# Questions tagged [gaussian-mixture]

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

156 questions
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### Finite mixture models with bounded data

I am trying to fit a finite mixture model to a dependent variable which is bounded (practically) between -0.594 and 1 (theoretically, the latent variable is bounded between -Inf - 1). The data are ...
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### 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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### 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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### Convergence of k-means or EM on Mixture of Gaussians

There are many algorithms for learning mixture of Gaussians but typically k-means/EM is used in practice. My question is related to the performance of k-means/EM for MoG. Recently, I came across this ...
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### Fit Gaussian Mixture model directly to the mixture density

The core of the question is: Can I estimate the parameters of a gaussian mixture model (with EM or Dirichlet Process) from a mixture density directly, that is, without using data drawn from such ...
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### How to calculate BIC for multidimensional problem

Sorry for this question, but I am really not sure how to calculate BIC for my situation. My models are mixtures of normals with different number of components. Variances are equal for all components ...
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### Diffusion coefficient from double-normal probability density function

The spread of individuals of species is often described by so-called dispersal kernels. The main parameter of spread is then often the variance defined as the average squared movement distance of a ...
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### Why isn't a gaussian mixture prone to overfitting?

Consider a Gaussian mixture of 2 components and a dataset of size $N$. The EM algorithm use the data to estimate: the model parameters: the means $\mu_1, \mu_2$ (say the covariances matrices are ...
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### A better bayesian way of modelling autoregressive mixtures

I have a JAGS hierarchical model which includes a temporal sub-model for the primary vote share between four party groups (LNP, Labor, Green, and Other). For each day in the temporal model, the vote ...
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### Understanding short animation about Dirichlet Process Mixture Model

On the wikipedia page of Dirichlet Process, there is the following video. I don't get the point of the video. My first impression was that the video was showing the fitting of one-dimensional data ...
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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-...
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### Programming a mixture of a Gamma with a Normal distribution using R

I have some data x in R which seems to be a mixture of a Gamma and Normal distribution. Therefore I'd like to model this as a mixture model consisting of said distributions, but I don't know how to ...
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### Variance of mix of normals

Suppose we have $n$ random variables distributed normally with the same mean and different variances. Suppose we know these variances. Which will be the variance of the marginal distribution induced ...
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### Can a Gaussian mixture model be specified using a regression equation?

From: https://stats.stackexchange.com/a/236297/22199, I quote A mixture distribution combines different component distributions with weights that typically sum to one (or can be renormalized). A ...
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### Which cluster analysis for ordinal temporal data?

I would like to perform a cluster analysis but I’m not sure which is the best algorithm to apply to my data. My dataset is made of 200 cases (but the sample size can be enlarged). For each case, I ...
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### Entropy of a set of categorical variables

In the context of Expectation-Maximization, I would like to compute te entropy factor in order to get the value of the lower bound when the algorithm converged. This lower bound can be expressed as: ...
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### Expectation Maximization Gaussian Mixture Example

I am a biologist trying to understand expectation maximization for a mixture of two Gaussian distributions. I think I understand how to deal with the means of the two distributions, but I don't know ...
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### Particle Filter and Gaussian Mixture

Let an observation model be given as $f(y_t|x_t)$ - this pdf is assumed to be nontrivial (not normal, not linear). The observation model is assumed to be known. Despite there is a state evolution ...
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### Calculate number of standard deviations separating two multivariate Gaussians?

Given a set of multivariate Gaussian distributions (from fitting a Gaussian mixture model) I would like to be able to calculate the likelihood that a data point drawn from one Gaussian will improperly ...
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### How can I measure separability between different number of instance of one feature vector?

How can I measure separability between different number of instance of one feature vector? For example the main vector is V=[1 1 2 3 4 5 7 8 10 100 1000 99 999 54] ...
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### Should I add noise to my truth data before before training my classifier?

My task is to develop a system that will take in a series of measurements and return the probability that an object is a type 1, type 2,... type n. I will refer to the system I have to create as a ...
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### skew G-Jensen-Shannon divergence between multivariate gaussian calculation discrepancy

I'm trying to calculate the Jensen-Shannon divergence between two multivariate Gaussians. I found a closed-form expression both for the KL divergence and JS divergence between two Gaussians in this ...
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### Hidden Markov Model for classification

I have fitted a Gaussian mixture model to my data. This Gaussian mixture model is the combination of two Gaussian distributions. I call the first Gaussian distribution state 1 and the second Gaussian ...
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### Stopping criteria for gaussian mixture models

As I can read from the source code of scikit-learn, the stopping criteria for the iterative algorithm of Expectation Maximization (in my case applied to fitting Gaussian mixture models) is to put a ...
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### Does mixture of sigmoids make sense given the theories about mixture of bernoullis?

Mixture of bernoullis is the combination of bernoulli distributions, which can be illustrated by the sampling process of K bags of D coins, here is a quick tutorial about it https://cedar.buffalo.edu/~...
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### Determining number of components in mixtures of normal distributions with common mean

This is a pretty simple question, suppose we want to fit a mixture distribution of multivariate normals with common mean $$y_i \sim \sum_k \pi_k N(\mu, \Sigma_k)$$ What is the preferred approach for ...
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### Is there any background for constraining covariances on fitting GMM?

On clustering data using GMM model, I often see the option to constrain covariances of each clustered GMM. For example, http://scikit-learn.org/0.16/auto_examples/mixture/plot_gmm_classifier.html ...
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### Gaussian Mixture Model with labels in Python

I have data X and corresponding labels y and want to fit a Gaussian Mixture model to it. In Matlab, one has the option of specifying initial labels. I am trying to do the same in Python. This is what ...
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### Conditional sampling from a multivariate Gaussian Mixture

I am using scikit-learn to fit a gaussian mixture on a non-parametric multivariate distribution with three variables $\mathbf{X} = (X_1, X_2, X_3)$ I want to sample from that distribution given ...
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### Entropy of a mixture of Gaussians

I need to estimate as fast and accurately as possible the differential entropy of a mixture of $K$ multivariate Gaussians:  \mathcal{H}[q] = -\sum_{k=1}^K w_k \int q_k(\textbf{x}) \log \left[\sum_{...
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### Can the hidden states of a HMM be interpreted as number of clusters underlying the data?

Trying to understand the physical significance of the number of hidden states of a HMM. Should they be interpreted as number of clusters in the data? If not, why? Or they should be interpreted as the ...
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### MIxture model in R to generate noise in data

I have a bit of code in R that adds noise to an harmonic series according to a normal distribution: ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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
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### How to interpret profiles / mixture components without any observations classified to them (when using MCLUST in R)

I am using the MCLUST software in R to fit normal mixture models, as part of what in my field are commonly called Latent Profile Analysis. Some of the time, ...
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### Approximating a 3D spline surface by a weighted sum of gaussians

I have spatial data(2D) with some quantity associated with each point - basically 3D data. I want to model the quantity distribution in the space and then use N clusters as a compact representation. ...
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### how can I integrate probabilities from two GMMs?

Without going into the details of why exactly I must do this, I have four GMMs (two sets for two classes), and I need to integrate their predictions. Two of them are trained on two classes from ...