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Questions tagged [gaussian-mixture]

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

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1answer
3k views

Fit mixture of distributions to your time-series data in R

I have time-series data containing 1440 observations and the plot of the data is I want to fit the Gaussian Mixture Models (GMM) to the above plot, and for the same I am using Mclust function of ...
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1answer
5k views

Mclust model selection

The R package mclust uses BIC as a criteria for cluster model selection. From my understanding, a model with the lowest BIC should be selected over other models (if ...
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2answers
29k views

EM algorithm manually implemented

I want to implement the EM algorithm manually and then compare it to the results of the normalmixEM of mixtools package. Of ...
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2answers
17k views

If k-means clustering is a form of Gaussian mixture modeling, can it be used when the data are not normal?

I'm reading Bishop on EM algorithm for GMM and the relationship between GMM and k-means. In this book it says that k-means is a hard assign version of GMM. I'm wondering does that imply that if the ...
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2answers
3k views

Significant difference between time series - Can I do this?

I'd like to know whether the solution proposed below is valid/acceptable and any justification available. We have two biological conditions, and for each condition we measured 3 time series, so at ...
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3answers
5k views

2-Gaussian mixture model inference with MCMC and PyMC

The problem I want fit the model parameters of a simple 2-Gaussian mixture population. Given all the hype around Bayesian methods I want to understand if for this problem Bayesian inference is a ...
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1answer
518 views

My MCMC do not overlap : Mixturemodel with JAGS and R

I fitted a JAGS model and I have those results : My questions are: Why do my chains not overlap, and how can I fix that? I used the following method: My model is a mixture Gaussian model of two ...
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5answers
38k views

Clustering a dataset with both discrete and continuous variables

I have a dataset X which has 10 dimensions, 4 of which are discrete values. In fact, those 4 discrete variables are ordinal, i.e. a higher value implies a higher/better semantic. 2 of these discrete ...
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5answers
5k views

Singularity issues in Gaussian mixture model

In chapter 9 of the book Pattern recognition and machine learning, there is this part about Gaussian mixture model: To be honest I don't really understand why this would create a singularity. Can ...
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0answers
3k views

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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4answers
11k views

How to train a Gaussian mixture hidden Markov model?

I want to build a hidden Markov model (HMM) with continuous observations modeled as Gaussian mixtures (Gaussian mixture model = GMM). The way I understand the training process is that it should be ...
12
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1answer
5k views

Quantiles from the combination of normal distributions

I have information on the distributions of anthropometric dimensions (like shoulder span) for children of different ages. For each age and dimension, I have mean, standard deviation. (I also have ...
8
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1answer
2k views

K-means as a limit case of EM algorithm for Gaussian mixtures with covariances $\epsilon^2 I$ going to $0$

My goal is to see that K-means algorithm is in fact Expectation-Maximization algorithm for Gaussian mixtures in which all components have covariance $\sigma^2 I$ in the limit as $\lim_{\sigma \to 0}$. ...
8
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2answers
3k views

What is “mixture” in a gaussian mixture model

We often study Gaussian Mixture model as a useful model in machine learning and its applications. What is the physical significance of this "Mixture"? Is it used because a Gaussian Mixture Model ...
8
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1answer
1k views

Simulate from a truncated mixture normal distribution

I want to simulate a sample from a mixture normal distribution such that $$p\times\mathcal{N}(\mu_1,\sigma_1^2) + (1-p)\times\mathcal{N}(\mu_2,\sigma_2^2) $$ is restricted to the interval $[0,1]$ ...
5
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1answer
962 views

Difference between GMM classification and QDA

I know that every class has the same covariance matrix $\Sigma$ in linear discriminant analysis (LDA), and in quadratic discriminant analysis (QDA) they are different. When using gaussian mixture ...
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2answers
2k views

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 ...
3
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1answer
641 views

Is there a numerical solution to a mixture model of two normal distributions?

I'm building a mixture model with the two normal distributions $\mathcal{N}(\mu_1,\sigma_{1}^{2})$ and $\mathcal{N}(\mu_2,\sigma_{2}^{2})$. So, the density function is $$ f(x) = p_1 N(x; \mu_1, \...
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1answer
132 views

What is the link (discrepancy?) between these PDF/CDF and p-value distributions?

I have created a mixed distribution model comprising 80% $H_0$ plus 20% $H_1$ to illustrate the link between the expected proportions of true and false positives and negatives in the PDF, CDF and p-...
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2answers
282 views

Finding out if your data belongs to normal distribution

Is there a way to find out if your data belongs to one or more (mixture) normal distributions? I probably could calculate what is the standard deviation of my data, but I'm not sure what else to do ...
0
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1answer
647 views

Standard error of normalmixEM fit?

I fitted a mixture denstiy of two gaussians two my data. I now want to calculated the standard errors of the estimates via the boot.se command of the mixtools package. My question is now, if the ...
8
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2answers
2k views

Why only the mean value is used in (K-means) clustering method?

In clustering methods such as K-means, the euclidean distance is the metric to use. As a result, we only calculate the mean values within each cluster. And then adjustments are made on the elements ...
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2answers
1k views

Why Expectation Maximization is important for mixture models?

There are many literature emphasize Expectation Maximization method on mixture models (Mixture of Gaussian, Hidden Markov Model, etc.). Why EM is important? EM is just a way to do optimization and is ...
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2answers
794 views

Show that a scale mixtures of normals is a power exponential

I'm trying to show that a scale mixture of normals yields a Laplace distribution. I've gotten to the point where I have $\int N(0,\tau)\times Ga(\tau\:;\:1,\frac{\lambda^{2}}{2}) \:d\tau$ should equal ...
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1answer
6k views

Different covariance types for Gaussian Mixture Models

While trying Gaussian Mixture Models here, I found these 4 types of covariances. ...
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1answer
1k views

Skewness of a mixture density

I am fitting a gaussian mixture to financial data. My mixture density is given by: $f(l)=πϕ(l;μ_1,σ^2_1)+(1−π)ϕ(l;μ_2,σ_2^2)$ I calculated the skewness of the data already. Now, I want to look at ...
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2answers
460 views

Why are hidden Markov models (HMM) also called mixture models?

Why are hidden Markov models (HMM) called mixture models? What does it mix?
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1answer
2k views

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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1answer
247 views

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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1answer
10k views

Generate sample data from Gaussian mixture model [duplicate]

I am given the values for mean, co-variance, initial_weights for a mixture of Gaussian Models. Now how can I generate samples given those: In brief, I need a function like ...
7
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1answer
3k views

When to use LDA over GMM for clustering?

I have a dataset containing user activity with 168 dimensions, where I want to extract clusters using unsupervised learning. It is not obvious to me whether to use a topic modelling approach in Latent ...
5
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2answers
449 views

How to tell if a mixture of Gaussians will be multimodal

Suppose I have a mixture of Gaussians and I know the mean and variance of each separate Gaussian. How can I tell whether or not the resulting distribution will be multimodal or, more specifically, ...
4
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1answer
2k views

Mclust function of mclust package overfitting Gaussians

I'm using the Mclust function of the mclust package in R to fit a mixture of Gaussians model. My simulated data obviously has 3 ...
3
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1answer
641 views

Mixture of Gaussians on Log of Data

I am practicing Mixture of Gaussians and found the below dataset snoq, which is the precipitation amounts recorded at a US region, with ...
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0answers
45 views

Distribution of difference of Gaussian mixtures: symmetric wrto zero?

I have the following 3-variate random vector $(X,Y,Z)$ which is distributed as a Gaussian mixture: (with some abuse of notation) $$ f(X,Y,Z)=\underbrace{w_a \mathcal{N}(\mu_a, \Sigma_a)}_{\text{...
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1answer
185 views

Conditional mean for mixture of multivariate normal distributions

If x = (x_1,x_2,...,x_n) is a vector whose components have a distribution that is a finite mixture of multivariate normals, is the expected value of x_1 still a linear function of the other components,...
2
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1answer
747 views

GMM with Bayes decision model

Given two classes of training data (A and B), I want to fit each class' distribution using a GMM with k components, and then use Bayes Decision Model for the classification. The first step was to ...
2
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2answers
167 views

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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1answer
142 views

Mixture Model Distributions

I wonder, if there could be a Pareto Mixture Model, just like the Gaussian Mixture Model (GMM). How am I supposed to build a Pareto Mixture Model (PMM)?
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2answers
770 views

Comparing K-Means and Expectation Maximization on the dataset generated - When does K-Means perform better?

I was experimenting with K-Means and Gaussian Mixture Models (Expectation-Maximization) on the data set that I generated. Here is how the plot for two distributions looks like: Since this was ...
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1answer
551 views

How can I find mean and covariance after EM iteration on GMM algorithmm?

I have a dataset divided in 2 class(lets call x1,x2) but I don't know their mean and covariance. For each class I looked their graph and made a guess about their sub-classes, then run an EM(...
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0answers
9 views

Typo in the definition of Finite Mixed Model in Machine Learning a probabilistic Perspective

In subsection 25.2.1 it's stated, regarding finite mixture model: The usual representation (of a finite mixture model) is as follows: $p(x_i|z_i = k, \boldsymbol\theta) = p(x_i|\boldsymbol\...
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1answer
96 views

Does assumption of normality of each mixture components implies that each margins is normal

I just would like to understand some information about the joint normality and the margins. I read that the normal joint distribution almost always implies that the univariate margins are all normal. ...
0
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1answer
94 views

Three component mixture model for element concentration using mixtools in R

As an update to a previously posed question, Fitting a mixture distribution for two approximately normally distributed populations using mixtools in R , I have now fit a three component mixture ...
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1answer
116 views

Why is my Gaussian mixture plot reduced proportional in size compared to their univariate normal pdf

I have created a multiples Gaussian distributions using this codes in MATLAB: ...
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3answers
669 views

Area under peaks considering mixture of normal distributions [closed]

I have a question regarding fitting mixture of normal distribution. I have the following data: I identified three peaks and using mixtools package, I fitted ...