# Questions tagged [gaussian-mixture]

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

438 questions
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### Gaussian Mixture for detecting outliers

I'm trying to make a simple outlier detection program that is able to correctly, or almost correctly, identify values in a data set that could be potential outliers because they don't fall in the ...
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### Negative loss while training Gaussian Mixture Density Networks

In classification problems, the usual negative log-likelihood loss function $L(\theta)=\sum_{i=1}^N -\log(p(y_i|x_i,\theta))$ is always non-negative, since the $y_i$'s are discrete random variables ...
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### comparing gaussian mixture models with and without regularization

I am using Gaussian mixture models for clustering a bunch of data sets. On some data sets a regularization value is often used/suggested (see the MATLAB example for Fisher's Iris data which sets ...
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### Fitting Gaussian mixture model to binary time data

I have data about the dates/times a user logs in and out of a system. I am trying to model the likelihood a user will be logged into the system at any particular time of day. I want to fit a Gaussian ...
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### Spark MLLib Gaussian Mixture Model feature or bug

Is this expected from Gaussian Mixture Model? Given a perfectly homogenous dataset, the cluster center is not exactly the same as the data point? ...
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### Choosing a model for my unsupervised machine learning problem

I need to choose a model for unsupervised machine learning problem. There are 4 clusters in 3D space. These are my requirements: I will run the same model multiple times with different training data (...
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### Approximating a 3D spline surface by a weighted sum of gaussians

I have spatial data(2D) with some quantity associated with each point - basically 3D data. I want to model the quantity distribution in the space and then use N clusters as a compact representation. ...
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### Distribution of the initializing set at K-means++

There is a well-known modification of the initializing step of K-means, named K-means++. It chooses cluster centers with probability proportional to its squared distance from the point's closest ...
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### Bimodal univariate distributions are always indicative of a mixture of two random variables. Is this correct? [duplicate]

Say I see a bimodal distribution like this (with the domain, or random variable, $Z$): Does that instantly mean that I am seeing not a distribution of one independent random variable $Z$, but ...
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### how can I integrate probabilities from two GMMs?

Without going into the details of why exactly I must do this, I have four GMMs (two sets for two classes), and I need to integrate their predictions. Two of them are trained on two classes from ...
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### Computing covariance matrix and mean in python for a Gaussian Mixture Model

I am studying Bishop's PRML book and trying to implement Gaussian Mixture Model from scratch in python. So I have prepared a synthetic dataset which is divided into 2 classes using the following ...
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### Sampling from a multivariate Gaussian mixture model [duplicate]

How can I generate multi-dimensional data from a (estimated) Gaussian mixture pdf? In general, what would be ways to generate multi-dimensional data from a pdf? I read rejection sampling can be used, ...
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### Which parameters need to be initialized random for gaussian mixture hidden markov model?

So, if I model observation probability for a given hidden state according to a multivariate gaussian mixture model, then which parameters need to be initialized random to perform parameter re-...
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### How can I find mean and covariance after EM iteration on GMM algorithmm?

I have a dataset divided in 2 class(lets call x1,x2) but I don't know their mean and covariance. For each class I looked their graph and made a guess about their sub-classes, then run an EM(...
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### 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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### Programming a mixture of a Gamma with a Normal distribution using R

I have some data x in R which seems to be a mixture of a Gamma and Normal distribution. Therefore I'd like to model this as a mixture model consisting of said distributions, but I don't know how to ...
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### Need intuition - how do they simplify the Q function for gaussian mixture EM?

Background - I'm trying to follow section 7.2.4 in this EM tutorial. Basically the setup is I have a vector with 10 points $x$, and each of them can be assigned ($y$) to either Gaussian 1 or to ...
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### Why Expectation Maximization is important for mixture models?

There are many literature emphasize Expectation Maximization method on mixture models (Mixture of Gaussian, Hidden Markov Model, etc.). Why EM is important? EM is just a way to do optimization and is ...
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### Intuition around weighted normal distributions standard deviations

I am looking at a set of normal distributed data and trying to figure out why my intuition is wrong here. If I have multiple normal distributions $N_m(M_m, S_m)$ the literature tells me that I can ...
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### Gaussian Mixture Model - Model selection using the held-out likelihood?

I am trying to understand how to select the number of components in a Gaussian Mixture Model (GMM). Most presentations mention the use of criteria such as AIC and BIC. But if we simply follow model ...
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### Why are hidden Markov models (HMM) also called mixture models?

Why are hidden Markov models (HMM) called mixture models? What does it mix?
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### Useful separation value in a mixture distribution

Assume we have a distribution that is the mixture of two normal distributions. The pdf of the overall distributions and their single parts may look like the following. In black, the combined ...
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### Creating observations to test gaussian mixture HMMs [closed]

I have a Gaussian mixture HMM $\lambda = (\pi, A, B)$ in which $\pi$ is the starting state probabilities, $A$ is the state transition matrix, and $B$ is the emissions matrix. I fit a GMM into the ...
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### Gaussian mixture distribution confusion

Have some confusion on Gaussian mixture distribution model (reference is from the book of Pattern Recognition and Machine Learning). My confusion is how below formula works? $\sum_kz_k=1$ My thought ...
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### What does 'vector-valued' mean?

What is the difference of a feature vector and a 'vector-valued observation' as described here? The term 'vector-valued' is used in the following context: "Most state-of-the-art [Automatic Speech ...
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\...