arXiv subjects

David Carlson

Publications and source records attributed to David Carlson.

40 records · Page 3Linked to original sources

arXiv2016

Partition Functions from Rao-Blackwellized Tempered Sampling

Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliary inverse temperature variable. Our method exploits the multinomial probability law of the inverse temperatures, and provides estimates of the partition function in terms of a simple quotient of Rao-Blackwellized marginal inverse temperature probability estimates, which are updated while sampling. We show that the method has interesting connections with several alternative popular methods, and offers some significant advantages. In particular, we empirically find that the new method provides more accurate estimates than Annealed Importance Sampling when calculating partition functions of large Restricted Boltzmann Machines (RBM); moreover, the method is sufficiently accurate to track training and validation log-likelihoods during learning of RBMs, at minimal computational cost.

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arXiv2016

Neuroprosthetic decoder training as imitation learning

Neuroprosthetic brain-computer interfaces function via an algorithm which decodes neural activity of the user into movements of an end effector, such as a cursor or robotic arm. In practice, the decoder is often learned by updating its parameters while the user performs a task. When the user's intention is not directly observable, recent methods have demonstrated value in training the decoder against a surrogate for the user's intended movement. We describe how training a decoder in this way is a novel variant of an imitation learning problem, where an oracle or expert is employed for supervised training in lieu of direct observations, which are not available. Specifically, we describe how a generic imitation learning meta-algorithm, dataset aggregation (DAgger, [1]), can be adapted to train a generic brain-computer interface. By deriving existing learning algorithms for brain-computer interfaces in this framework, we provide a novel analysis of regret (an important metric of learning efficacy) for brain-computer interfaces. This analysis allows us to characterize the space of algorithmic variants and bounds on their regret rates. Existing approaches for decoder learning have been performed in the cursor control setting, but the available design principles for these decoders are such that it has been impossible to scale them to naturalistic settings. Leveraging our findings, we then offer an algorithm that combines imitation learning with optimal control, which should allow for training of arbitrary effectors for which optimal control can generate goal-oriented control. We demonstrate this novel and general BCI algorithm with simulated neuroprosthetic control of a 26 degree-of-freedom model of an arm, a sophisticated and realistic end effector.

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arXiv2015

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.

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arXiv2015

Deep Temporal Sigmoid Belief Networks for Sequence Modeling

Deep dynamic generative models are developed to learn sequential dependencies in time-series data. The multi-layered model is designed by constructing a hierarchy of temporal sigmoid belief networks (TSBNs), defined as a sequential stack of sigmoid belief networks (SBNs). Each SBN has a contextual hidden state, inherited from the previous SBNs in the sequence, and is used to regulate its hidden bias. Scalable learning and inference algorithms are derived by introducing a recognition model that yields fast sampling from the variational posterior. This recognition model is trained jointly with the generative model, by maximizing its variational lower bound on the log-likelihood. Experimental results on bouncing balls, polyphonic music, motion capture, and text streams show that the proposed approach achieves state-of-the-art predictive performance, and has the capacity to synthesize various sequences.

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