Questions tagged [gaussian-mixture-distribution]
A type of mixed distribution or model which assumes subpopulations follow Gaussian distributions.
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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 ...
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33 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.
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96 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....
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1answer
164 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 ...
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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 ...
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76 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 ...
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1answer
722 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 ...
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1answer
218 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 ...
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13 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 ...
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2answers
84 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 ...
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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 ...
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1answer
285 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 ...
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1answer
518 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)^{...
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42 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 ...
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0answers
15 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 ...
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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?
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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 "...
3
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1answer
425 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 ...
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1answer
59 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 ...
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2answers
52 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 ...
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154 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, ...
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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 ...
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1answer
76 views
Upper bound on total variation between two Gaussian mixture
For two random variables $P$ and $Q$ over $R^d$ with distributions $p$ and $q$, respectively, the total variation is defined as
$$
TV(P,Q)=\frac{1}{2}\int_{R^d}\ |p(x)-q(x)|dx.
$$
Consider the case ...
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1answer
104 views
Question about sums of Gasussian Mixture models
This question is strongly based on the result given in HERE
Due to some research I am currently conducting, I've found myself in a situation, where I deal with mixtures of gaussian densities, called ...
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22 views
Gaussian Mixture Models, application?
I'm analyzing the energy consumption behavior of a population that is increasing monthly (panel data). The population is segmented by both gender and 5 geographical locations. I gather from the data ...
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0answers
31 views
Expectation-Maximisation derivations [duplicate]
I've come across a few different sources on expectation-maximisation which I can't quite match up.
The CS229 lecture 8 [1] states that the function we must write down and maximise is:
$$
Q_1 = \sum_{...
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1answer
78 views
How to calculate log likelihood for gaussian mixture model
I'm trying to check the calculation of the log likelihood of a 2 component Gaussian Mixture Model using optim, but I get the wrong answer (it should return mu, sigma, alpha actual).
The log ...
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0answers
14 views
Fitting a mixture model distribution to kurtotic data
I need to fit a parametric distribution to data that has non-zero (unknown) kurtosis. First I tried to fit a Pearson type VII / Student's t, but the fitting is especially poor in the two tails, ...
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0answers
17 views
Building a mixture model that fits well to the tail of a kurtotic distribution
I need to fit a distribution to data that has non-zero (unknown) kurtosis. I tried to fit a Pearson type VII / Student's t, but the fitting is especially poor in the two tails, possibly due to less ...
4
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1answer
214 views
Are Neural Networks Mixture Models?
To my understanding, Gaussian Mixture models are a set of parameterized gaussian distributions that collectively describe an entire, aggregate distribution.
^ from McGonagle et al
Also to my ...
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2answers
241 views
Can a variational autoencoder be interpreted as a mixture of Gaussians?
In a variational autoencoder (VAE) we have an encoder network $E_{\phi}$ that maps inputs $x$ to the distribution parameters of the approximate posterior $q_{\phi}(z \vert x)$. Most commonly we model ...
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1answer
66 views
M step EM algorithm in Mixture Models. Expected value of the indicator variable under the posterior [closed]
I am not able to solve the following expectation. In the EM algorithm, the first step in the M step is to compute the expected value of $\log p(x,z)$ where $x$ are observations and $z$ indicator ...
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47 views
Mixture or Convolution
tl;dr is final paragraph at the bottom.
I have read the posts explaining the differences between mixture distributions and convolutions of distributions, but am having a hard time understanding which ...
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0answers
91 views
Initialisation strategies for learning Hidden Markov Models
I used hmmlearn library to initialize an HMM (Hidden Markov Model). sampled observations from the HMM, and used the sampled data to re-estimate the parameters of ...
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0answers
21 views
Gaussian mixture models for image matrix not determining E step
I want to calculate responsibility for each of the data points, for the given MU, SIGMA and PI.
...
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1answer
79 views
Simulating with mixture distribution
I have fitted a gaussian mixture distribution to residuals, and now I want to simulate the residuals. However, I want the model to be independent of the time steps(have it as an input to the model).
...
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1answer
55 views
Speaker Recognition ML tasks are supervised or unsupervised?
Given the scenario:
We have a speech recording from an unknown person.
We have a speech recording from a known person.
We have a large database of speech recordings from different persons.
We would ...
5
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1answer
402 views
Derivation of maximum likelihood for a Gaussian mixture model
I'm working my way through the derivation of EM in Bishop (p. 435).
I'm stuck trying to derive to MLE for $\mu_k$ for the gaussian mixture model.
Basically I get an extra sum in the numerator.
For ...
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1answer
45 views
What is the Q distribution in expectation maximization in the following explanation?
I am reading a blog on expectation maximization - http://krasserm.github.io/2019/11/21/latent-variable-models-part-1/
Here, I encounter the following expression:
When you look at the above ...
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1answer
436 views
Modeling time series with Gaussian Mixture Model
I'm reading Song and Wang's paper on incremental estimation of GMM for online data streaming clustering. I assumed that we could apply the same idea to model time series, as a time series is a data ...
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0answers
54 views
Numerical Integration with respect to a mixture of Normals [closed]
I have a likelihood function that contains an integral of a latent parameter. I would like to numerically integrate it using Monte Carlo, as in, $L = \prod_{i=1}^N \int f(X, \tilde{\theta}; \beta) d ...
2
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2answers
242 views
interpretation of the estimated parameters of a gaussian mixture model
I need to find/fit a model for the color of an object. Suppose its color is generally yellow and we have 10000-by-3 data which are pixel values for R, G, B channels.
Firstly I choose a Multivariate ...
2
votes
2answers
176 views
fitting a Gaussian mixture with a constraint in python
Suppose I have data and I want to fit a two component Gaussian mixture to
it. I don't know how to do it in python but worse than that
is that I have an additional constraint that the mean of one ...
1
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1answer
190 views
Gaussian Mixture model - Penalized log-likelihood in EM algorithm not monotone increasing
I am working on a multivariate Gaussian Mixture Model in R. The goal is to do regularized clustering on the data, where each component represents a cluster.
I wrote an EM algorithm to maximize a ...
0
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1answer
149 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 ...
5
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2answers
599 views
the approximation power of Gaussian mixture models?
What are the probability density functions that GMM can approximate? a reference in appreciated about this.
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1answer
1k views
Compute mean and variance of mixture of Gaussians given mean/variance of component gaussians [duplicate]
Given $N$ means and variances $\{\mu_1,\mu_2,....\mu_N\}$ , $\{\sigma_1^2,\sigma_2^2,....\sigma_N^2 \}$ ,and the fact that combined they make a gaussian mixture, how do I compute for that mixture $M$, ...
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1answer
33 views
Fitting mixture model on data with duplicate values
What is the correct procedure to fit finite mixture models on data with many duplicate values using EM? Let's say I have N(0,1) distributed data and try to fit a 2 component mixture using EM. There ...
2
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0answers
60 views
testing whether data comes from a bi-modal distribution (python) [duplicate]
I have a variable which seems to be a mix of two Gaussian distributions (it is bi-modal with each mode looking normally distributed).
I would like to identify anomalous samples.
So my idea is to ...
2
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0answers
244 views
Can someone verify if the following Bayesian Information Criterion (BIC) model selection algorithm is correct for Gaussian mixture models?
I am trying to find an automated way of picking the number of clusters $K \in \mathbb{N}$ for unsupervised learning scenarios, specifically for GMM.
I was suggested to use something called the "...
