# Questions tagged [gaussian-mixture]

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

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### Fit mixture of distributions to your time-series data in R

I have time-series data containing 1440 observations and the plot of the data is I want to fit the Gaussian Mixture Models (GMM) to the above plot, and for the same I am using Mclust function of ...
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### Different covariance types for Gaussian Mixture Models

While trying Gaussian Mixture Models here, I found these 4 types of covariances. ...
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### EM algorithm manually implemented

I want to implement the EM algorithm manually and then compare it to the results of the normalmixEM of mixtools package. Of ...
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### If k-means clustering is a form of Gaussian mixture modeling, can it be used when the data are not normal?

I'm reading Bishop on EM algorithm for GMM and the relationship between GMM and k-means. In this book it says that k-means is a hard assign version of GMM. I'm wondering does that imply that if the ...
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### Mclust model selection

The R package mclust uses BIC as a criteria for cluster model selection. From my understanding, a model with the lowest BIC should be selected over other models (if ...
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### Significant difference between time series - Can I do this?

I'd like to know whether the solution proposed below is valid/acceptable and any justification available. We have two biological conditions, and for each condition we measured 3 time series, so at ...
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### Why is optimizing a mixture of Gaussian directly computationally hard?

Consider the log likelihood of a mixture of Gaussians: $$l(S_n; \theta) = \sum^n_{t=1}\log f(x^{(t)}|\theta) = \sum^n_{t=1}\log\left\{\sum^k_{i=1}p_i f(x^{(t)}|\mu^{(i)}, \sigma^2_i)\right\}$$ I was ...
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### 2-Gaussian mixture model inference with MCMC and PyMC

The problem I want fit the model parameters of a simple 2-Gaussian mixture population. Given all the hype around Bayesian methods I want to understand if for this problem Bayesian inference is a ...
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### What is “mixture” in a gaussian mixture model

We often study Gaussian Mixture model as a useful model in machine learning and its applications. What is the physical significance of this "Mixture"? Is it used because a Gaussian Mixture Model ...
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### Compute quantile function from a mixture of Normal distribution

I have this mixture of normal distribution: $$X \sim \frac{1}{2}\mathcal{N}(\mu_{x_1}=10,\,\sigma_{x_1}^{2}=1)+\frac{1}{2}\mathcal{N}(\mu_{x_2}=13,\,\sigma_{x_2}^{2}=1)$$ How can i compute the ...
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### Simulate from a truncated mixture normal distribution

I want to simulate a sample from a mixture normal distribution such that $$p\times\mathcal{N}(\mu_1,\sigma_1^2) + (1-p)\times\mathcal{N}(\mu_2,\sigma_2^2)$$ is restricted to the interval $[0,1]$ ...
634 views

### 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 ...
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### Clustering a dataset with both discrete and continuous variables

I have a dataset X which has 10 dimensions, 4 of which are discrete values. In fact, those 4 discrete variables are ordinal, i.e. a higher value implies a higher/better semantic. 2 of these discrete ...
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### Singularity issues in Gaussian mixture model

In chapter 9 of the book Pattern recognition and machine learning, there is this part about Gaussian mixture model: To be honest I don't really understand why this would create a singularity. Can ...
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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 ...
7k views

### Quantiles from the combination of normal distributions

I have information on the distributions of anthropometric dimensions (like shoulder span) for children of different ages. For each age and dimension, I have mean, standard deviation. (I also have ...
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### K-means as a limit case of EM algorithm for Gaussian mixtures with covariances $\epsilon^2 I$ going to $0$

My goal is to see that K-means algorithm is in fact Expectation-Maximization algorithm for Gaussian mixtures in which all components have covariance $\sigma^2 I$ in the limit as $\lim_{\sigma \to 0}$. ...
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### How to train a Gaussian mixture hidden Markov model?

I want to build a hidden Markov model (HMM) with continuous observations modeled as Gaussian mixtures (Gaussian mixture model = GMM). The way I understand the training process is that it should be ...
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### Difference between GMM classification and QDA

I know that every class has the same covariance matrix $\Sigma$ in linear discriminant analysis (LDA), and in quadratic discriminant analysis (QDA) they are different. When using gaussian mixture ...
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### 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 ...
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### Sum of Gaussian mixture and Gaussian scale mixture

What will be the distribution of the sum of two independent random variables, say $X$ and $Y$, when $X$ has a Gaussian mixture distribution (when we take Gaussian distribution with different location ...
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### Conditional mean for mixture of multivariate normal distributions

If x = (x_1,x_2,...,x_n) is a vector whose components have a distribution that is a finite mixture of multivariate normals, is the expected value of x_1 still a linear function of the other components,...
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### 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 ...
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### 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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### GMM with Bayes decision model

Given two classes of training data (A and B), I want to fit each class' distribution using a GMM with k components, and then use Bayes Decision Model for the classification. The first step was to ...
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### Derivation of M-step in EM algorithm for mixture of Gaussians

I am trying to derive the parameter estimation equations for the M-step of the expectation maximization (EM) algorithm for a mixture Gaussians when all Gaussians share the same covariance matrix \$\...