...
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### How to obtain the p-values ​of a gamlssMX model?

I am working with a dataset that includes a binary target variable (0 or 1). I have built a model with the gamlssMX() function included on the "gamlss.mx" package to explain a continuous ...
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### Are gaussian mixture models for clustering robust to data sparsity?

I would like to cluster customers based on their product usage data (20-40 products/dimensions) on the same scale. Overall, the data is reasonably log-normally distributed for all products (the ...
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