Questions tagged [gaussian-mixture]

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

438 questions
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can I fit a GMM over probability distributions?

We have been using a GMM to fit gaussians over a set of ~ 3M vectors. Now the input are not vectors but probability distributions (coming from a topic model like LDA). Is it still mathematically ...
391 views

How to fit a gaussian mixture model in R with fixed parameters

I am using R to analyse experimental, two dimensional data via gaussian mixture modeling with the mclust package in order to find the mean of each component. I ...
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Gaussian Mixture description

Looking at this link on Gaussian Mixtures and EM: http://www.ics.uci.edu/~smyth/courses/cs274/notes/EMnotes.pdf from the link: Given a data set D = {$x_1, x_N$} where $x_i$ is a d-dimesional vector. ...
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Generate sample data from Gaussian mixture model [duplicate]

I am given the values for mean, co-variance, initial_weights for a mixture of Gaussian Models. Now how can I generate samples given those: In brief, I need a function like ...
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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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How to use Bayes' Theorem to detect an event in a noisy signal

I'm trying to use Bayes' Theorem to solve a question that's come up in work, but I don't know if I've done it correctly, because the result seems a bit strange. The problem involves a stochastic ...
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Mclust model selection

The R package mclust uses BIC as a criteria for cluster model selection. From my understanding, a model with the lowest BIC should be selected over other models (if ...
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doubt regarding the gaussian mixture model definition

With reference to the following definition of GMM (see snapshot from Reynolds (1)), I have two doubts: In the definition of probability density, the covariance matrix (denoted by sigma) is ...
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anomaly detection with gaussian mixture models

I am new to the topic, and I am trying to understand how it is possible to perform anomaly detection by using gaussian mixture models. Could you please give me some hints about literature on the topic?...
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What is “mixture” in a gaussian mixture model

We often study Gaussian Mixture model as a useful model in machine learning and its applications. What is the physical significance of this "Mixture"? Is it used because a Gaussian Mixture Model ...
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Gaussian Mixture Modeling - Determining More Than One Component

Let us follow the convention that a lower information criteria score is considered better. Suppose we have a ground-truth Gaussian mixture model (GMM) with $k$ components. Suppose also that we (1) ...
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How to derive the MLE of a Gaussian mixture distribution

In my self-study, I consider a Gaussian mixture distribution: $$p(x)= p(k=1) N(x|\mu_1,\sigma^2_1) + p(k=0) N(x|\mu_0,\sigma^2_0)$$ where $p(k=1)+p(k=0)=\pi_1+\pi_0=1$. I am now asked to do three ...
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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 ...
3k views

How to use Kullback-leibler divergence if mean and standard deviation of of two Gaussian Distribution is provided?

With Apache Spark MLLib library I am trying to find Clusters within a dataset by using Gaussian Mixture Model (number cluster =3) . Now it returns 3 different values of mean and standard deviation. 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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Decomposition of multimodal distributions

I have decomposed a multimodal distribution into the constituent single distributions for for further analysis. I have spent some time researching various approaches and I have not found one that that ...
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Bayesian Networks - CPD representation and inference for non-Gaussian continuous variables

I'm trying to implement an approximate inference algorithm based on junction tree algorithm for a Bayesian Network that has continuous variables which happen to have non-linear relationships, and in ...
202 views

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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The number of parameters in Gaussian mixture model

I have D-dimensional data with K components. How many parameters if I use a model with full covariance matrices? and How many if I use diaogonal covariance matrices?
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Mixture Model Distributions

I wonder, if there could be a Pareto Mixture Model, just like the Gaussian Mixture Model (GMM). How am I supposed to build a Pareto Mixture Model (PMM)?
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incremental gaussian mixture model [closed]

I have trained GMM on small train data set, I would like to update the GMM parameters on the fly when new samples arrive. Please direct on how to do that? Please inform if some existing implementation ...
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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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upper limit on number of clusters in GMM

I am using Gaussian Mixture Models (GMM) to fit a small data set with ~60 observations and 4 dimensions. This data was generated from the raw data with 14 dimensions after retaining principal ...
436 views

When using a Gaussian Mixture Model GMM, is it possible at all to infer the number of clusters to use?

When using a gaussian mixture model, you usually need to specify the number the number of clusters in the data. However, are there methods whereby you could infer the number of clusters to use, given ...
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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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QDA vs EM with Gaussian likelihoods

QDA (quadratic discriminant analysis) assumes that the K different classes are generated by K different multivariate Gaussians, each with potentially different mean vector and covariance matrix. If ...
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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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Mix of n normals with known locations

I have data points that are generated with the $n$ normal distributions with the same $\sigma$ and different means. I do not know $n$, but I know that $1 \leq n \leq 4$. I know the possible set of ...
556 views

Defining overlapping periods

I have a dataset containing the abundance of migrating bird species. In the figure below you can see that there are two "bell" shapes that are overlapping somewhere around September. One of the bell ...
113 views

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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How to evaluate multiple density estimations in one space?

Let's say we have several users, each represented by a set of document vectors in $\mathbb{R}^n$. We fit the generative distributions using one Gaussian mixture model for each user. The goal is to use ...
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Significant difference between time series - Can I do this?

I'd like to know whether the solution proposed below is valid/acceptable and any justification available. We have two biological conditions, and for each condition we measured 3 time series, so at ...