Questions tagged [gaussian-mixture-distribution]
A type of mixed distribution or model which assumes subpopulations follow Gaussian distributions.
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Bayesian MCMC and Only Updating Some Variables at a Time
I want to do Bayesian MCMC on a Gaussian Mixture Model. But, I want to update the means, weights, and covariance matrix for a single component separate from the others. Would there be the issue of ...
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EM-algorithm for spatial data
I am very new to Geostatistics (Modeling spatial data) and have some questions:
1- I found that in many literature, the spatial random field is divided into spatial bins. That is, suppose I am ...
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Testing for Gaussian Mixtures
Suppose I observe data from a univariate distribution $\mathcal{D}$ with zero mean, and unit variance. We know that either $\mathcal{D} = \mathcal{D}_0 = \mathcal{N}(0,1)$ is standard Gaussian or $\...
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Linear Regression with gaussian mixture prior
In linear regression, we assume that the output variable is Normally distributed, i.e., $p(y|\mathbf{x}, \mathbf{w}) = N (y | \mathbf{w}^T\mathbf{x}, \sigma^2_y)$. I want to assign a mixture of ...
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Can a Gaussian Process predict random events?
I know that we can use Gaussian processes effectively for function approximation and regression. However,suppose there is a sequence of points in time $S = \{s_1, s_2, \dots, s_n\}$, where $s_i$ can ...
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Closed Form Solution for MLE parameter defining Linear Combination of two multivariate normal distributions
I have one set of $n$ observations which can be described as a single vector sampled from a multivariate normal distribution of the following form:
$$
(1-\lambda)\mathbb{I}_n + \lambda \Sigma_{n}
$$
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What is the function space corresponding to the Gaussian-mixture parameter space?
If the parameter $\theta$ is Gaussian with mean $0$ and covariance matrix $\Sigma$, then the function $f(x;\theta)=x^T\theta$ is a Gaussian process indexed by $x$, which can be characterized by a mean ...
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GMM derivation for diagonal covariance matrices
I was trying to understand the derivation of M step in the EM algorithm for GMM. All the resources available consider only "full covariance" matrices. I wanted to implement GMM for "...
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Interpretation of $\sigma$ in Gaussian mixture
I have a distribution of a variable that was normalized with plt.hist and then fitted with a sum of gaussian curves $g_M = \displaystyle\sum_i\frac{w_i}{\sigma_i \...
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Under What Conditions Does a Gaussian Mixture Model (GMM) Have Maximum Entropy?
Introduction
I'm delving into Gaussian Mixture Models (GMMs) within unsupervised learning frameworks and am particularly interested in their statistical properties, with a focus on entropy. Entropy ...
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Expected Variance of EM Estimator in GMM with Respect to Observations
Title:
Variance of EM Estimator in GMM with Respect to Observations
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I'm estimating a parameter S from observations X and <...
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Multivariate mixture models with INLA: Relating CAR random effect to the MVN covariance matrix
For a research project I am trying to implement a multivariate mixture model on areal data using Integrated Nested Laplace Approximation (INLA). Let $y_{i,d}$ be a data point, where $i = 1, 2, \cdots, ...
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Online mixture inference; better alternatives than windowed EM?
I have an online Gaussian mixture estimation problem that I would appreciate some input on. To be more precise, I have a stream of scalar observations $x_1, x_2, \dotsc$ arriving over time which are ...
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Can I assume that this is a GMM?
I'm trying to find the MLE for the parameters of the following distribution:
$$f(x) = a \ \mathcal{N}(\mu_a, 1) + \beta \ \mathcal{N}(\mu_\beta, 1)$$
Taking the log likelihood of this complicates ...
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X and Y are correlated, errors in both X and Y but error variances unknown; How to predict X|Y or Y|X? Deming, bivariate gaussian ellipses, other?
Seeking relationships between two variable, both with random gaussian errors; ratio of error variances is unknown, no correlation of errors in X and Y, but another unknown variable Z (unmeasured) may ...
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