# Questions tagged [gaussian-mixture]

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

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113 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. ...
106 views

### Introduction to Gaussian mixture models

First of all, I am sorry if this question is not acceptable by some of the readers. However, I really read many, many sources about Gaussian mixture models, but all what I found was a short tutorial ...
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### Does the distribution of each mixture components have any information of the margins of the variables? [closed]

I just start working with Gaussian mixture models and I just confused about some information, which I really would like to make sure that I understand the model very well. A Gaussian mixture model ...
394 views

### Gaussian Mixture Model

with the following code I fit a Gaussian Mixture Model to arbitrarily created data. The code is working. The only thing I encounter is that during the calculation of the multivariate_normal I ...
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### Statistical test for comparing two-gaussian mixture

I have a distribution of shape sizes under two different (biological) conditions. From prior knowledge, I do expect there to be two populations. I fit each condition to a two-Gaussian mixture model. ...
151 views

### Gaussian mixture models with constrained mixing proportions

I am fitting a Gaussian mixture model to multivariate data and my application suggests constraining the mixing proportions to lie in a pre-determined sub-space. I am curious if such an approach has ...
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### fitting curve to my data and calculating fwhm

Hello and thank you in advance for your inputs. I am trying to find a model in R that will give me curves that fit my data. I am aiming for 2 peaks (i am thinking of normal distributions but might be ...
234 views

### Gaussian Bayesian Networks and covariance calculation

I have difficulties in understanding the way of calculation of covariance matrix in Gaussian Bayesian Nets (from conditional to joint): The last formula is about to calculates covariance between ...
273 views

### Doesn't the non-Gaussian source assumption of ICA render it practically useless?

Gaussian distributions appear everywhere in nature, indeed this was largely the justification for most classical methods' reliance on assumption of normality. ICA assumes non-Gaussian sources, indeed ...
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### Possible statistical tests to separate two distributions within a dataset

I have a dataset that contains a range of values. I have created a frequency distribution of the values, and have included the plot below. To my untrained eye, it appears that the frequency ...
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### In a normal mixture model, what general happens if the number of groups to be summed far exceeds the dimensions of each normal?

Suppose that we have a mixture model: $$p_\theta(y) = \sum_{k = 1}^{K}w_k \phi(y;\mu_k, \sigma^2_kI_d)$$ where $\phi(y;\mu_k, \sigma^2_k)$ is the normal density at $y$ with mean vector $\mu$ and d-...
754 views

### Correct number of components in GMM according to BIC and AIC plots

I have applied GMM(Gaussian Mixture Model) to my data set and I have plotted the resulting BIC(Bayesian Information Criterion) and AIC(Akaike Information Criterion) for different number of components. ...
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### Interpretation of plots for outlier detection in healthcare

Christy et al. propose cluster-based approach to outlier detection as part of the preprocessing step. However, I don't think the plots are very interpretable. The authors use the R mclustbic function ...
81 views

### how to model hourly wind speed data

I am trying to forecast hourly wind speed (HWS) data in Trinidad and Tobago and I have read in the literature that "Direct application of stochastic models (ARMA & ARIMA models) to HWS series is ...
219 views

### Number of parameters mixture model

In order to do a LRT between two mixture models with different numbers of components, I need to know the number of parameters. I would like to know the answer both for: a) Gaussian mixture model b) ...
376 views

### GMM EM algorithm complexity per iteration

I was fitting GMM clusters with diagonal covariance on my data using EM with $n$ (=5e6) points, each having $m$ (=160) ...
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### JAGS mixture models with exogenous regressors

This is my first post,I hope this is the right forum for such a question and I formulate it correctly. I am working with a time series data set where the response y seems to follow a mixture of two ...
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### Mean and variance of a vector $W = (X', Y')'$

$(X_i,Y_i)$, $i = 1,2, ... ,n$, is a random sample from a bivariate normal distribution, with means $\mu_x$ and $\mu_y$, variances $\sigma_x$ and $\sigma_y$, and correlation $\rho$. How do I formally ...
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### Mixture modelling of data with measurement uncertainty

I have a dataset that consists of a population radiometric ages (300>n>600). A dataset can have ages can range on the order of billions of years. Each age measurement has an associated uncertainty ...
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### For Multivariate Gaussian Mixture Models, What will happen if all mixing probabilities are equal? [closed]

$$p(\boldsymbol{x}) =\sum_{k=1}^K \pi_k \mathcal{N}(\boldsymbol{x}|\boldsymbol{\mu}_k, \boldsymbol{\Sigma}_k)$$ This is the formula for MGMM, where $\pi_k$ is the mixing probability. I am very ...
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### Gaussian Mixture Division

In the study of probabilistic graphical models (PGMs), the loopy belief update propagation (LBUP) message passing algorithm requires the division of unnormalised probability distributions. If the ...
2k views

### How to extract components of Gaussian mixture?

I'm trying to model a dataset as a mixture of two Gaussian distributions in MATLAB and find the Bhattacharyya distance between the two. Using MATLAB's fitgmdist ...
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### This is Gaussian mixture model?

Here is a problem that I am looking at. Is this model really commonly known as a Gaussian mixture model (the one often appears as an illustration of EM algorithm)? I am confused because Gaussian ...
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### Finding a Dominant Cluster

Super-basic question here: I'm looking for a way to find the dominant cluster of a set of clusters (as in the first image): This is not what I get when I run a Gaussian Mixture model with one ...
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### Mixed data in Gaussian Mixture Models

Is it possible to use a dataset with mixed variables such as continuous, ordered, and categorical variables and cluster the data using the Gaussian Mixed Model with EM algorithm. I cannot find ...
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### Difference between class conditional distribution and likelihood in the context of Mixture of Gaussians?

I am reading some Mahchine learning lecture notes, and the writer is introducing Maximum Likelihood (ML) method of parameter estimation of $\theta$ as $\text{argmax}_{\theta}Pr_{\theta}(x|H)$ where $H$...
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### 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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### Different covariance types for Gaussian Mixture Models

While trying Gaussian Mixture Models here, I found these 4 types of covariances. ...
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### Why use EM algorithm instead of just plain old ML for mixture model?

Let's say I have some [multivariate] data and want to fit a GMM to it. So I have $P_x=\sum_{i=1}^{n}\alpha_i{N(x;\theta_i)}$, where $x$ is an observation from the data, $\theta_i$ is the mean and ...
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### Any trick to swap order of determinant and matrix inverse operation?

Been thinking through fitting a kind of Gaussian mixture model in more of a neural network style (kind of similar to RNADE or RMADE by Larochelle, without going into details) and see that this could ...
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### How to match sample points to a probabilistic model?

This might be a trivial question I have a probabilistic model, say a Gaussian mixture model of known parameters, and with that I have a set of defined sample points. I would like to know how likely ...
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### Is it a known phenomenon for the variance of a component (GMM) to increase without stopping?

I know it can happen for it to decrease dramatically as it overfits on a single datapoint. But I've never read about a component "taking everything over". See the following images (circles are stddevs)...
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### How to prevent the creation of redundant mixtures while training a GMM?

I'm currently trying to train a GMM(UBM) with 1024 Gaussian mixtures for speaker verification. However, after training the GMM, it appears that some mixtures are useless/redundant. (little to no ...
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### Very steep decrease in information criteria for mixture models with more components

I am analyzing data using mixture modeling. When I plot the information criteria (the BIC) for a series of models (with different model specifications and different number of mixture components), I ...
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### Fitting Gaussian mixture models with dirac delta functions

I was told that using gradient methods for Gaussian mixture models may end up with Dirac delta function(s). I hadn't thought of this problem before, but when I verify this, it does seem to be a ...
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### Gaussian Mixture Model - marginal likelihood

I am studying gaussian mixture models. The first step defines the following equation. They then proceed to marginalize $z_n$ out My question is, how did they arrive at that equation ? Where did the ...
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### What's the difference between Multivariate Gaussian and Mixture of Gaussians?

What's the difference between Multivariate Gaussian and Mixture of Gaussians? If I have a Multivariate Gaussian and making all the data into ONE vector, is that a Mixture of Gaussians in 1 dimension?...