54,261 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
Infinite factorization of multiple non-parametric views
Combined analysis of multiple data sources has increasing application interest, in particular for distinguishing shared and source-specific aspects. We extend this rationale of classical canonical correlation analysis into a flexible, generative and non-parametric clustering
setting, by introducing a novel non-parametric hierarchical
mixture model. The lower level of the model describes each source with a flexible non-parametric mixture, and the top level combines these to describe commonalities of the sources. The lower-level clusters arise from hierarchical Dirichlet Processes, inducing an infinite-dimensional contingency table between the views. The commonalities between the sources are modeled by an infinite block
model of the contingency table, interpretable as non-negative factorization of infinite matrices, or as a prior for infinite contingency tables. With Gaussian mixture components plugged in for continuous measurements, the model is applied to two views of genes, mRNA expression and abundance of the produced proteins, to expose groups of genes that are co-regulated in either or both of the views.
Cluster analysis of co-expression is a standard simple way of screening for co-regulation, and the two-view analysis extends the approach to distinguishing between pre- and post-translational regulation
A non-parametric hierarchical clustering model
© 2015 IEEE. We present a novel non-parametric clustering model using Gaussian mixture model (NHCM). NHCM uses a novel Dirichlet process (DP) prior allowing for more flexible modeling of the data, where the base distribution of DP is itself an infinite mixture of Gaussian conjugate prior. NHCM can be thought of as hierarchical clustering model, in which the low level base prior governs the distribution of the data points forming sub-clusters, and the higher level prior governs the distribution of the sub-clusters forming clusters. Using this hierarchical configuration, we can maintain low complexity of the model and allow for clustering skewed complex data. To perform inference, we propose a Gibbs sampling algorithm. Empirical investigations have been carried out to analyse the efficiency of the proposed clustering model
Model-based clustering via linear cluster-weighted models
A novel family of twelve mixture models with random covariates, nested in the
linear cluster-weighted model (CWM), is introduced for model-based
clustering. The linear CWM was recently presented as a robust alternative
to the better known linear Gaussian CWM. The proposed family of models provides
a unified framework that also includes the linear Gaussian CWM as a special
case. Maximum likelihood parameter estimation is carried out within the EM
framework, and both the BIC and the ICL are used for model selection. A simple
and effective hierarchical random initialization is also proposed for the EM
algorithm. The novel model-based clustering technique is illustrated in some
applications to real data. Finally, a simulation study for evaluating the
performance of the BIC and the ICL is presented
Hierarchical Bayesian sparse image reconstruction with application to MRFM
This paper presents a hierarchical Bayesian model to reconstruct sparse
images when the observations are obtained from linear transformations and
corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is
well suited to such naturally sparse image applications as it seamlessly
accounts for properties such as sparsity and positivity of the image via
appropriate Bayes priors. We propose a prior that is based on a weighted
mixture of a positive exponential distribution and a mass at zero. The prior
has hyperparameters that are tuned automatically by marginalization over the
hierarchical Bayesian model. To overcome the complexity of the posterior
distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be
used to estimate the image to be recovered, e.g. by maximizing the estimated
posterior distribution. In our fully Bayesian approach the posteriors of all
the parameters are available. Thus our algorithm provides more information than
other previously proposed sparse reconstruction methods that only give a point
estimate. The performance of our hierarchical Bayesian sparse reconstruction
method is illustrated on synthetic and real data collected from a tobacco virus
sample using a prototype MRFM instrument.Comment: v2: final version; IEEE Trans. Image Processing, 200
Posterior Regularization on Bayesian Hierarchical Mixture Clustering
Bayesian hierarchical mixture clustering (BHMC) improves on the traditional
Bayesian hierarchical clustering by, with regard to the parent-to-child
diffusion in the generative process, replacing the conventional
Gaussian-to-Gaussian (G2G) kernels with a Hierarchical Dirichlet Process
Mixture Model (HDPMM). However, the drawback of the BHMC lies in the
possibility of obtaining trees with comparatively high nodal variance in the
higher levels (i.e., those closer to the root node). This can be interpreted as
that the separation between the nodes, particularly those in the higher levels,
might be weak. We attempt to overcome this drawback through a recent
inferential framework named posterior regularization, which facilitates a
simple manner to impose extra constraints on a Bayesian model to address its
weakness. To enhance the separation of clusters, we apply posterior
regularization to impose max-margin constraints on the nodes at every level of
the hierarchy. In this paper, we illustrate the modeling detail of applying the
PR on BHMC and show that this solution achieves the desired improvements over
the BHMC model
Hierarchical Mixture-of-Experts Model for Large-Scale Gaussian Process Regression
We propose a practical and scalable Gaussian process model for large-scale
nonlinear probabilistic regression. Our mixture-of-experts model is
conceptually simple and hierarchically recombines computations for an overall
approximation of a full Gaussian process. Closed-form and distributed
computations allow for efficient and massive parallelisation while keeping the
memory consumption small. Given sufficient computing resources, our model can
handle arbitrarily large data sets, without explicit sparse approximations. We
provide strong experimental evidence that our model can be applied to large
data sets of sizes far beyond millions. Hence, our model has the potential to
lay the foundation for general large-scale Gaussian process research
A dimensionally reduced finite mixture model for multilevel data
AbstractRecently, different mixture models have been proposed for multilevel data, generally requiring the local independence assumption. In this work, this assumption is relaxed by allowing each mixture component at the lower level of the hierarchical structure to be modeled according to a multivariate Gaussian distribution with a non-diagonal covariance matrix. For high-dimensional problems, this solution can lead to highly parameterized models. In this proposal, the trade-off between model parsimony and flexibility is governed by assuming a latent factor generative model
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