# Questions tagged [gaussian-mixture]

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

163 questions
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### Universal Approximation Capabilities of Mixture Models

I am looking for two reference incl. proofs showing 1) that a discrete Mixture of Gaussians can asymptotically approximate any (well behaved) continuous density 2) that a discrete Mixture of ...
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### Check on intuition behind infinite mixture models for clustering

I'm trying to better understand the intuition and practical application of infinite mixture models (Dirichlet Process) and finite mixture models. For example, say I have a data set on which I run a ...
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### Estimate Gaussian (mixture) density from a set of weighted samples

I am trying to find if there exists a way to find the spatial distribution over a set of points where the points are weighted. If I have "n" points in the (x,y) space, I can fit a mixture of Gaussians ...
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### Gaussian clusters and original distributions

In Gaussian clustering (i.e. General Mixture Models) we model the data with some clusters. For example, in the below figure, we have two clusters $C_1, C_2$, each of which are modeled with a Gaussian (...
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### What is the assumption on the distribution of data in gaussian mixture models?

I am reading about Gaussian mixture models from this slide https://www.ics.uci.edu/~smyth/courses/cs274/notes/EMnotes.pdf However, I am super confused at the very first line. It says: We ...
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### Latent variable in Gaussian Mixture Model

Whenever I look up material pertaining to Gaussian Mixture Models, it always mentions latent variable $z$, where $z \in \{1, ..., K\}$ and is one-hot encoded. I completely understand the objective of ...
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### 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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### 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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### 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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### 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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### How to interpret a GMM and a predict_GMM output

I would like to do outlier detection in a dataset by using e Mixture Model. I'm using the R functions GMM and predict_GMM but I can't understand which is the outlier factor and how to indentify ...
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### Calculating BIC for sklearn.mixture BayesianGaussianMixture

The GaussianMixture function easily allows calculation of BIC. In the source code it is defined as: ...
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### How to select the best Baysian GMM with Dirichlet process

I am very new to GMM models and currently trying to make a unsupervised clustering on data. The data has 34 features (dimension). I am thinking of using GMM with Dirichlet process and trying to code ...
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### 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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### 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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### 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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### 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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### 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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### Why did log-likelihood decrease in EM in this step-by-step example?

I'm using Expectation Maximization algorithm to determine the parameters of Gaussian distributions in a mixture. To get a better understanding of the algorithm, I executed it manually step by step on ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### How to make the most of a Gaussian mixture assumption in a model?

I have a dataset with 100 columns and approximately 100000 lines. I have a variable to predict that is Y (0,1 so it's a classification problem). I have an other categorical variable with two values ...
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### Approximating a binomial distribution with a mixture normal

This is purely a theoretical question (I legitimately can't think of a real application), but if you wanted to approximate a binomial distributed variable with a two-component mixture normal, is there ...
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### How to use Gaussian mixture model for multivariate pattern classification

I am new to statistical pattern recognition and trying to learn.To begin with I am trying to work with two class problems and trying to classify motion activities as mentioned in the paper "Object ...