# Questions tagged [gaussian-mixture]

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

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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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### Implementation of EM algorithm confusion

Here EM algorithm manually implemented, there's a question of the implementation in R of the EM algorithm for 2 mixed gaussians. The answer has a supposedly correct implementation. However, don't the ...
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### Finite mixture models with bounded data

I am trying to fit a finite mixture model to a dependent variable which is bounded (practically) between -0.594 and 1 (theoretically, the latent variable is bounded between -Inf - 1). The data are ...
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### Ftting a mixture of two Gaussians

I want to fit a mixture of two gaussian densities to my financial data. The data can be found here: http://uploadeasy.net/upload/2a7mw.rar the variable is called dat. The probability density of a ...
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### Possible statistical tests to separate two distributions within a dataset

I have a dataset that contains a range of values. I have created a frequency distribution of the values, and have included the plot below. To my untrained eye, it appears that the frequency ...
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### Correct number of components in GMM according to BIC and AIC plots

I have applied GMM(Gaussian Mixture Model) to my data set and I have plotted the resulting BIC(Bayesian Information Criterion) and AIC(Akaike Information Criterion) for different number of components. ...
2answers
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### 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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### Convergence of k-means or EM on Mixture of Gaussians

There are many algorithms for learning mixture of Gaussians but typically k-means/EM is used in practice. My question is related to the performance of k-means/EM for MoG. Recently, I came across this ...
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835 views

### Fit Gaussian Mixture model directly to the mixture density

The core of the question is: Can I estimate the parameters of a gaussian mixture model (with EM or Dirichlet Process) from a mixture density directly, that is, without using data drawn from such ...
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### How to calculate BIC for multidimensional problem

Sorry for this question, but I am really not sure how to calculate BIC for my situation. My models are mixtures of normals with different number of components. Variances are equal for all components ...
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### Diffusion coefficient from double-normal probability density function

The spread of individuals of species is often described by so-called dispersal kernels. The main parameter of spread is then often the variance defined as the average squared movement distance of a ...
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### Why isn't a gaussian mixture prone to overfitting?

Consider a Gaussian mixture of 2 components and a dataset of size $N$. The EM algorithm use the data to estimate: the model parameters: the means $\mu_1, \mu_2$ (say the covariances matrices are ...
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### A better bayesian way of modelling autoregressive mixtures

I have a JAGS hierarchical model which includes a temporal sub-model for the primary vote share between four party groups (LNP, Labor, Green, and Other). For each day in the temporal model, the vote ...
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### Understanding short animation about Dirichlet Process Mixture Model

On the wikipedia page of Dirichlet Process, there is the following video. I don't get the point of the video. My first impression was that the video was showing the fitting of one-dimensional data ...
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### In a normal mixture model, what general happens if the number of groups to be summed far exceeds the dimensions of each normal?

Suppose that we have a mixture model: $$p_\theta(y) = \sum_{k = 1}^{K}w_k \phi(y;\mu_k, \sigma^2_kI_d)$$ where $\phi(y;\mu_k, \sigma^2_k)$ is the normal density at $y$ with mean vector $\mu$ and d-...
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### Programming a mixture of a Gamma with a Normal distribution using R

I have some data x in R which seems to be a mixture of a Gamma and Normal distribution. Therefore I'd like to model this as a mixture model consisting of said distributions, but I don't know how to ...
1answer
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### Check on intuition behind infinite mixture models for clustering

I'm trying to better understand the intuition and practical application of infinite mixture models (Dirichlet Process) and finite mixture models. For example, say I have a data set on which I run a ...
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### Variance of mix of normals

Suppose we have $n$ random variables distributed normally with the same mean and different variances. Suppose we know these variances. Which will be the variance of the marginal distribution induced ...
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### Can a Gaussian mixture model be specified using a regression equation?

From: https://stats.stackexchange.com/a/236297/22199, I quote A mixture distribution combines different component distributions with weights that typically sum to one (or can be renormalized). A ...
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### Which cluster analysis for ordinal temporal data?

I would like to perform a cluster analysis but I’m not sure which is the best algorithm to apply to my data. My dataset is made of 200 cases (but the sample size can be enlarged). For each case, I ...
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### Entropy of a set of categorical variables

In the context of Expectation-Maximization, I would like to compute te entropy factor in order to get the value of the lower bound when the algorithm converged. This lower bound can be expressed as: ...
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### Expectation Maximization Gaussian Mixture Example

I am a biologist trying to understand expectation maximization for a mixture of two Gaussian distributions. I think I understand how to deal with the means of the two distributions, but I don't know ...
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### Can the hidden states of a HMM be interpreted as number of clusters underlying the data?

Trying to understand the physical significance of the number of hidden states of a HMM. Should they be interpreted as number of clusters in the data? If not, why? Or they should be interpreted as the ...
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### MIxture model in R to generate noise in data

I have a bit of code in R that adds noise to an harmonic series according to a normal distribution: ...