# Questions tagged [finite-mixture-model]

Finite mixture model represents the presence of subpopulations within an overall population and describes the data in terms of mixture distribution. Finite mixture models are commonly used for model-based clustering, but they can be used also for other problems, like cluster-wise regression, mixture of generalized linear models and other mixtures. Finite mixture models for binary and categorical data are known under the name of latent class analysis.

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### Is there any algorithm combining classification and regression?

I'm wondering if there's any algorithm could do classification and regression at the same time. For example, I'd like to let the algorithm learn a classifier, and at the same time within each label, ...
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### PyMC3: Mixture Model with Latent Variables

I have a rather basic knowledge of Bayesian inference and I'm somewhat new to MCMC and PyMC3. Can I model data that looks like this? ...
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### Finite Beta mixture model in stan — mixture components not identified

I'm trying to model data $0 < Y_i < 1$ with a finite mixture of Beta components. To do this, I've adapted the code given in section 5.3 of the Stan manual. Instead of (log)normal priors, I am ...
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### How to fit a statistical distribution data to a mixure of normal and lognormal distributions

I have a data set that is a mixture of one normal and one lognormal distribution. How can I fit the data to get the fit parameters? Can somebody help me with this.
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### Calculation of AIC in finite mixture modeling

I have a question about calculation the AIC to find my optimal amount of clusters. I am applying mixture modeling with the EM algorithm. I know the formula AIC = -2ln(log-lik) + 2k. These are my log-...
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### Reversible Jump for normal mixtures in R^d

I'm reading the article "Multivariate mixtures of normals with unknown number of components" (Dellaportas and Papageorgiou 2006). In this article they describe in great details how to ...
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### Estimating two-component mixture of Weibull distributions?

Is there any existing package (preferably in Python or Matlab) to estimate the parameters of a two-component Weibull mixture model? And failing that, I am hoping to get some pointers towards rolling ...
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### Gaussian Mixture Model - Model selection using the held-out likelihood?

I am trying to understand how to select the number of components in a Gaussian Mixture Model (GMM). Most presentations mention the use of criteria such as AIC and BIC. But if we simply follow model ...
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### What is (are) scenerios and practical settings that can possibly lead to the weibull-log-Logistic mixture distribution?

In my paper I studied Weibull-loglogistic mixture distributions in reliability and life testing, some structural properties of the model are presented including moments, reliability, hazard rate ...
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### Latent profile analysis - Gaussian models and which one to choose?

When performing LPA different models are possible depending on shape, volume and orientation (Figure 1. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5096736/). Can someone, please, explain in simple ...
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### How many parameters are present in a (general) discrete mixture of five normal distributions?

What is the minimal amount of parameters that can be retained in a particular context?
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### Composition of Normals — Finite mixture with some known parameters

I.e., the data was generated from 5 normal distributions: ...
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### What is the difference between the latent variable and the cluster weights in mixture models?

$p(x|\theta) = w_1 \mathcal{N}(x|\mu_1,\,\sigma_1^{2})\ + w_2 \mathcal{N}(x|\mu_2,\,\sigma_2^{2}) + w_3 \mathcal{N}(x|\mu_3,\,\sigma_3^{2})\,$ What is the difference between the the $w$ and the ...
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### Why mixture model with Gibbs sampling works?

I just have a question about why Gibbs sampling can correctly estimate parameters with random initial value? That is to say,we can sample z by: \begin{align} p(z_i=k \,|\, \cdot) &\...
326 views

### Universal Approximation Capabilities of Mixture Models

I am looking for two reference incl. proofs showing 1) that a discrete Mixture of Gaussians can asymptotically approximate any (well behaved) continuous density 2) that a discrete Mixture of ...
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### How to latently cluster regressors based on regressors' relationship with the outcome?

What is the best way/method to model patterns across coefficients and reduce number of coefficients based on these patterns? We have hundreds of regressors on the same scale and try to reduce the ...
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### Is there a way to determine the number of the mixture components prior to run EM algorithm

I am working with mixture models. The common way to determine the number of the mixture components is fitting several mixture models with a different number of mixture components and then select the ...
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### What is the relationship between gaussian mixture models and covariate regression?

Consider a histogram of observations $y$ which look a bit like this, Imagine that the two bell-curve shaped histograms (ignore the actual fitted curves) correspond to observations from females and ...
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### latent variables in EM algorithm are assumed to be i.i.d from multinomial distribution, from what they are idependent

In EM algorithm we introduce a latent variables, say $z_i$, $i=1,...n$, $n$ is the number of the mixture component. These variables ($z_i$) are assumed to be independent and identically distributed ...
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### Random variable defined as A with 50% chance and B with 50% chance

Note: this is a homework problem so please don't give me the whole answer! I have two variables, A and B, with normal distributions (means and variances are known). Suppose C is defined as A with 50% ...
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### When can a finite mixture of distributions drawn from a distributional family be well-described by a distribution from the same family?

This question is motivated by a situation that we frequently encounter in economic variables. We believe that the overall distribution of some variable is well approximated by a particular ...
I'm confused on the following equivalent way of rewriting a two-component mixture. Consider the two-component conditional mixture $$F(z|x)=\lambda F_1(z|x)+(1-\lambda)F_2(z|x)$$ where all the $F$'...