55 research outputs found
Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks
Effective training of deep neural networks suffers from two main issues. The
first is that the parameter spaces of these models exhibit pathological
curvature. Recent methods address this problem by using adaptive
preconditioning for Stochastic Gradient Descent (SGD). These methods improve
convergence by adapting to the local geometry of parameter space. A second
issue is overfitting, which is typically addressed by early stopping. However,
recent work has demonstrated that Bayesian model averaging mitigates this
problem. The posterior can be sampled by using Stochastic Gradient Langevin
Dynamics (SGLD). However, the rapidly changing curvature renders default SGLD
methods inefficient. Here, we propose combining adaptive preconditioners with
SGLD. In support of this idea, we give theoretical properties on asymptotic
convergence and predictive risk. We also provide empirical results for Logistic
Regression, Feedforward Neural Nets, and Convolutional Neural Nets,
demonstrating that our preconditioned SGLD method gives state-of-the-art
performance on these models.Comment: AAAI 201
Efficient Bayesian Model Selection in PARAFAC via Stochastic Thermodynamic Integration
International audienceParallel factor analysis (PARAFAC) is one of the most popular tensor factorization models. Even though it has proven successful in diverse application fields, the performance of PARAFAC usually hinges up on the rank of the factorization, which is typically specified manually by the practitioner. In this study, we develop a novel parallel and distributed Bayesian model selection technique for rank estimation in large-scale PARAFAC models. The proposed approach integrates ideas from the emerging field of stochastic gradient Markov Chain Monte Carlo, statistical physics, and distributed stochastic optimization. As opposed to the existing methods, which are based on some heuristics, our method has a clear mathematical interpretation, and has significantly lower computational requirements, thanks to data subsampling and parallelization. We provide formal theoretical analysis on the bias induced by the proposed approach. Our experiments on synthetic and large-scale real datasets show that our method is able to find the optimal model order while being significantly faster than the state-of-the-art
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