# Questions tagged [gaussian-mixture-distribution]

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

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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 ...
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### Gaussian Mixture Model - Model selection using the held-out likelihood?

I am trying to understand how to select the number of components in a Gaussian Mixture Model (GMM). Most presentations mention the use of criteria such as AIC and BIC. But if we simply follow model ...
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### Is a GMM-HMM equivalent to a no-mixture HMM enriched with more states?

I'm trying to model sequence data that has 5 hidden states. Observation data conditional to each state is gaussian except for one state for which mixture of 2 gaussians seems more appropriate. ...
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### Is it important to make a feature scaling before using Gaussian Mixture Model?

Is it important to make a feature scaling before using Gaussian Mixture Model? and why is it important while we are using probability in getting our clusters's parameters (mean and covariance matrix). ...
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### Number of Gaussian mixture components needed to approximate any distribution

I remember reading an actual proven number of components, that can approximate any distribution. Somehow I think it was 18. Can someone point me to a book/article stating something of the sort? Might'...
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### Choosing a model for my unsupervised machine learning problem

I need to choose a model for unsupervised machine learning problem. There are 4 clusters in 3D space. These are my requirements: I will run the same model multiple times with different training data (...
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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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### How to decompose a distribution with two peaks?

I'm modeling saving account's amount, whose change looks like a log-normal distribution. It means suppose $y$ is total saving account's amount; $x = \ln(y)$ is the natural log; $dx$, the daily change, ...
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### MLE of the mixture parameter in mixing two normal densities

Imagine that we have mixture of two normal distributions with mixture parameter $\theta$: $$p(y_i|\theta) = \theta\phi(y_i;\mu_1, \sigma_1^2) + (1 - \theta)\phi(y_i; \mu_2, \sigma_2^2)$$ Assume that ...
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### A proof that the median is a nonlinear statistical functional

This question is with reference to the top answer (by @StephanKolassa) to this question. Let $F$ and $G$ be CDFs and define $$H(x)=aF(x)+(1-a)G(x)$$ with $a\in [0, 1]$. Now suppose $F$ and $G$ are ...
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### Clustering methods for unknown number of clusters

Matrix $X=[x_1,...,x_i,...,x_N]$ is a data-set containing $N$ data-points that each data-point $x_i$ is a vector of $D$ dimensions. Each dimension is a feature. The number of clusters ($K$) is unknown....
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### Grouping similar subjects based on slopes

I am studying the responses of 500 subjects to temperature increase using a linear regression on each degree of temperature (from 10°C to 28°C). Thus, it was possible for me to compute the intercept ...
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### Metropolis sampling with different proposals

I implemented a metroplis sampler for a 1D gaussian mixture, the target distribution looks like this: I use a 1D normal distribution as propsal, that is each candidate is sampled from a normal ...
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### Selecting the number of mixtures / hidden states / latent variables

My question is regarding Gaussian Mixture models, Hidden Markov models (HMM) or any type of clustering or latent variable model, for which we can devise a likelihood function. Specifically, I train a ...
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### gaussian mixture model - approximate a matrix

I have a similarity matrix M - the value M(i,j) indicates the similarity between two elements i and j. I want to approximate that matrix using a Gaussian Mixture model or I want to cluster that ...
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### Derivation of maximum likelihood for a Gaussian mixture model

I'm working my way through the derivation of EM in Bishop (p. 435). I'm stuck trying to derive to MLE for $\mu_k$ for the gaussian mixture model. Basically I get an extra sum in the numerator. For ...
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### anomaly detection with gaussian mixture models

I am new to the topic, and I am trying to understand how it is possible to perform anomaly detection by using gaussian mixture models. Could you please give me some hints about literature on the topic?...
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### PyMC for Categorical Latent Model

I'm learning PyMC and am trying to fit a simple categorical mixture model but the sampling estimates don't converge to the true values. I'm wondering if I've specified the model incorrectly or am ...
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### Gaussian Mixture Model parameters from density

How do I estimate parameters of subpopulations in a 1D gaussian mixture model when I already have density (measured on a grid) of the mixture? All the algorithms I can find (like the well-known EM ...
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### how to discard values that are far from center of cluster in mixture model

I am trying to fit a bivariate cluster model with X and Y. What I would like to do is discard (make not clustered / un-grouped) that are far from the cluster center (for example $\mu$ + 2*standard ...
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### Align noisy point clouds

I have a point cloud $X$ that, I suspect, is a translate of a Gaussian-corrupted version of a subset of a larger cloud $Y$, both high-dimensional ($d$ is at least 100 and ideally 10,000). What is the ...
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### Maximum likelihood estimation for Gaussian mixture

When doing maximum likelihood (ML) inference on a Gaussian mixture model (GMM), Bishop notes in PRML that if there is more than one mixture component in the GMM and the mean of one Gaussian collapses ...
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### How to build a Bayesian regression model of a response that is a Gaussian mixture

Context: My response looks like a mixture model with two classes as you can see on the picture. I have a couple of predictors that perform relatively well in a linear regression (Bayesian or not). In ...
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### How to derive the MLE of a Gaussian mixture distribution

In my self-study, I consider a Gaussian mixture distribution: $$p(x)= p(k=1) N(x|\mu_1,\sigma^2_1) + p(k=0) N(x|\mu_0,\sigma^2_0)$$ where $p(k=1)+p(k=0)=\pi_1+\pi_0=1$. I am now asked to do three ...
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### Convergence of EM for Mixture of Gaussians

Is the Mixture of Gaussians model (an example of latent class analysis) gauranteed to converge on a viable solution even on Unimodal data using the Expectation Maximization algorithm to estimate the ...
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### Given two normal populations,, classifying a given data point

I have two normal populations S1 and S2, where S1 ~ N (μ1, σ1) and S2 ~ N (μ2, σ2) respectively. The populations are independent of each other and a data point X has to be either from S1 or from S2. ...
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### Gaussian mixture model - does an improper uniform prior give a proper posterior?

We draw $n$ i.i.d. points $x_1 , x_2 , ..., x_n$ from the following Gaussian mixture: $$p(x|\mu_1,\mu_2) = \frac{1}{2} \text{N} (x|\mu_1,1) + \frac{1}{2} \text{N} (x|\mu_2,1).$$ The prior is the ...
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### How to use Kullback-leibler divergence if mean and standard deviation of of two Gaussian Distribution is provided?

With Apache Spark MLLib library I am trying to find Clusters within a dataset by using Gaussian Mixture Model (number cluster =3) . Now it returns 3 different values of mean and standard deviation. I ...
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### Which metric is used in the EM algorithm for GMM training ?

My question concerns the expectation-maximisation algorithm used to estimate the hyper-parameters of a Gaussian mixture model in z multivariate setup. I understand that the EM algorithm uses the ...
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### Median of mixture of two Gaussian distributions with equal weights

I am given a population $P$ that is equally divided into subsets $A$ and $B$. I know that a property $H$ of the population $P$ is normally distributed with mean $\mu_1$ and variance $\sigma_1^2$ for ...
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### What should be the covariance matrices and weights for initializing EM/GMM with kmeans?

It's typical to initialize EM for Gaussian Mixture Models using the result of kmeans clustering. However, kmeans only gives you the means (centers) of the starting GMM, but EM initialization often ...
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### 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 ...