Recurrent neural networks (RNNs) are a vital modeling technique that rely on internal states learned indirectly by optimization of a supervised, unsupervised, or reinforcement training loss. RNNs are used to model dynamic processes that are characterized by underlying latent states whose form is often unknown, precluding its analytic representation inside an RNN. In the Predictive-State Representation (PSR) literature, latent state processes are modeled by an internal state representation that directly models the distribution of future observations, and most recent work in this area has relied on explicitly representing and targeting sufficient statistics of this probability distribution. We seek to combine the advantages of RNNs and PSRs by augmenting existing state-of-the-art recurrent neural networks with Predictive-State Decoders (PSDs), which add supervision to the network's internal state representation to target predicting future observations. PSDs are simple to implement and easily incorporated into existing training pipelines via additional loss regularization. We demonstrate the effectiveness of PSDs with experimental results in three different domains: probabilistic filtering, Imitation Learning, and Reinforcement Learning. In each, our method improves statistical performance of state-of-the-art recurrent baselines and does so with fewer iterations and less data.

We study the generalization properties of ridge regression with random features in the statistical learning framework. We show for the first time that $O(1/\sqrt{n})$ learning bounds can be achieved with only $O(\sqrt{n}\log n)$ random features rather than $O({n})$ as suggested by previous results. Further, we prove faster learning rates and show that they might require more random features, unless they are sampled according to a possibly problem dependent distribution. Our results shed light on the statistical computational trade-offs in large scale kernelized learning, showing the potential effectiveness of random features in reducing the computational complexity while keeping optimal generalization properties.

We address the problem of setting the kernel bandwidth, epps, used by Manifold Learning algorithms to construct the graph Laplacian. Exploiting the connection between manifold geometry, represented by the Riemannian metric, and the Laplace-Beltrami operator, we set epps by optimizing the Laplacian's ability to preserve the geometry of the data.

Inference using deep neural networks is often outsourced to the cloud since it is a computationally demanding task. However, this raises a fundamental issue of trust. How can a client be sure that the cloud has performed inference correctly? A lazy cloud provider might use a simpler but less accurate model to reduce its own computational load, or worse, maliciously modify the inference results sent to the client. We propose SafetyNets, a framework that enables an untrusted server (the cloud) to provide a client with a short mathematical proof of the correctness of inference tasks that they perform on behalf of the client. Specifically, SafetyNets develops and implements a specialized interactive proof (IP) protocol for verifiable execution of a class of deep neural networks, i.e., those that can be represented as arithmetic circuits. Our empirical results on three-and four-layer deep neural networks demonstrate the run-time costs of SafetyNets for both the client and server are low.

Self-localization during navigation with noisy sensors in an ambiguous world is computationally challenging, yet animals and humans excel at it. In robotics, {\em Simultaneous Location and Mapping} (SLAM) algorithms solve this problem through joint sequential probabilistic inference of their own coordinates and those of external spatial landmarks. We generate the first neural solution to the SLAM problem by training recurrent LSTM networks to perform a set of hard 2D navigation tasks that require generalization to completely novel trajectories and environments. Our goal is to make sense of how the diverse phenomenology in the brain's spatial navigation circuits is related to their function. We show that the hidden unit representations exhibit several key properties of hippocampal place cells, including stable tuning curves that remap between environments. Our result is also a proof of concept for end-to-end-learning of a SLAM algorithm using recurrent networks, and a demonstration of why this approach may have some advantages for robotic SLAM.

Computationally intensive distributed and parallel computing is often bottlenecked by a small set of slow workers known as stragglers. In this paper, we utilize the emerging idea of ``coded computation'' to design a novel error-correcting-code inspired technique for solving linear inverse problems under specific iterative methods in a parallelized implementation affected by stragglers. Example machine-learning applications include inverse problems such as personalized PageRank and sampling on graphs. We provably show that our coded-computation technique can reduce the mean-squared error under a computational deadline constraint. In fact, the ratio of mean-squared error of replication-based and coded techniques diverges to infinity as the deadline increases. Our experiments for personalized PageRank performed on real systems and real social networks show that this ratio can be as large as $10^4$. Further, unlike coded-computation techniques proposed thus far, our strategy combines outputs of all workers, including the stragglers, to produce more accurate estimates at the computational deadline. This also ensures that the accuracy degrades ``gracefully'' in the event that the number of stragglers is large.

We present a data-efficient reinforcement learning method for continuous state-action systems under significant observation noise. Data-efficient solutions under small noise exist, such as PILCO which learns the cartpole swing-up task in 30s. PILCO evaluates policies by planning state-trajectories using a dynamics model. However, PILCO applies policies to the observed state, therefore planning in observation space. We extend PILCO with filtering to instead plan in belief space, consistent with partially observable Markov decisions process (POMDP) planning. This enables data-efficient learning under significant observation noise, outperforming more naive methods such as post-hoc application of a filter to policies optimised by the original (unfiltered) PILCO algorithm. We test our method on the cartpole swing-up task, which involves nonlinear dynamics and requires nonlinear control.

Finding the maximum a-posteriori (MAP) assignment is a central task in graphical models. Since modern applications give rise to very large problem instances, there is increasing need for efficient solvers. In this work we propose to improve the efficiency of coordinate-minimization-based dual-decomposition solvers by running their updates asynchronously in parallel. In this case message-passing inference is performed by multiple processing units simultaneously without coordination, all reading and writing to shared memory. We analyze the convergence properties of the resulting algorithms and identify settings where speedup gains can be expected. Our numerical evaluations show that this approach indeed achieves significant speedups in common computer vision tasks.

Calcium imaging permits optical measurement of neural activity. Since intracellular calcium concentration is an indirect measurement of neural activity, computational tools are necessary to infer the true underlying spiking activity from fluorescence measurements. Bayesian model inversion can be used to solve this problem, but typically requires either computationally expensive MCMC sampling, or faster but approximate maximum-a-posteriori optimization. Here, we introduce a flexible algorithmic framework for fast, efficient and accurate extraction of neural spikes from imaging data. Using the framework of variational autoencoders, we propose to amortize inference by training a deep neural network to perform model inversion efficiently.

Deep Learning has revolutionized vision via convolutional neural networks (CNNs) and natural language processing via recurrent neural networks (RNNs). However, success stories of Deep Learning with standard feed-forward neural networks (FNNs) are rare. FNNs that perform well are typically shallow and, therefore cannot exploit many levels of abstract representations. We introduce self-normalizing neural networks (SNNs) to enable high-level abstract representations. While batch normalization requires explicit normalization, neuron activations of SNNs automatically converge towards zero mean and unit variance. The activation function of SNNs are scaled exponential linear units (SELUs), which induce self-normalizing properties.