# Questions tagged [gaussian-mixture]

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

432 questions
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### Biased viterbi training result

I try to use GMM-HMM model to infer the topic of sentences in a short paragraph. While instead of using normal Baum-Welch optimization, I use viterbi training as follows. I use average of word ...
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### Can we use a mixture of normal distributions while optimising likelihood?

Let's assume that we generate some values by a mixture of two Gaussians. Now we want to find the parameters of the two Gaussians by likelihood maximisation. One good expect that the optimisation will ...
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### Gaussian mixture model (GMM) to cluster high dimensional dataset

My data set has ~20.000 dimensions. I want to use "Gaussian mixture model " to cluster them. To Construct mixtures, multivariate distributions are required. the multinomial distribution is the ...
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### Compute quantile function from a mixture of Normal distribution

I have this mixture of normal distribution: $$X \sim \frac{1}{2}\mathcal{N}(\mu_{x_1}=10,\,\sigma_{x_1}^{2}=1)+\frac{1}{2}\mathcal{N}(\mu_{x_2}=13,\,\sigma_{x_2}^{2}=1)$$ How can i compute the ...
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### Quantiles from the combination of normal distributions

I have information on the distributions of anthropometric dimensions (like shoulder span) for children of different ages. For each age and dimension, I have mean, standard deviation. (I also have ...
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### What is the different between the set of all model parameters and the parameter vector of the nth component

I read many articles about mixture models. I read that the author called the model parameters as "a set of all model parameters", while they said "parameter vector for the n-th component". I wonder ...
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### Stopping criteria for gaussian mixture models

As I can read from the source code of scikit-learn, the stopping criteria for the iterative algorithm of Expectation Maximization (in my case applied to fitting Gaussian mixture models) is to put a ...
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Consider a random vector $$X\equiv \begin{pmatrix} X_1\\ X_2\\ X_3 \end{pmatrix}$$ with pdf $$f(x)=\overbrace{\sum_{k=1}^ K \frac{1}{K} f_k(x)}^{\text{finite mixture}}$$ and $\forall k=1,...,K$ $... 1answer 38 views ### Clustering circles with different radii with Gaussian Mixture Models I am interested in clustering$N$circles in the plane with varying radii using a Gaussian mixture model. The radius of each circle is an integer number$R_i\in\mathbb{N}$determined from observation. ... 1answer 39 views ### Calculating the probability that an observation comes from either population A or B If I have two normal distributions A (mean = 0, variance = 4) and B (mean = 0, variance = 16), how can I calculate the probability that an observation with magnitude 2 comes from A? 1answer 106 views ### Inferring GMM parameters with Gibbs Sampling On my book, "Machine Learning A Probabilistic Approach". It's stated that is straightforward to derive a Gibbs sampling algorithm to fit a mixture model, especially if we use conjugate priors. So ... 1answer 38 views ### Gibbs sampling allocations for time dependent observations from this model I observe$N$observations$\{x_{1,t_1}, \dots, x_{N,t_N}\}$from a$k$component Gaussian Mixture model. The$i$th observation is seen at time stamp$t_i$and is distributed such that each$x_{i,t_i}|...
My question is similar to this one but considers a more general situation. Suppose that $\vec{x} = (x_1, \dots, x_d)$ and let  p(\vec{x}) = \sum_{k=1}^{n} \pi_k \mathcal{N}(\vec{x} | \mu_k, \...