# Questions tagged [gaussian-mixture-distribution]

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

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### Conjugate prior bayesian inference on multivariate GMM

I am trying to understand how the posterior looks like when running Bayesian inference on a multivariate Gaussian-mixture model. $p(\mathbf{x}) \propto \sum_{i=1}^M w_iN(\mathbf{x}|\mu_i,\Sigma_i)$. ...
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### Is there a formula for the optimal weights for a Gaussian mixture model when the components are considered "correct"?

For simplicity consider two models predicting $Y=Z_0 + \sigma Z_1$, where $Z_i$ are independent $\mathcal{N}(0, 1)$ and each model only take one of the $Z_i$ as a factor. So we have $Y|Z_0$ and $Y|Z_1$...
1 vote
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### Assumption of Gaussian mixture model [closed]

I am still confused when I read about the Gaussian Mixture Model and how does it work. One thing that I do not understand is that "GMM assumes the data is a mixture of Gaussian or i.i.d (...
13 views

### Are the subsets of Mixture Models necessarily parametrized?

Im just learning about mixture models and they are described as a "mix of parametric and non parametric models". My question is how a non-parametric subset would look like? How would e.g. EM-...
1 vote
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### Clustering with gaussian mixtures: choice of hyperparameters

Question: I am interest in general in understanding how to choose the hyperparameters if we are interested in clustering bivariate vectors assuming a mixture of Gaussian mixture with conjugate Normal-...
1 vote
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### How to evaluate the loss on a Gaussian Mixture Model?

I successfully modeled my data using a Gaussian Mixture Model in scikit-learn but I can't figure out how I should say "how good" the model is by calculating the loss. My first thought was to ...
403 views

### 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 ...
931 views

### Understanding the log-likelihood calculation of sklearn Gaussian mixture model

I am trying to understand how the Scipy is calculating the score of a sample in the Gaussian Mixture model(log-likelihood). Below is the equation I got for log-likelihood from the book C.M. Bishop, ...
1 vote
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### Finding maximum likelihood solution for mean when data is given which share the same mean but have different variance

I have some 'X sample points say (x1,x2,x3 ...) each of the samples form a Gaussian distribution with mean 'm' and variance v1,v2, ... All the distributions have the same mean but differ in variance. ...
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### Upgrading weight parameters to random variable in Gaussian mixtures

In a Gaussian mixture model we model a density like: $p(\mathbf{x}|\pi,\mu,\sigma)=\sum \pi_i N(\mathbf{x}|\mu_i,\sigma_i)$  where $\pi,\mu$ and $\sigma$ are parameters. I would like to know if the ...
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### About the derivation of EM for mixture of Gaussians

I'm reading Andrew Ng's note about Mixtures of Gaussians and the EM algorithm He writes the likelihood of data as where random variables $z^{(i)}$'s indicate which of the $k$ Gaussians each $x^{(i)}$ ...
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### Fitting Gaussian mixture model with constraints (eg. mu1<mu2) in Python

My question is similar to this one, but while the OP there has constrains such as mu1 being <=0 and mu2 being >=0, my constraints are following: It's a three component mixture model. mu1 < ...
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### Mixture model when K=1

Assume that I want to estimate the parameters of a distribution like for example the Gaussian distribution, but I have the code only for the estimation of the parameters of a mixture of Gaussian ...
1 vote
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### Likelihood parameters estimation in mixed data type

How to estimate parameters of a Gaussian mixture model with a mix of categorical and continuous data using log-likelihood? Indeed, I have a set of data consisting of categorical and continuous data. I ...
44 views

### Closed form posterior for a mixtures of two univariate Gaussians

Giving a univariate Gaussian mixture model $$\pi_1N(x|\mu_1,\sigma_1)+(1-\pi_1)N(x|\mu_2,\sigma_2),$$ are there any priors for $\pi_1$, $\mu_1$, $\sigma_1$, $\mu_2$, $\sigma_2$ which gives a closed ...
1 vote
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### Do Gaussian Mixture Models monotonically decrease the sum of squared distances when number of clusters increases?

I am comparing the clustering performance of two closely related machine learning methods: K-means and Gaussian Mixture Models (GMM). Part of this research is selecting the best number of clusters K. ...
307 views

### Gaussian Mixture Model based clustering for unimodal, time series data

Problem: I have a simulated data set which is comprised of multiple sub-populations (or samples), each sub-population is drawn from, and described by, its own Gaussian distribution (although by chance,...
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### Cutoff for a poisson-gaussian mixture model

I have count data that is bounded on one side at zero (see image). It is bimodal and I think it results from two different processes. I would like to fit a poisson distribution around the hump around ...
150 views

### 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 ...
1 vote
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### what are the main differences between parametric and non-parametric machine learning algorithms?

I am interested in parametric and non-parametric machine learning algorithms, their advantages and disadvantages and also their main differences regarding computational complexities. In particular I ...
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### Vatiational inference in GMM

I am learning about VI and am implementing a GMM model for clustering using variational inference. However, my implementation is not fitting the data at all, even when initializing the cluster means ...
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### Fitting mixture model of Gaussians and uniform distributions to real data

I have times series of wind direction and velocity. For now, I leave aside the velocity and focus on the distribution of wind directions. Over there, there is usually three main wind directions, and ...
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### What is the marginal posterior distribution?

Based on this question: How to build a Bayesian regression model of a response that is a Gaussian mixture Consider the mixture of normal, y_j\sim (N(0,\sigma_1))^{\pi}(N(0, \sigma_2))^{1-\pi}, j=1,... 48 views

### Confusion about two Gaussian distributions

From here, it says that, linear combination of two Gaussian distribution, are always Gaussians. However, Let 𝑋 be standard normal and 𝜀=±1 with probability 1/2 each, independently of 𝑋. Let 𝑌=𝜀𝑋...
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### How does maximising ELBO for a Gaussian mixture model fit the model to data?

I am following along in Bishop's Pattern Recognition and ML chapters 9 and 10, and I understand that the EM algorithm works by iteratively updating model parameters using equations derived from ...
231 views

### Bayesian mixture model joint posterior

I am just starting to learn about bayesian mixture models. There is a few clarifications that I want to make which I am not sure myself. The graphical model below describes a gaussian mixture model ...
1 vote
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### What distribution best describes multiple, sequential normal distributions: What is the sum of more than two normal distributions?

I am curious as to what describes the following distribution. If we were to record some data which are all from a normal distribution, but the standard-deviation changes for blocks of points recorded. ...