Distributed Regularization of Binary Blockmodels


Distributed Regularization of Binary Blockmodels – In this paper we address the problem of sparse learning with multivariate binary models, e.g., the Gaussian model and its variant, the Gaussian process (GP-beta). Our motivation is to use the recently developed framework of the variational approximation as a generic and intuitive solution for the sparse learning problem, where the likelihood matrix is composed of a binary weight of the same dimension, and a sparse distribution manifold. Here, for each weight, the likelihood matrix is assumed to be a Gaussian and its posterior distribution is computed by an unbiased estimator. The posterior distribution of the underlying distribution manifold is computed by Gaussian minimization and can be used to obtain the posterior distribution of a binary distribution. For the GP-beta, the likelihood matrix is computed from the posterior distribution and its regularization regularized by a variational approximation. To estimate the posterior distribution over a multivariate binary model, we consider a variational approximation problem with a sparse distribution and the posterior distribution is computed from the regularized distribution manifold. Our experimental results on MNIST and its variants show the effectiveness of the proposed framework.

We propose a new probabilistic estimator for the Markov random variable model. It extends both Markov random domain models and Markov random process models, for which we provide a new conditional independence criterion. An analysis of the data under our estimator shows that the new model outperforms both Markov and Markov random processes on the MNIST and SVHN datasets respectively. In contrast, our method’s conditional independence criterion is non-parametric, so does not perform as well when the number of sample points is large and the number of variables is sparse. Nevertheless, the proposed estimator demonstrates promising results relative to state-of-the-art estimators. The experimental results reported here suggest that our estimator and a new Markov random process model can be a valuable tool for both MNIST and SVHN verification.

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Distributed Regularization of Binary Blockmodels

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    Stochastic gradient descent with two-sample testsWe propose a new probabilistic estimator for the Markov random variable model. It extends both Markov random domain models and Markov random process models, for which we provide a new conditional independence criterion. An analysis of the data under our estimator shows that the new model outperforms both Markov and Markov random processes on the MNIST and SVHN datasets respectively. In contrast, our method’s conditional independence criterion is non-parametric, so does not perform as well when the number of sample points is large and the number of variables is sparse. Nevertheless, the proposed estimator demonstrates promising results relative to state-of-the-art estimators. The experimental results reported here suggest that our estimator and a new Markov random process model can be a valuable tool for both MNIST and SVHN verification.


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