# Questions tagged [gaussian-mixture]

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

477 questions
Filter by
Sorted by
Tagged with
16 views

9 views

46 views

### Convergence of EM algorithm

I am aware that EM eventually converges. However, I still have some confusions regarding this property: 1: As far as I am aware, HMM, Gaussian mixture model and MCMC can converge and all of them use ...
87 views

### what is wrong with my Gaussian Mixture density estimation fitting (Python)?

I have a data set (1D) link: dataset, which has values ranging from 21,000 to 8,000,000. When i plot histogram of the log values, i can see there are two peaks, roughly. I tried to fit Gaussian ...
56 views

### Closed form for Finite Gaussian Mixture Model when weights are known and prior variance can be 0

Suppose I have a normal likelihood $x|\theta \sim N(\theta, \sigma^2_{known})$ where the variance is known and a mixture prior $\theta \sim p * N(\mu_1, \sigma^2_1) + (1-p) * N(\mu_2, \sigma^2_2)$, ...
136 views

### What is the interpretation of the weights in the GMM?

GMM is $p(x|\theta) = w_1 \mathcal{N}(x|\mu_1,\,\sigma_1^{2})\ + w_2 \mathcal{N}(x|\mu_2,\,\sigma_2^{2}) + w_3 \mathcal{N}(x|\mu_3,\,\sigma_3^{2})\,$ What is the interpretation of the weights here? Do ...
26 views

### Why mixture model with Gibbs sampling works?

I just have a question about why Gibbs sampling can correctly estimate parameters with random initial value? That is to say,we can sample z by: \begin{align} p(z_i=k \,|\, \cdot) &\...
29 views

### How to deduct the complete likelihood of mixture normal in EM algorithm

We have the well known complete likelihood of mixture normal in EM algorithm: Here $Z$ is a random variable that it has probability $\pi_k$ to choose k-th normal variable $X_k:N(\mu_k,\sigma_k).$ We ...
109 views

### Suggest a model for this dataset

I have a time series data set (the Old Faithful geyser data available here: http://www.gatsby.ucl.ac.uk/teaching/courses/ml1-2012/geyser.txt). Plotting the eruption duration on the x axis and the ...
62 views

### 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 ...
44 views

### Can Gaussian Mixture Model Clustering tell me something about the distribution of my data?

I have 10,000 vectors originating from 5 separate classes (2,000 each). I use Gaussian Mixture Model clustering (in Python) to cluster the 10,000 vectors, telling the algorithm to cluster the data ...
22 views

### Why is Matlab's cluster method able to accept only two inputs? What does it mean when it does? Ex: clusterX = cluster(gmfit,X); [closed]

Matlab's cluster method documentation says cluster takes in 3 arguments: T = cluster(Z,'Cutoff',C) https://www.mathworks.com/help/stats/cluster.html But line 56 inside the cluster function seems to ...
12 views

### Decompose 2D matrices into mixture of Gaussians

I have a 2D array that roughly represents a probability distribution in the 2D space. That is, all values in this 2D matrix sum up to 1. I want to decompose this 2D matrix into a sum of Gaussians. ...
58 views

### Implementation of EM algorithm confusion

Here EM algorithm manually implemented, there's a question of the implementation in R of the EM algorithm for 2 mixed gaussians. The answer has a supposedly correct implementation. However, don't the ...
41 views

### How do I properly scale the covariance matrix in a weighted Gaussian mixture model for new samples?

I am trying to implement the method for computing a Gaussian mixture model from samples with known weights as detailed in section III of: EM Algorithms for Weighted-Data Clustering with Application ...
10 views

### How to normalize data by mapping data points from one mixture of multivariate normal distributions to another mixture

How to normalize data by mapping data points from one mixture of multivariate normal distributions to another mixture Problem description I am trying to normalize multivariate time series data. The ...
22 views

### Expected Misclustering rate

I am reading this paper on minimax clustering error rates on high-dimensional Gaussian mixtures. The authors define a metric for expected misclustering rate as follows: For a two-component ...
In EM algorithm we introduce a latent variables, say $z_i$, $i=1,...n$, $n$ is the number of the mixture component. These variables ($z_i$) are assumed to be independent and identically distributed ...
Suppose I have a gaussian mixture model with 2 parameters $(u,v)$ and 2 parts. The model is $P({x_i}|u,v)=uN(x_i|\mu_1^{i} = x_i^2/v,\sigma_1^{i}) + (1-u)N(x_i|\mu_2^{i} = x_i^3/2v^2,\sigma_2^i)$. ...