Fast Adaptive Weight Noise

Marginalising out uncertain quantities within the internal representations or parameters of neural networks is of central importance for a wide range of learning techniques, such as empirical, variational or full Bayesian methods. We set out to generalise fast dropout (Wang & Manning, 2013) to cover a wider variety of noise processes in neural networks. This leads to an efficient calculation of the marginal likelihood and predictive distribution which evades sampling and the consequential increase in training time due to highly variant gradient estimates. This allows us to approximate variational Bayes for the parameters of feed-forward neural networks. Inspired by the minimum description length principle, we also propose and experimentally verify the direct optimisation of the regularised predictive distribution. The methods yield results competitive with previous neural network based approaches and Gaussian processes on a wide range of regression tasks.

[1]  Max Welling,et al.  Auto-Encoding Variational Bayes , 2013, ICLR.

[2]  Geoffrey E. Hinton,et al.  Keeping the neural networks simple by minimizing the description length of the weights , 1993, COLT '93.

[3]  Radford M. Neal.  Probabilistic Inference Using Markov Chain Monte Carlo Methods , 2011 .

[4]  Alex Graves,et al.  Practical Variational Inference for Neural Networks , 2011, NIPS.

[5]  Alex Graves,et al.  Generating Sequences With Recurrent Neural Networks , 2013, ArXiv.

[6]  Wray L. Buntine,et al.  Bayesian Back-Propagation , 1991, Complex Syst..

[7]  David Mackay,et al.  Probable networks and plausible predictions - a review of practical Bayesian methods for supervised neural networks , 1995 .

[8]  Yann LeCun,et al.  Regularization of Neural Networks using DropConnect , 2013, ICML.

[9]  Nitish Srivastava,et al.  Improving neural networks by preventing co-adaptation of feature detectors , 2012, ArXiv.

[10]  Julien Cornebise,et al.  Weight Uncertainty in Neural Networks , 2015, ArXiv.

[11]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[12]  G. Grimmett,et al.  Probability and random processes , 2002 .

[13]  Ryan P. Adams,et al.  Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks , 2015, ICML.

[14]  David J. C. MacKay,et al.  A Practical Bayesian Framework for Backpropagation Networks , 1992, Neural Computation.

[15]  Jorma Rissanen,et al.  Minimum Description Length Principle , 2010, Encyclopedia of Machine Learning.

[16]  Christopher D. Manning,et al.  Fast dropout training , 2013, ICML.

[17]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[18]  Ariel D. Procaccia,et al.  Variational Dropout and the Local Reparameterization Trick , 2015, NIPS.