Questions tagged [gaussian-mixture-distribution]

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

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Gaussian mixture model parameter updates derivation?

I've been following a helpful tutorial and I'm trying to understand the parameter updates. For example, the mu_k parameter update is below. I'm unsure why the sum(Bk) does not cancel out as it's in ...
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Gaussian Mixture Model Clustering - cluster means are assigned to a different cluster

I ran a gaussian mixture model with 7 clusters on my data. My data has been PCA transformed with 200 components. Then I extracted the means of each cluster and applied the predict_proba function on ...
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Variance when sampling from a GMM? [duplicate]

I am doing some work with Gaussian mixture models and we want to find the standard deviation of samples from the model. Our current methodology is to run a Monte-Carlo sim, and just take a bunch of ...
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172 views

Mixture of normal distributions, all with the same variance and with normally distributed means

Say you have a mixture distribution with the following properties: It is made up of multiple normal distributions The variances of all those component normal distributions are all the same The means ...
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30 views

Ponderate two gaussian mixture

I have 2 independent random variables $X$ and $Y$ with gaussian mixture distribution like: $$f(x) = \sum_{i=1}^{m} \phi_{X,i} \mathcal{N}(\mu_{X,i} , \sigma_{X,i}^{2})$$ $$f(y) = \sum_{i=1}^{m} \phi_{...
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expectation of normal mixture density by given cut off point

I am self-study multivariate statistics with book "A First Course in Multivariate Statistics", I don't know how to solve the problem from section 2.8 of exercise 11 which states that: consider a ...
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429 views

Comparing 2 mixture models using mixtools

I have 2 mixture models I'd like to compare. Specifically, I want to compare lamda (i.e. proportion/area under each distribution) as it looks like there are differences there. Is this possible? ...
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83 views

Marginal distributions of a mixture of two Gaussian distributions

In the Mathematics for Machine Learning book (Section 6.4), the author introduces a mixture of two Gaussian distributions as $$0.4 \mathcal{N}\Bigg(\begin{bmatrix}10 \\ 2\end{bmatrix}, \begin{...
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274 views

Feature importance for Gaussian Mixture Model

After GMM clustering I've got quite logical clusterization and the question is how can measure the importance of the exact feature in clustering.
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37 views

Determining Link for GLM

I am having a great deal of difficulty understanding how to use the Generalized linear model for my data set. The response variable of interest is hatch success of sea turtles, which is a %. The ...
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What is the difference between the latent variable and the cluster weights in mixture models?

$p(x|\theta) = w_1 \mathcal{N}(x|\mu_1,\,\sigma_1^{2})\ + w_2 \mathcal{N}(x|\mu_2,\,\sigma_2^{2}) + w_3 \mathcal{N}(x|\mu_3,\,\sigma_3^{2})\,$ What is the difference between the the $w$ and the ...
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224 views

Gibbs Sampler for GMM

In Rasmussen's paper it is introduced a Gibbs sampler to make inference about a standard Gaussian Mixture Model. To simplify, assume the 1-d case with basic hierarchical structure, that is: $x_i|...
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latent variables in EM algorithm are assumed to be i.i.d from multinomial distribution, from what they are idependent

In EM algorithm we introduce a latent variables, say $z_i$, $i=1,...n$, $n$ is the number of the mixture component. These variables ($z_i$) are assumed to be independent and identically distributed ...
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How to 'normalize' the product of two variables from Gaussian distribution?

I have two variables, x1 and x2, which are sampled from two Gaussian distributions respectively. I created an iteraction term x3 which is x1 multiply x2. Not surprisingly, x3 has very fat tail, ie., ...
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41 views

What does it means for “fit a less parsimonious model” in a clustering algorithm?

I'm now trying to implement the algorithm presented in https://www.stat.washington.edu/raftery/Research/PDF/fraley2005.pdf. The algorithm is the following one: First I get a mixture model for ...
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Redefining latent variables as observed data

This was just a thought that occurred to me, but technically, is it possible to redefine what I treat as latent variables and what I treat as data? For example, lets assume I have a set of latent ...
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182 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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131 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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37 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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155 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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296 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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132 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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420 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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144 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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143 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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172 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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38 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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290 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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202 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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70 views

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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703 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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366 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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151 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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424 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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204 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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78 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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102 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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571 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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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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748 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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323 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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141 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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116 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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179 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 ...
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402 views

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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296 views

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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2k views

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 ...
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694 views

How to decide whether the distribution is unimodal or bimodal in grain size distribution?

In the examples given at this link, I am not able to decide whether the distribution is unimodal or bimodal. I think it is in between unimodal and bimodal, but I do not know if this kind of class ...

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