Towards learning programs from data, we introduce the problem of sampling programs from posterior distributions conditioned on that data. Within this setting, we propose an algorithm that uses a symbolic solver to efficiently sample programs. The proposal combines constraint-based program synthesis with sampling via random parity constraints. We give theoretical guarantees on how well the samples approximate the true posterior, and have empirical results showing the algorithm is efficient in practice, evaluating our approach on 22 program learning problems in the domains of text editing and computer-aided programming.

Recently proposed adversarial classification methods have shown promising results for cost sensitive and multivariate losses. In contrast with empirical risk minimization (ERM) methods, which use convex surrogate losses to approximate the desired non-convex target loss function, adversarial methods minimize non-convex losses by treating the properties of the training data as being uncertain and worst case within a minimax game. Despite this difference in formulation, we recast adversarial classification under zero-one loss as an ERM method with a novel prescribed loss function. We demonstrate a number of theoretical and practical advantages over the very closely related hinge loss ERM methods. This establishes adversarial classification under the zero-one loss as a method that fills the long standing gap in multiclass hinge loss classification, simultaneously guaranteeing Fisher consistency and universal consistency, while also providing dual parameter sparsity and high accuracy predictions in practice.

Sobolev quantities (norms, inner products, and distances) of probability density functions are important in the theory of nonparametric statistics, but have rarely been used in practice, partly due to a lack of practical estimators. They also include, as special cases, L^2 quantities which are used in many applications. We propose and analyze a family of estimators for Sobolev quantities of unknown probability density functions. We bound the finite-sample bias and variance of our estimators, finding that they are generally minimax rate-optimal. Our estimators are significantly more computationally tractable than previous estimators, and exhibit a statistical/computational trade-off allowing them to adapt to computational constraints. We also draw theoretical connections to recent work on fast two-sample testing and empirically validate our estimators on synthetic data.

Stochastic gradient MCMC (SG-MCMC) has played an important role in large-scale Bayesian learning, with well-developed theoretical convergence properties. In such applications of SG-MCMC, it is becoming increasingly popular to employ distributed systems, where stochastic gradients are computed based on some outdated parameters, yielding what are termed stale gradients. While stale gradients could be directly used in SG-MCMC, their impact on convergence properties has not been well studied. In this paper we develop theory to show that while the bias and MSE of an SG-MCMC algorithm depend on the staleness of stochastic gradients, its estimation variance (relative to the expected estimate, based on a prescribed number of samples) is independent of it. In a simple Bayesian distributed system with SG-MCMC, where stale gradients are computed asynchronously by a set of workers, our theory indicates a linear speedup on the decrease of estimation variance w.r.t. the number of workers.

The recent success of deep neural networks relies on massive amounts of labeled data. For a target task where labeled data is unavailable, domain adaptation can transfer a learner from a different source domain. In this paper, we propose a new approach to domain adaptation in deep networks that can jointly learn adaptive classifiers and transferable features from labeled data in the source domain and unlabeled data in the target domain. We relax a shared-classifier assumption made by previous methods and assume that the source classifier and target classifier differ by a residual function. We enable classifier adaptation by plugging several layers into deep network to explicitly learn the residual function with reference to the target classifier. We fuse features of multiple layers with tensor product and embed them into reproducing kernel Hilbert spaces to match distributions for feature adaptation. The adaptation can be achieved in most feed-forward models by extending them with new residual layers and loss functions, which can be trained efficiently via back-propagation. Empirical evidence shows that the new approach outperforms state of the art methods on standard domain adaptation benchmarks.

We develop a general duality between neural networks and compositional kernel Hilbert spaces. We introduce the notion of a computation skeleton, an acyclic graph that succinctly describes both a family of neural networks and a kernel space. Random neural networks are generated from a skeleton through node replication followed by sampling from a normal distribution to assign weights. The kernel space consists of functions that arise by compositions, averaging, and non-linear transformations governed by the skeleton's graph topology and activation functions. We prove that random networks induce representations which approximate the kernel space. In particular, it follows that random weight initialization often yields a favorable starting point for optimization despite the worst-case intractability of training neural networks.

Scalable and effective exploration remains a key challenge in reinforcement learning (RL). While there are methods with optimality guarantees in the setting of discrete state and action spaces, these methods cannot be applied in high-dimensional deep RL scenarios. As such, most contemporary RL relies on simple heuristics such as epsilon-greedy exploration or adding Gaussian noise to the controls. This paper introduces Variational Information Maximizing Exploration (VIME), an exploration strategy based on maximization of information gain about the agent's belief of environment dynamics. We propose a practical implementation, using variational inference in Bayesian neural networks which efficiently handles continuous state and action spaces. VIME modifies the MDP reward function, and can be applied with several different underlying RL algorithms. We demonstrate that VIME achieves significantly better performance compared to heuristic exploration methods across a variety of continuous control tasks and algorithms, including tasks with very sparse rewards.

SEBOOST applies a secondary optimization process in the subspace spanned by the last steps and descent directions. The method was inspired by the SESOP optimization method for large-scale problems, and has been adapted for the stochastic learning framework. It can be applied on top of any existing optimization method with no need to tweak the internal algorithm. We show that the method is able to boost the performance of different algorithms, and make them more robust to changes in their hyper-parameters. As the boosting steps of SEBOOST are applied between large sets of descent steps, the additional subspace optimization hardly increases the overall computational burden. We introduce two hyper-parameters that control the balance between the baseline method and the secondary optimization process. The method was evaluated on several deep learning tasks, demonstrating promising results.

Faced with saturation of Moore's law and increasing size and dimension of data, system designers have increasingly resorted to parallel and distributed computing to reduce computation time of machine-learning algorithms. However, distributed computing is often bottle necked by a small fraction of slow processors called stragglers that reduce the speed of computation because the fusion node has to wait for all processors to complete their processing. To combat the effect of stragglers, recent literature proposes introducing redundancy in computations across processors, e.g., using repetition-based strategies or erasure codes. The fusion node can exploit this redundancy by completing the computation using outputs from only a subset of the processors, ignoring the stragglers. In this paper, we propose a novel technique - that we call Short-Dot - to introduce redundant computations in a coding theory inspired fashion, for computing linear transforms of long vectors. Instead of computing long dot products as required in the original linear transform, we construct a larger number of redundant and short dot products that can be computed more efficiently at individual processors. Further, only a subset of these short dot products are required at the fusion node to finish the computation successfully. We demonstrate through probabilistic analysis as well as experiments on computing clusters that Short-Dot offers significant speed-up compared to existing techniques. We also derive trade-offs between the length of the dot-products and the resilience to stragglers (number of processors required to finish), for any such strategy and compare it to that achieved by our strategy.

Recent progress on many imaging and vision tasks has been driven by the use of deep feed-forward neural networks, which are trained by propagating gradients of a loss defined on the final output, back through the network up to the first layer that operates directly on the image. We propose back-propagating one step further---to learn camera sensor designs jointly with networks that carry out inference on the images they capture. In this paper, we specifically consider the design and inference problems in a typical color camera---where the sensor is able to measure only one color channel at each pixel location, and computational inference is required to reconstruct a full color image. We learn the camera sensor's color multiplexing pattern by encoding it as layer whose learnable weights determine which color channel, from among a fixed set, will be measured at each location. These weights are jointly trained with those of a reconstruction network that operates on the corresponding sensor measurements to produce a full color image. Our network achieves significant improvements in accuracy over the traditional Bayer pattern used in most color cameras. It automatically learns to employ a sparse color measurement approach similar to that of a recent design, and moreover, improves upon that design by learning an optimal layout for these measurements.