# 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.

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### Universal Approximation Capabilities of Mixture of Weibulls

Can a mixture of $N$ Weibull distributions approximate any continuous density with non-negative support, if $N$ is sufficiently large? (If so, a reference to the proof would be greatly appreciated). (...
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### Is there a good package to implement latent profile analysis in R, which allows use of FIML for missing data

We are looking to conduct latent profile analysis in R, using a large number of continuous variables (physical activity level at different times of day). We have objective measurement of physical ...
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### How to identify a mixture of poisson distribution and Gaussian distribution from the data?

Here is the distribution of the data. It seeme to me that it is a mixture of a poisson distribution at the begining of zero value and a Gaussian distribution. I also used the ...
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### Distribution of sum of $n$ random variables with mixture of two exponential distributions

Suppose that the random variable $Y$ follows a mixture of two exponential distributions, that is $$f_Y(y) = \sum_{i=1}^{2}\pi_i f(y| \lambda_i)$$ where $\pi$ stands for ...
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### Monte Carlo for Dirichlet Multinomial Model

Problem I am trying to implement Markov Chain Monte Carlo for the Dirichlet Multinomial mixture, described in this reference (where one used the expectation maximization algorithm). The model is as ...
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### mixture of finite regressions without a response variable

In finite mixture modelling, in particular mixture of regressions modelling, we are interested in finding latent trajectories against a response variable. But what if there is no known response ...
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### Simultaneous Bayes Estimation

Given $\theta_i$, $0 < \theta_i < 1$, a sequence of independent Bernoulli ($\theta_i$) random variables from i subpopulations, that are also independent across subpopulations. Suppose i=2 (2 ...
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### Anomaly detection with strong prior assumptions about data generating process

I have data that can be described using the model $$y \sim \mathcal{N}\big(f(x; \Theta), \, \sigma^2)$$ where $f$ is some function with known functional form, but unknown parameters. I also can make ...
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### Model choice with expectation maximization: which likelihood?

When deciding about the number of mixture components using Akaike or bayesian information criteria, should one use the full likelihood or the likelihood marginalized over the latent variables? Both ...
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### Expectation maximization: does the likelihood always increase monotonically?

When working with (gaussian) mixture models, I always took it for a mathematical fact that the marginal likelihood increases with every iteration step. If it were not the case, it always meant an ...
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### Using regression to both estimate and attribute a single value to a subset of established categories

I am using Stata 15.1 I have a dataset with some 12,000 observations with a continuous dependent variable and 4 continuous independent variables. Each observation is also prior assigned to one of ...
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### What is truncated gaussian mixture model?

I am interested in the Gaussian mixture model. I read about it and I think I am good with it. However, found that there is something called truncated Gaussian mixture model, which I do not understand. ...
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### How to implement a mixture model for Dirac Delta and Normal distributions?

How could I fit data with observations from one Dirac delta component and $n$ normal distributed components? Where $n$ usually is between 1 and 5. My prior knowledge is that one component really is a ...
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### How do you differentiate between time-varying covariate versus nontime-varying covariate in growth mixture models/latent class growth analysis in r?

I am attempting to run a LCGA / GMM analysis in R but I am not sure how to control for time-varying covariates. I understand that R only has the capability to do the 1-step approach. Does this mean ...
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### R mix function from DepmixS4 package provide different results with exactly same codes

I am testing the mix model from the Depmix4 package using simulating data. In the model, I provide the starting values to all parameters to be estimated. However, when I run the same code twice, I get ...
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### Regression or mutual information when we have mix of discrete and continuous variables

I am trying to identify relevant features for a problem. The features are discrete and continuous in [0,1]. The target variable is [0,1]. I have tried linear regression by standardizing(subtract mean ...
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### Mixture model for decomposing bimodal or multimodal distributions

The gaussian mixture model (GMM) is fed mixture components or features whose time series each have differing means and variances from one another, but are unimodal (have one mode) with each component ...
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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 ...
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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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