# Questions tagged [gaussian-mixture-distribution]

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

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### 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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### Gaussian Mixture: is this plot right?

I'm studying about Gaussian Mixtures and I decided to play around with it in Python, but I'm not entirely sure if I understand it fully. I generated some data, and then calculated the Gaussian ...
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### What is the best function to fit onto a “flat top gaussian”?

I am studying some signal and I am trying to make an automated algorithm that can extract the parameters for my signal. First let me describe a bit, I have a light emiting object crossing a window of ...
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### fitting a Gaussian mixture with a constraint in python

Suppose I have data and I want to fit a two component Gaussian mixture to it. I don't know how to do it in python but worse than that is that I have an additional constraint that the mean of one ...
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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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### Conditional distribution for Gibbs sampling for Gaussian mixture

If we draw $n$ i.i.d. points $x_1,x_2,\dots,x_n$ from the following Gaussian mixture: $$\frac 12 \mathcal N(x \mid \mu_1,1) + \frac 12 \mathcal N(x\mid \mu_2,1)$$ and the prior $p(\mu_1 , \mu_2 )$ ...
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### Doesn't the non-Gaussian source assumption of ICA render it practically useless?

Gaussian distributions appear everywhere in nature, indeed this was largely the justification for most classical methods' reliance on assumption of normality. ICA assumes non-Gaussian sources, indeed ...
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### When would I use EM instead of k-means?

When would I want to assign cluster probabilities to patterns instead of hard assignments to clusters? Can someone elaborate?
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### Interpreting mixture of Gaussians (Variational Inference)

I've recently stated reading about mixture models and variational inference in this excellent paper, but I'm having troubles dissecting the models described, and have a couple of questions. Please see ...
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### Understanding the log-likelihood (score) in scikit-learn GMM

I have been training a GMM (Gaussian Mixture, clustering / unsupervised) on two version of the same dataset: one training with all its features and one training after a PCA truncated to its 2 first ...
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### what is marginal density based on this picture?

I am studying Gaussian mixtures from the book Pattern Recognition and Machine Learning by Chris Bishop. Figure (a) are contours of the mixture components (Gaussians) with the corresponding weights. ...
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### Why are hidden Markov models considered 'mixture models'?

I'm a bit confused by the conception of "mixture model" I'm studying hidden Markov model, which is frequently referred to as a "mixture model". But I don't know what the term "mixture" implies. ...
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### Scikit learn - GMM log-likelihood. Why use Cholesky's precision matrix instead of covariance matrix?

This is my first post, please let me know if I am not being clear. I am trying to understand the sklearn.mixture.GaussianMixture.score(X). As I understand that the ...
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### Figueiredo and Jain's Gaussian mixture EM convergence criterion

I have implemented and been playing around Figueiredo & Jain 's trainer in this paper http://www.lx.it.pt/~mtf/IEEE_TPAMI_2002.pdf for Gaussian mixture. Fig. 2 in the paper depicts the full ...
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### Gaussian mixture distribution confusion

Have some confusion on Gaussian mixture distribution model (reference is from the book of Pattern Recognition and Machine Learning). My confusion is how below formula works? $\sum_kz_k=1$ My thought ...
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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 ...
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### Applying Akaike Information Criterion on collection of Gaussian fits

I am trying to apply Akaike Information Criterion on a collection of Gaussian mixtures fitted on some data points. My question is, can I use AIC even if the number of components of Gaussian mixtures ...
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### Time varying Gaussian distribution

Does there exist time varying Gaussian model? To be specific, a 2D Gaussian model whose mean and covariance matrix is varying with another parameter called time. The $\mu$(mean) and $\sigma$(...
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### Best approach to classifying 3-point trajectories?

I have a sample of about 300 subjects who have been measured at 3 different times (morning, afternoon, evening). The variable of interest can be assumed to be approximately normal. It appears that ...
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### Whitening a mixture of Gaussians

Suppose I have a dataset that was sampled from a mixture of Gaussians: $$X \sim \sum_i w_i \mathcal{N}(\mu_i, \Sigma_i)$$ Technically, I can center and then whiten $X$ so that it has zero mean and ...
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### EM-algorithm for two clusters (when one of the distributions is uniform)

I am having a hard time with the EM-algorithm. Here's the problem that I am trying to solve. Dealing with noisy annotations is a common problem in computer vision, especially when using ...
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### Is this equivalent to a Gaussian mixture model?

Similar to how you can derive the normal distribution as the distribution where the probability near a point exponentially decays with the square of the number of standard deviations you are away from ...
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### Estimating weights of known component distributions in a mixture distribution

Given $n$ probability density functions ($p_1$, ..., $p_n$) with known distributions, what are the ways of estimating the weights ($w_1$, ..., $w_n$) of these component distributions given a sample ...
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### Clarifying Dirichlet Process Mixture Probability Terms

Suppose I have a Dirichlet Process Mixture model defined as follows: $\alpha \sim G(a,b)\\ \pi|\alpha \sim \text{Dir}(\alpha)\\ z|\pi \sim \text{Cat}(\pi)\\$ where $G$ is just a standard Gamma ...
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### What is the assumption on the distribution of data in gaussian mixture models?

I am reading about Gaussian mixture models from this slide https://www.ics.uci.edu/~smyth/courses/cs274/notes/EMnotes.pdf However, I am super confused at the very first line. It says: We ...
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### How to use GMMs for acoustic signal classification?

There are a number of applications of the Gaussian Mixture Model (GMMs) to acoustics/audio data for the purposes of classification; ex paper1 and ex paper2. GMMs ...