# Questions tagged [gaussian-mixture]

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

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### Introduction to Gaussian mixture models

First of all, I am sorry if this question is not acceptable by some of the readers. However, I really read many, many sources about Gaussian mixture models, but all what I found was a short tutorial ...
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365 views

### Gaussian Mixture Model

with the following code I fit a Gaussian Mixture Model to arbitrarily created data. The code is working. The only thing I encounter is that during the calculation of the multivariate_normal I ...
2answers
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### This is Gaussian mixture model?

Here is a problem that I am looking at. Is this model really commonly known as a Gaussian mixture model (the one often appears as an illustration of EM algorithm)? I am confused because Gaussian ...
1answer
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### Gaussian Mixture Model - marginal likelihood

I am studying gaussian mixture models. The first step defines the following equation. They then proceed to marginalize $z_n$ out My question is, how did they arrive at that equation ? Where did the ...
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### Use gradient methods for maximum likelihood estimation of Gaussian mixture

I have some questions concerning estimating maximum likelihood of Gaussian mixture model. As I have read around some material, they usually use EM algorithm for maximizing the complete likelihood ...
1answer
964 views

### How to deal with categorical feature in a Gaussian Mixture model clustering model

I am performing clustering by Gaussian Mixture model using EM algorithm in R. U use the mclust package. My data (205 observations and 25 variables) has both ...
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### Useful separation value in a mixture distribution

Assume we have a distribution that is the mixture of two normal distributions. The pdf of the overall distributions and their single parts may look like the following. In black, the combined ...
1answer
500 views

### Mixture Density Network: What is C?

I'm currently trying to implement a Mixture Density Network (MDN) based off of the original paper here. Most of the equations seem pretty straight forward but on page 6 (7 of the PDF) equation 23 has ...
2answers
598 views

### The pointwise product of densities of a Gaussian mixuture and a Gaussian

Let's say that I have a mixture of Gaussians representing a likelihood: $$p(\mathbf{x}) = \sum_{i=1}^K\phi_i \mathcal{N}(\boldsymbol{\mu_i,\Sigma_i})$$ What is the posterior distribution given a ...
1answer
358 views

### One-class Classification of multidimensional vectors

I have a m x k User-feature matrix (m >> k) obtained by factorizing an original User-websites matrix (m x n) that has #page views as entries. Additionally, there are users (say r) who have been ...
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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 ...
0answers
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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 ...
0answers
416 views

### 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 ...
0answers
873 views

### 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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### Skewness of fitted mixture not correct?

I fitted a gaussian mixture to my financial data. The values are: $\pi= 0.3$ $\mu_1= -0.01$ $\mu_2= 0.01$ $\sigma_1=0.01$ $\sigma_2=0.03$ One can see, that both single distributions have a ...
2answers
995 views

### Comparing K-Means and Expectation Maximization on the dataset generated - When does K-Means perform better?

I was experimenting with K-Means and Gaussian Mixture Models (Expectation-Maximization) on the data set that I generated. Here is how the plot for two distributions looks like: Since this was ...
2answers
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### Mixed data in Gaussian Mixture Models

Is it possible to use a dataset with mixed variables such as continuous, ordered, and categorical variables and cluster the data using the Gaussian Mixed Model with EM algorithm. I cannot find ...
1answer
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### How to use Bayes' Theorem to detect an event in a noisy signal

I'm trying to use Bayes' Theorem to solve a question that's come up in work, but I don't know if I've done it correctly, because the result seems a bit strange. The problem involves a stochastic ...
1answer
3k views

### The number of parameters in Gaussian mixture model

I have D-dimensional data with K components. How many parameters if I use a model with full covariance matrices? and How many if I use diaogonal covariance matrices?
1answer
509 views

### How to do batch learning for Gaussian Mixture Models?

I have a huge dataset of features on which I want to fit a Gaussian Mixture Model using standard expectation maximization, as it is implemented by sklearn. Since not all features fit into the memory ...
1answer
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### Bimodal univariate distributions are always indicative of a mixture of two random variables. Is this correct? [duplicate]

Say I see a bimodal distribution like this (with the domain, or random variable, $Z$): Does that instantly mean that I am seeing not a distribution of one independent random variable $Z$, but ...
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### What does 'vector-valued' mean?

What is the difference of a feature vector and a 'vector-valued observation' as described here? The term 'vector-valued' is used in the following context: "Most state-of-the-art [Automatic Speech ...
1answer
11k views

### Generate sample data from Gaussian mixture model [duplicate]

I am given the values for mean, co-variance, initial_weights for a mixture of Gaussian Models. Now how can I generate samples given those: In brief, I need a function like ...
1answer
151 views

### Mixture Model Distributions

I wonder, if there could be a Pareto Mixture Model, just like the Gaussian Mixture Model (GMM). How am I supposed to build a Pareto Mixture Model (PMM)?
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### I want to show a local optimum in my paper, how do I generate the data for it?

I'm writing a paper where I am explaining the problems of local optimum in my clustering algorithm. While clustering, in my data I would at times get local optimums. But I've tried and I cannot ...
1answer
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### My MCMC do not overlap : Mixturemodel with JAGS and R

I fitted a JAGS model and I have those results : My questions are: Why do my chains not overlap, and how can I fix that? I used the following method: My model is a mixture Gaussian model of two ...