Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [finite-mixture-model]

a model that represents the presence of subpopulations within an overall population and describes the data in terms of a mixture distribution.

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 (see ).

Finite mixture models are described in detail in:

McLachlan, G. and Peel, D. (2000). Finite Mixture Models. John Wiley & Sons.

and latent class analysis in:

McCutcheon, A.L. (1987). Latent Class Analysis. Sage.

Hagenaars J.A. & McCutcheon, A.L. (2009). Applied Latent Class Analysis. Cambridge University Press.

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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, it also learns a continuous target. Thus, for each…
Shudong
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How can we simulate from a geometric mixture?

If $f_1,\ldots,f_k$ are known densities from which I can simulate, i.e., for which an algorithm is available. and if the product $$\prod_{i=1}^k f_i(x)^{\alpha_i}\qquad \alpha_1,\ldots,\alpha_k>0$$ is integrable, is there a generic approach to…
Xi'an
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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% chance and B with 50% chance. How would I go…
Bluefire
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Population Monte Carlo Algorithm

I am trying to wrap my head around the Population Monte Carlo Algorithm. I want to implement it for a mixture model, but I am uncertain on how to proceed. I am mostly looking for references or potentially code. I have already implemented a naive…
Gumeo
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Observations for a bivariate Gaussian mixture

Consider two random vectors $X\equiv(X_1, X_2),Y\equiv(Y_1, Y_2)$ distributed as below 1) $X\sim N(\begin{pmatrix} \mu_{X,1}\\ \mu_{X,2}\\ \end{pmatrix}, \begin{pmatrix} v_{X,1} & 0\\ 0 & v_{X,2} \end{pmatrix})$ 2) $Y\sim…
TEX
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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 selection approaches for supervised learning, we…
usual me
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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 understanding, in a neural network classifier with 1…
Matt W
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Number of components for Gaussian mixture model?

I have a vector of numeric values. My hypothesis is that this vector is a mixture drawn from two Gaussian distributions (ie k = 2). However, it is possible that there is only one Gaussian underlying my data (k = 1). I am attempting to answer this…
Brandon
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How to calculate likelihood for a mixture model with missing data?

Toy explanation: I have set of different cars of different colours. There can be green, blue, red, etc. cars. I have a set of classes i.e.: "The set contains blue, red and pink cars" or "The set contains only green cars". Let's assume that colour of…
German Demidov
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Question about the latent variable in EM algorithm

In mixture models, Expectation maximization algorithm (EM) is a commonly used method to estimate the model parameters. Suppose that I have bivariate mixture model with two mixture components, with mixture weights, $\pi_1$ and $\pi_2$, respectively.…
Maryam
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Mixture models vs Mixed models

I was wondering what is the difference between Mixture models and Mixed models in Statistics? Explaining with Any practical example would be appreciated.
user178953
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Standard deviation for weighted sum of normal distributions

I have 2 normally distributed random variable $H_0$ and $H_1$, which are combined to give the weighted distribution $H$ as follows: $H_0 \sim N(\mu_0, \sigma_0)$ $H_1 \sim N(\mu_1, \sigma_1)$ $$f_H = p * f_1(x) + (1-p) * f_0(x),$$ where $H$ has pdf…
Kelvin
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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 using $\mathrm{Exponential}(1)$ priors for the $\alpha$…
Maximilian Aigner
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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 number of coefficients with respect to the…
Dirk Buttke
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Generate a finite mixture distribution by sampling mixture component parameters

Assume I have a some mixture distribution, $H$, with mean $\mu$ and variance $\sigma^2$. $H$ is a mixture of $n$ component distributions where all component weights are equal. Let $\mu_i$ be the mean of component distribution $H_i$ and $\sigma^2_i$…
Collin
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