Questions tagged [gaussian-mixture]

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

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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. ...
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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 ...
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1answer
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. ...
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1answer
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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246 views

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 ...
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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 ...
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1answer
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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37 views

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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25 views

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-...
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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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1answer
686 views

General conditional distributions for multivariate Gaussian mixtures

My question is similar to this one but considers a more general situation. Suppose that $ \vec{x} = (x_1, \dots, x_d) $ and let $$ p(\vec{x}) = \sum_{k=1}^{n} \pi_k \mathcal{N}(\vec{x} | \mu_k, \...
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Sampling posterior of empty cluster in GMM and Gibbs

Consider performing inference via a standard Gibbs sampler for a standard Gaussian Mixture Model (GMM) with $k$ components that are Gaussians $$\mathcal{N}(\mu_{k}, \sigma^{2}_{k})$$ where we assume ...
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208 views

How does scikit-learn calculate a data point's probability of belong to normal distribution?

In GMM calculating, we need to calculate the probability of data point $X$ belong to the $kth$ Gaussian Distribution $\mathcal{N}(X_n|\mu_k,\Sigma_k)$. I have read How to calculate the probability of ...
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1answer
528 views

Anomaly detection on 1D data with multiple gaussian distributions

My core problem is to set a cutoff to my one dimension data between normal with abnormal. I think this is a 'anomaly detection' problem. My Data My data is one dimension, consists with below: (...
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51 views

A transformation from uniform random variable to Gaussian mixture

I am attempting to describe a prior_transform for a multivariate Gaussian mixture in order to estimate the evidence integral of that prior convolved with another likelihood distribution. This is ...
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1answer
229 views

Prior for covariance matrices in Gaussian Mixtures Model

I am looking to choose a prior that helps me avoid singularities (as mentioned in this answer) in the covariance matrices of a GMM model. The Jeffrey prior (or a simple improper prior) would be very ...
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1answer
215 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,...
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174 views

Meaning of Gaussian mixture model parameters

I came across this question from a tutorial: Suppose we have observations $x_1$ , $x_2$ , $\ldots$, $x_n$ of a continuous r.v. $X$ known to be drawn from a “mixture” of $k$ Gaussian distributions. ...
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1answer
554 views

Estimating truncation point in Gaussian mixture

I have data modeled as a mixture of two Gaussian distributions. The data is "clipped" i.e., there is data only for values greater than a threshold $t$, even though it is feasible for data to exist in ...
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66 views

Reducing the number of Gaussians in a Gaussian Mixture Model

I build a kernel density estimation (KDE) of Gaussian kernels. I have many samples, but the distribution is not too complicated. I think it should be possible to approximate the resulting KDE by a ...
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35 views

Multimodality of mixtures of more than two Normal distributions

Let $$\phi(x;\mu,\sigma) = \frac{1}{\sigma \sqrt{2\pi}} \exp \left(- \frac{(x-\mu)^2}{2\sigma^2}\right)$$ denote the Gaussian density function ($\sigma > 0$). Let $$f(x) = \sum_{i=1}^N p_i \...
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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 ...
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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 ...
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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) ...
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1answer
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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202 views

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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52 views

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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1answer
32 views

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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1answer
248 views

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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71 views

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 ...
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2answers
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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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2answers
223 views

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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1answer
88 views

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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2answers
1k views

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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1answer
567 views

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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1answer
7k 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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482 views

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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1answer
29 views

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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1answer
100 views

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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1answer
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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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1answer
31 views

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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1answer
498 views

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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1answer
492 views

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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3answers
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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?...
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1answer
789 views

Number of components for Gaussian mixture model?

I have a vector of numeric values. My hypothesis is that this vector is a mixture drawn from two Gaussian distributions (ie k = 2). However, it is possible that there is only one Gaussian underlying ...
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298 views

Using Gaussian Mixture Model for outlier detection

Can someone summarize how to use Gaussian Mixture Model for outlier detection purpose. I am more interested in a general method and not so much the mathematical aspects of GMM's