# Questions tagged [gaussian-mixture-distribution]

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

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### What determines performance in recoverying K in Gaussian Mixture Model?

My question is about what determines how hard it is to recover the number of components $K$ in a Gaussian mixture model (GMM), e.g. with the EM-algorithm. For simplicity, let's consider the case in ...
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### Is Mixture Modelling the Standard Regression Technique for Dealing with Irregular Distributions?

Is Mixture Modelling the Standard Regression Technique for Dealing with Irregular Distributions? Recently, I came across the use of Gaussian Mixture Distributions being used to model the response ...
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### How to calculate the covariance matrix in (Xu and Knight 2010)?

Setup I'm reading (Xu and Knight 2010), which is a paper about estimating finite Gaussian mixture models using the CECF (Continuous Empirical Characteristic Function) method. The basic idea is to ...
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### K Means as a special case of GMM (using EM Algorithm)

I am looking for a tutorial/gentle introduction (preferably with mathematics/proofs) on K-means as a special case of Gaussian Mixture Model using the EM Algorithm. I have found this: https://www....
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### Compute log-likelihood in Bernoulli Gaussian Mixture

I'm working on this exercise about Gaussian Mixtures: Here's part of the solution: I don't understand how they came up with this equation for the log-likelihood (red arrow). From what I know, the ...
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### Help students understand Gaussian Kernel in mean shift segmentation

I am creating a image mean shift segmentation algorithm for a class. So far what I've done is basically Iterate through each point/pixel on the image and with a given bandwidth(radius) calculate the ...
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### Are linear combinations (i.e. "sums") of gaussian distributions also gaussian?

I have always assumed that this is fact : but are there any mathematical theorems that state: finite sums of gaussian distributions are gaussian themselves? In the above picture, does p(x) have a ...
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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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### computing the mutual information of a mixture of Gaussians

How can one compute the mutual information of Gaussian mixture distribution \begin{equation} \mathrm{I}(X;C|Y)=H[C|Y]-H(C|X,Y)=-\int\int\sum_{C}P(X,C,Y)\log\frac{P(X,C|Y)}{P(C|Y)P(X|Y)}\mathrm{d}X\...
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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 $Y|Z_1$...
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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 (...
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### 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-...
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### Machine learning models cannot fit, unless gaussian mixture probabilities are used

I was working on the scikit-learn-london dataset (on kaggle) and I was trying to do a binary classification task. The dataset is shortly described below: 40 features (all numerical, not categorical) ...
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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-...
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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 ...
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### Partial derivative of composite function of functional data

I would like to find the partial derivative of $f(y)$ with respect to c where $y$ follows multivariate normal/Gaussian density $N(x(t),\sigma^2I_n)$ i.e. \$f(y)=(2\pi)^{-n/2}|\sigma^2I_n|^{-1/2}exp[-1/...
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### Find the difference in treatment and control groups during segments of time series data

I have time-series data for a control group and treatment group. I would like to measure the change in current flowing through a cell membrane before and after drug treatment. Each cell is treated ...