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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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Standard deviation in multimodal data

I have a dataset, 90% of observations are unimodal normal (with couple of outliers per feature), 10% are mixture of normals, components have the same standard deviations. Data contains outliers => ...
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15 views

What is the different between the set of all model parameters and the parameter vector of the nth component

I read many articles about mixture models. I read that the author called the model parameters as "a set of all model parameters", while they said "parameter vector for the n-th component". I wonder ...
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27 views

Mixture of $K$ components

Consider a random vector $$ X\equiv \begin{pmatrix} X_1\\ X_2\\ X_3 \end{pmatrix} $$ with pdf $$f(x)=\overbrace{\sum_{k=1}^ K \frac{1}{K} f_k(x)}^{\text{finite mixture}}$$ and $\forall k=1,...,K$ $...
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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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218 views

Inferring GMM parameters with Gibbs Sampling

On my book, "Machine Learning A Probabilistic Approach". It's stated that is straightforward to derive a Gibbs sampling algorithm to fit a mixture model, especially if we use conjugate priors. So ...
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33 views

GMM model of the joint distribution from multivariate marginals

I have two multivariate Gaussian variables $X \sim \mathcal{N}(\boldsymbol {\mu}_X \in \mathcal R^d,\boldsymbol {\Sigma}_X \in \mathcal R^{d \times d})$ and $Y \sim \mathcal{N}(\boldsymbol {\mu}_Y \...
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33 views

Concise way to visualize / compare many Gaussian mixtures

I have 5,000 samples drawn from each of approximately 50,000 distributions. I have good reason to expect most of them to be normally distributed, and I expect some of them to be multi-modal (mixture ...
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25 views

Imposing independence constraints in mixture modeling of correlated data?

For 1-D signals (spectra) or 2-D signals (images), is there a way to impose the constraint that the data within a group is uncorrelated? I am iteratively applying background correction model fitted to ...
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7 views

Guassian Mixture Classification: interpretating component x variable means matrix

The Guassian Mixture model output by mclust::Mclust() function has a $parameters$mean element which is a matrix with dimensions ...
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130 views

Output Size of Mixture Density Networks

I am working on a neural network in which the final output layer will be a Mixture Density Network (MDN), but am confused about the shape of the values that final layer should return. In the paper in ...
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115 views

Decompose/split a single multivariate gauss into random gaussian mixture

Say, there is a single $n$-dimensional multivariate Gaussian. $$Gauss_a(\mu_a,\Sigma_a) $$ $\mu_a$ is $1\times n$ vector and $\Sigma_a$ is $n\times n$ matrix. Is there any easy way to decompose/...
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67 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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84 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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238 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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210 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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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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100 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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33 views

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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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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103 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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225 views

Mixture modelling with skewed distributions

I am trying to find a R library that splits a distribution into a symmetric and asymmetric components. I have a distribution that I want to split into two components, one skewed and the other most ...
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98 views

Mixture model with covariance matrix with varying variances and equal covariances

In some illustrations of mixture models, the covariance matrix is structured to have varying variances and equal covariances between mixture components. For example, Pastor et al. (2007) (I'm sorry ...
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How to choose closer gaussian?

Suppose, I have two random number generators with normal distribution, which generated a number. How to decide, to which one it is most probably belong? Should I calculate probability density of each ...
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257 views

Multi dimensionnal Gaussian Mixture Model

I'm a little confused about the GMM. I need to make clusterization. Actually, I have four dimensions : speed in Km/H, mileAge in Km, acceleration in m/s^2 and braking in m/s(^2). Each of those ...
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906 views

Negative loss while training Gaussian Mixture Density Networks

In classification problems, the usual negative log-likelihood loss function $L(\theta)=\sum_{i=1}^N -\log(p(y_i|x_i,\theta))$ is always non-negative, since the $y_i$'s are discrete random variables ...
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118 views

Two variables in Multivariate Gaussian pdf

I have problem with computing multivariate gaussian probability density function(pdf) value. As I found the equation is, $$p(\textbf{x}|\mu, \Sigma) = \frac{1}{(2\pi )^{\frac{n}{2}} |\Sigma|^{\frac{1}...
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126 views

How to determine cluster on EM-Gaussian Mixture clustering with 2 or more variables

I'm trying to compute EM Gaussian Mixture clustering algorithm. As I found in Bishop(2009), it explained the algorithm. Which is we have E-step and M-step in the iteration process. And we could ...
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137 views

upper bound on number of components of GMM

I want to fit GMM to a data set with N data points in D dimensions. I am using the full GMM in MATLAB, i.e., each component has a complete covariance matrix (as opposed to diagonal covaraices which ...
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36 views

System of Gaussian equations

Let $N(x\ |\ \mu,\sigma^2)$ be the pdf of a normal random variable with mean $\mu$ and variance $\sigma^2$. Question: Given $n$ data points $(x_i,y_i)_{i=1,\dots,n}$, compute $\{w_i\}_i$,$\{\sigma_i^2\...
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268 views

Why is gradient used in Fisher Vectors?

My understanding of Fisher vectors can be described in the following manner: A GMM is trained on all data, which gives $p(X,\theta)$, then, for each image/video ($X_i$), the gradient of $p(X,\theta)$ ...
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140 views

Mixture Proposal Distributions

I have a target distribution $\mu$ which I would like to investigate using, for instance Metropolis-Hastings-Green (MHG). So, given a Gaussian prior, $\pi$, and a likelihood $L$ such that $\mu(dx) \...
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Given a pdf which is a mixture of Gaussians, how do I infer the position (mean), variance, and number of Gaussians?

I have the following data, which when plotted as a histogram, are a mixture of Gaussians: I would like to write an algorithm that would infer: (1) the number of "peaks" or normal distributions in ...
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662 views

Predicting intensity of Poisson process, given event data

I have a dataset of events: each row is an event, and each column is a feature. There are millions of events and several dozen features. The features are mostly numerical (a few are categorical and I ...
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304 views

How to explain the Gath-Geva algorithm for Gaussian mixture models intuitively?

I have used the Gath-Geva algorithm for my geophysical research. One of the reviewers responded that he does not understand the algorithm and asked for a flow chart. What should I do? I have explained ...
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213 views

mixture of Gaussians vs mixture of quadratic denominators (Cauchy)

It is known that mixture of Gaussians are dense in the set of all distribution functions. A 1-dimensional Gaussian has the following density: $$ \frac{1}{\sqrt{2\pi \sigma^2}} e^{-\frac{(\omega-\beta)^...
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125 views

How to calculate the value for a multivariate Gaussian

How to evaluate the value for a multivariate Gaussian. For instance, to evaluate the 20 dimensional Gaussian function value with respect to a 20 dimensional input vector x, I need calculate a 20 by 20 ...
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292 views

Is it possible to convert a Gaussian Mixture Model implementation into a Categorical Mixture Model?

I am modelling whether a customer will spend when given a voucher. I have a theory that a customer falls into one of two latent classes: call them spendthrift and miser. So I would like to fit a ...
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131 views

Question about prior in bayesian image processing

I am learning Bayesian image processing. Bayesian approach will take prior knowledge about image into account. From one material, it says knowledge is expressed via probability functions. I understand ...
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71 views

How to estimate a mixture of gaussians? [duplicate]

I have a set of points which I can fit a Gaussian model on them using Maximum likelihood estimation. but this estimation is weak and I want to improve it. I want to fit a mixture of Gaussian on these ...
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97 views

Chi-square approximation in homogeneity

I am interested in testing homogeneity in mixture of Gaussians (testing no mixture vs. 2 populations) given that we know the weights of the two distributions. We can first use MLE to estimate the mean ...
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424 views

Gaussian Mixture Model with Custom Distance Metric

I have some 1D data that I want to cluster using Mixture of Gaussian. However, the data "wraps around" at two extremes. Specifically, I have a list of angles from $-\pi$ to $\pi$ and the data near two ...
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248 views

Confirmatory latent variable cluster analysis with mplus

I would like to do a confirmatory latent class cluster analyses (finite mixtures) with a continuous and several categorical variables. I know how I can constrain binary variables (such as Cluster A ...
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1k views

How to pool more than two sample means and standard deviations?

I have 4 independent samples from one population, with their respective sample sizes, means and standard deviations. I don't have the raw data, and all of them follow gaussian distributions. Sample 1:...
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730 views

Novelty and Outlier Detection in Unsupervised Learning Style

Currently I am looking for some method to do novelty and outlier detection. I found some good example here using scikit-learn (Link1). However, it is based on supervised learning and I believe the ...
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258 views

Fitting a mixture model to spatially correlated data

When the data are spatially correlated, is the usual GMM likelihood function overweighted? The data. Scattering experiment, sensor is like a CCD. Can't see individual events, only density estimate ...
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130 views

To model an unknown bounded probability density function by a Gaussian mixture

I have points in dimension 10 coming from an unknown probability distribution. The nature of data strongly suggests that this distribution is bounded. But the boundaries are not precisely known and ...
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103 views

Simulating Gaussian Mixture signals

I am trying to simulate a signal produced from a GMM of 3 mixtures. Here's MATLAB code ...
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1k views

Fitting for a Poisson-Gaussian Mixture Distribution

First of all, I am rather new to statistics, so go easy on me. I am aware that the negative binomial distribution can be thought to arise as a result of letting the $\lambda$ parameter in a Poisson ...
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38 views

Test is data is derived from mixture or just noisy normal

Is there a way to quantify \ test \ describe how likely it is that high dimensional data come from a single Gaussian or a mixture of Gaussians (with different means \ SDs) or not? What I am thinking ...
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171 views

Too good results from EM for gaussian mixture

My task is to identify parameters (mean, standard deviation, height) of gaussian peaks in given histogram data with as lowest CV as possible. Number of peaks and approximate means are known (pointed ...