LogLikelihood for Gaussian Mixture ModelsAlfred UltschCatharina Lippmann
The inaccuracies appear in the function _estimate_log_gaussian_prob.The log-probabilities can be off by 0.2 (see the very last example), which really is not small if those probabilities are used for likelihoods.I uploaded the full script at https://github.com/JohannesBuchner/gmm-tests/blob/...
The Log Marginal Likelihood refers to the logarithm of the marginal likelihood function, which is maximized to obtain the optimal set of hyperparameters in Gaussian Process Models. AI generated definition based on: Computer Aided Chemical Engineering, 2018 ...
For example, with 2000 examples of 8 features with 3 gaussian clusters, the loglikelihood looks like this (30 iterations) - So this is very bad. But on other tests I ran, for example one test with 15 examples of 2 features and 2 clusters, the loglikelihood is this - Better but still...
That's why it is useful, for example in model inference. The log-likelihood function then is ℓ(θ|x)=∑i=1Nlog(gθ(xi))ℓ(θ|x)=∑i=1Nlog(gθ(xi)) with in your case of a gaussian mixture model gθ(xi)gθ(xi) being the density estimate f(xi)f(xi) f(xi)=...
Therefore, this diagnostic fails to discriminate among sets of candidate models that generate identical slope values. Clearly, an alternative method is needed. Akaike's information criterion (AIC) is a flexible, likelihood-based approach to model selection (Akaike, 1973). A particular advantage of ...
def GMM(y, mu, sig, coeff): """ Gaussian mixture model negative log-likelihood Parameters --- y : TensorVariable mu : FullyConnected (Linear) sig : FullyConnected (Softplus) coeff : FullyConnected (Softmax) """ n_dim = y.ndim shape_y = y.shape y = y.reshape((-1, shape_y[-...
pi = Nk / N# LikelihoodLnew = sp.sum( sp.log2( sp.sum( sp.apply_along_axis(lambdax: sp.fromiter( (pi[k] * gauss_mixture_calculate(x, mu[k], sigma[k])forkinxrange(K)), dtype=float ),1, X, ),1, ) ) )ifabs(L - Lnew) < tol:breakL = Lnewprint"log likelihood=%s"...
Recently, the Expected Patch Log Likelihood (EPLL) method has been introduced, arguing that the chosen model should be enforced on the final reconstructed image patches. In the context of a Gaussian Mixture Model (GMM), this idea has been shown to lead to state-of-the-art results in image...
log-normal distribution; non-singular information matrix; modified likelihood; modified score; bias prevention MSC: 62E15; 62E20 1. Introduction The log-normal distribution is commonly used to model the behavior of data with positive asymmetry, in which most of the observations are concentrated ...