191,192 research outputs found
Deep Gaussian Mixture Models
Deep learning is a hierarchical inference method formed by subsequent
multiple layers of learning able to more efficiently describe complex
relationships. In this work, Deep Gaussian Mixture Models are introduced and
discussed. A Deep Gaussian Mixture model (DGMM) is a network of multiple layers
of latent variables, where, at each layer, the variables follow a mixture of
Gaussian distributions. Thus, the deep mixture model consists of a set of
nested mixtures of linear models, which globally provide a nonlinear model able
to describe the data in a very flexible way. In order to avoid
overparameterized solutions, dimension reduction by factor models can be
applied at each layer of the architecture thus resulting in deep mixtures of
factor analysers.Comment: 19 pages, 4 figure
Adaptive Seeding for Gaussian Mixture Models
We present new initialization methods for the expectation-maximization
algorithm for multivariate Gaussian mixture models. Our methods are adaptions
of the well-known -means++ initialization and the Gonzalez algorithm.
Thereby we aim to close the gap between simple random, e.g. uniform, and
complex methods, that crucially depend on the right choice of hyperparameters.
Our extensive experiments indicate the usefulness of our methods compared to
common techniques and methods, which e.g. apply the original -means++ and
Gonzalez directly, with respect to artificial as well as real-world data sets.Comment: This is a preprint of a paper that has been accepted for publication
in the Proceedings of the 20th Pacific Asia Conference on Knowledge Discovery
and Data Mining (PAKDD) 2016. The final publication is available at
link.springer.com (http://link.springer.com/chapter/10.1007/978-3-319-31750-2
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Model Selection for Gaussian Mixture Models
This paper is concerned with an important issue in finite mixture modelling,
the selection of the number of mixing components. We propose a new penalized
likelihood method for model selection of finite multivariate Gaussian mixture
models. The proposed method is shown to be statistically consistent in
determining of the number of components. A modified EM algorithm is developed
to simultaneously select the number of components and to estimate the mixing
weights, i.e. the mixing probabilities, and unknown parameters of Gaussian
distributions. Simulations and a real data analysis are presented to illustrate
the performance of the proposed method
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