Questions tagged [gaussian-mixture]

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

Filter by
Sorted by
Tagged with
1
vote
0answers
14 views

Bayesian Gaussian Mixture Models | Model selection & Selecting the number of active components [closed]

I have generated 2 groups of 1-D data points which are visually clearly separable and I want to use a Bayesian Gaussian Mixture Model (BGMM) to ideally recover 2 clusters. Since BGMMs maximize a lower ...
0
votes
0answers
12 views

Cutoff for a poisson-gaussian mixture model

I have count data that is bounded on one side at zero (see image). It is bimodal and I think it results from two different processes. I would like to fit a poisson distribution around the hump around ...
1
vote
1answer
16 views

Estimating weights of known component distributions in a mixture distribution

Given $n$ probability density functions ($p_1$, ..., $p_n$) with known distributions, what are the ways of estimating the weights ($w_1$, ..., $w_n$) of these component distributions given a sample ...
1
vote
0answers
74 views

what are the main differences between parametric and non-parametric machine learning algorithms?

I am interested in parametric and non-parametric machine learning algorithms, their advantages and disadvantages and also their main differences regarding computational complexities. In particular I ...
0
votes
0answers
8 views

How to parameterize variational Dirichlet distribution

I am learning about variational inference and am implementing a couple of things from scratch. I am trying to build a Gaussian mixture model where the prior on the mixture component selection is a ...
0
votes
1answer
12 views

Vatiational inference in GMM

I am learning about VI and am implementing a GMM model for clustering using variational inference. However, my implementation is not fitting the data at all, even when initializing the cluster means ...
0
votes
0answers
13 views

Gaussian mixture model for image labelling task

I'm trying to solve an image labelling task by using Gaussian Mixture Models. The total number of classes in my dataset is 9, each representing a different variety of vegetable (Class1, Class2, Class3)...
0
votes
0answers
16 views

GMM for nonlinear mean

In conventional GMM, observations $\mathbf{X} = \left\lbrace \mathbf{x}_1,\mathbf{x}_2,\ldots\right\rbrace$ are draw from a distribution $$ \mathbf{x}_n \sim \sum_{k=1}^{K}\pi_k\mathcal{N}\left( \...
0
votes
0answers
30 views

Fitting mixture model of Gaussians and uniform distributions to real data

I have times series of wind direction and velocity. For now, I leave aside the velocity and focus on the distribution of wind directions. Over there, there is usually three main wind directions, and ...
4
votes
1answer
212 views

What is the marginal posterior distribution?

Based on this question: How to build a Bayesian regression model of a response that is a Gaussian mixture Consider the mixture of normal, $$y_j\sim (N(0,\sigma_1))^{\pi}(N(0, \sigma_2))^{1-\pi}, j=1,...
2
votes
0answers
20 views

Confusion about two Gaussian distributions

From here, it says that, linear combination of two Gaussian distribution, are always Gaussians. However, Let 𝑋 be standard normal and 𝜀=±1 with probability 1/2 each, independently of 𝑋. Let 𝑌=𝜀𝑋...
0
votes
0answers
28 views

What is the nature of $r_i^t$?

Using Expectation Maximization (EM) algorithm, I want to vary the number of clusters used according to $K = [2,4, ... 50]$ for a normal distribution initialized randomly (...
2
votes
0answers
24 views

How does maximising ELBO for a Gaussian mixture model fit the model to data?

I am following along in Bishop's Pattern Recognition and ML chapters 9 and 10, and I understand that the EM algorithm works by iteratively updating model parameters using equations derived from ...
0
votes
0answers
7 views

Estimating the means in an equal mixture of two Gaussians with known variance 1

Consider data from an equal mixture of two Gaussians with variance 1: $X \sim 1/2 \mathcal{N}(\mu_1, 1) + 1/2 \mathcal{N}(\mu_2, 1)$. The means can be estimated with an EM algorithm, but is there ...
0
votes
0answers
18 views

gaussian mixture model bic using simulated data

I'm trying to generate data for a Gaussian Simulation model, and then test if mclustBIC (mclust package) can correctly suggest the number of components. There are three methods of generating data: ...
1
vote
0answers
14 views

Does Label Switching of Mixture model impact the inference of the whole mixture

I have a mixture of experts with multivariate normal as experts. Those multivariate normals all have diagonal variance covariance. I tried to estimate those parameters in Bayesian way. But the Gibbs ...
0
votes
0answers
9 views

Finding posterior probabilities on GMM

I was searching for how to properly implement GMM in a Bayesian setting, and I have read in a PyMC3 example the following: Marginalizing [the categorical labels] out of the model generally leads to ...
3
votes
1answer
61 views

Bayesian mixture model joint posterior

I am just starting to learn about bayesian mixture models. There is a few clarifications that I want to make which I am not sure myself. The graphical model below describes a gaussian mixture model ...
0
votes
0answers
14 views

Why does the smallest eigenvalue of the covariance matrix of a GMM equal the common variance?

I've been reading a paper "Introduction to Tensor Decompositions and Their Applications in Machine Learning". In it, the author describes an algorithm for estimating the means of the ...
1
vote
0answers
24 views

What distribution best describes multiple, sequential normal distributions: What is the sum of more than two normal distributions?

I am curious as to what describes the following distribution. If we were to record some data which are all from a normal distribution, but the standard-deviation changes for blocks of points recorded. ...
4
votes
1answer
63 views

Given two normal populations,, classifying a given data point

I have two normal populations S1 and S2, where S1 ~ N (μ1, σ1) and S2 ~ N (μ2, σ2) respectively. The populations are independent of each other and a data point X has to be either from S1 or from S2. ...
0
votes
1answer
45 views

Derive cauchy distribution as a scale mixture of normal distributions

I doing Bayesian modelling these days. I found that cauchy distribution can be written as a scale mixture of normal based on following source. Link So I started to derive this. Somehow, I am not ...
0
votes
0answers
16 views

Probabilistic generative models for clustering and classification

I have a question regarding the probabilistic setting of clustering and classification. More specifically regarding Gaussian Mixture Models and probabilistic generative models for classification. In ...
1
vote
1answer
36 views

Is 0 the unique center for the mixture density of $N(-a,\sigma^2)$ and $N(a,\sigma^2)$, each with weight 0.5? [duplicate]

Suppose $f_{-a}(x)$ is the pdf for $N(-a,\sigma^2)$ and $f_{a}(x)$ is the pdf for $N(a,\sigma^2)$. Let $f(x)=0.5f_{-a}(x)+0.5f_{a}(x)$ be the mixture density. Is $c=0$ the unique center for $f(x)$ in ...
11
votes
4answers
1k views

In cluster analysis, how does Gaussian mixture model differ from K Means when we know the clusters are spherical?

I understand how main difference between K-mean and Gaussian mixture model (GMM) is that K-Mean only detects spherical clusters and GMM can adjust its self to elliptic shape cluster. However, how do ...
1
vote
1answer
59 views

How to get number of iterations in EM-algorithm using R mclust gaussian mixture model

I am clustering data using the mclust function from the R mclust package. I am struggling to get the number of iterations the EM ...
1
vote
1answer
109 views

Bayes' theorem in Gaussian mixture model for $p(z_i = k | x_i, \mu_k,\Sigma_k)$

Given the $k$th Gaussian distribution $N \sim (\mu_k, \Sigma_k)$, the probability that $x_i$ generated from this Gaussian $k$ can be found via Bayes' rule $$\begin{align}p(z_i = k | x_i,\mu_k, \...
0
votes
1answer
28 views

Gaussian Mixture Model $p(x_i | z_i = k)$ a likelihood or probability?

In Gaussian Mixture models, the probability of observing the data $x$ given that it was generated from $M$ gaussian models is given by the following equation $$p(x) = \sum_{k=1}^m p(x|z=k)p(z = k)$$ ...
0
votes
1answer
54 views

Probability Density Function and Maximum Likelihood Estimation for Multinomial Logistic Regression and GMM

I have some confusion about a few very basic concepts and terminology. Let's assume we have two models for classification, a multinomial logistic regression (MLR) model and a GMM classifier. I'm not ...
0
votes
0answers
28 views

Derivation of maximum likelihood estimation of Gaussian mixture model

I want to derive the following formula. The meaning of each expression is as follows It's easy to solve with Kronecker's delta.
0
votes
0answers
49 views

Confidence intervals for mixture of Gaussian distributions

I have a mixture distribution of 2 Gaussians. Here, the left has a weight of 0.1 and the right has a weight of 0.9. In this example, they have identical $\sigma$, but that may not always be the case....
0
votes
1answer
74 views

Order and interpretation of Gaussian Mixture Model with strong overlap between components

Most examples for Gaussian Mixture Models (GMMs) employ datasets with fairly obvious underlying structure (well-separated clusters). How should one determine the order of a GMM (and interpret the ...
0
votes
0answers
12 views

How to obtain equation for evidence given equation for joint density of latent and observed variables (Variational Inference)

I am working through the following review paper: https://arxiv.org/pdf/1601.00670.pdf and would like to gain some insight into arriving at the formulae for joint density of latent and observed ...
0
votes
0answers
24 views

Mixture model for decomposing bimodal or multimodal distributions

The gaussian mixture model (GMM) is fed mixture components or features whose time series each have differing means and variances from one another, but are unimodal (have one mode) with each component ...
3
votes
1answer
253 views

Meaning of Gaussian mixture weights?

other posts with similar title do not actually ask what's in their title, so I ask here: What is the meaning of the weights in the Gaussian Mixture Model (GMM)? Does the GMM weight more heavily to ...
2
votes
1answer
109 views

Can a Gaussian Mixture model be fit with a continuous response variable?

Does the Gaussian Mixture model require binary and multiclass response/target variable (classification), or can the target vector consist of all real numbers (continuous variable, regression)? Why is ...
0
votes
0answers
11 views

Can Gaussian mixture models help an algorithm target a specific cluster?

In the chart below is a Gaussian Mixture model (GMM) based on three time series or datasets that the model was able to easily cluster into three different colored classes. Class 1 is the blue ellipse ...
0
votes
2answers
73 views

Probability or likelihood under normal distribution(s)?

I've modeled my data with a mixture model of two gaussians centered at approximately 0.33 and 0.5, respectively. Now I want to "assign" a probability to each data point that it belongs to ...
0
votes
0answers
22 views

Noise learning in GMM

The Gaussian mixture model is a parametric model that learns the underlying distribution of data. If data contains the noisy attributes and noisy samples then will the model learn that noisy data too ...
1
vote
1answer
137 views

Calculate log likelihood of mixture of gaussians “by hand” in R

I'm trying to ensure the the method of calculating log likelihood for a model produced using mixtools vs a model produced using MLE estimates of mu and sigma are the same. The best way I can think of ...
4
votes
1answer
241 views

Derivation of M step for Gaussian mixture model

Summary So to summarize my question, how can I take \begin{align} = \sum_{i=1}^{n}W_{i1} \left(log (1-\sum_{j=2}^{K}\pi_j) -\frac{1}{2} log(|\Sigma_1|) -\frac{d}{2} log(2\pi) -\frac{1}{2}(x_i-\mu_1)^{...
0
votes
0answers
26 views

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 ...
0
votes
0answers
14 views

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 ...
0
votes
0answers
11 views

Are there any advantages of k-means over Gaussian Mixture (Expectation minimization)?

In other words, if I already included Gaussian mixture into the analysis, does it make sense to add also k-means, as GM clustering is a generalization of k-means?
0
votes
0answers
4 views

Id+s this kind of data (picture) suitable for gaussian mixture models)?

I have a dataset with two features A and B. I was wondering if this kind of data is suitable for GMM since distributions don't follow exact gaussian. As you can each feature has two or more "...
2
votes
1answer
211 views

Difference Between Latent Class Analysis and Mixture Models

I have been trying to look into latent class analysis and don't exactly understand what it is. Is it basically the expectation maximization using and analyzing the classes formed? The resources on the ...
1
vote
1answer
52 views

Understanding Loss functions in Stacked Capsule Autoencoders

I was reading Stacked Capsule Autoencoder paper published by Geoff Hinton's group last year in NIPS. While reading section 2.1 about constellation autoencoders I couldn't understand how the expression ...
0
votes
2answers
38 views

Derivation of gaussian mixture models assuming that hidden variable is known

I saw the following notes from CS229 (screenshotted below). I am confused how the two equations are equivalent. How were they able to distribute the $log$ inside the summation? I don't see how knowing ...
0
votes
0answers
72 views

How does scikit-learn handle high dimensionality in its Gaussian Mixture Model implementation?

I have a dataset of 50,000 rows that I plan to fit with scikit-learn's GMM model. The dataset has 15 features, therefore I treat each row as a vector in the space $\mathbb{R}^{15}$. My question is, ...
0
votes
0answers
16 views

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 ...

1
2 3 4 5
11