Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection between tensor networks and probabilistic graphical models, and show that it motivates the definition of generalized tensor networks where information from a tensor can be copied and reused in other parts of the network. We discuss the relationship between generalized tensor network architectures used in quantum physics, such as String-Bond States and Entangled Plaquette States, and architectures commonly used in machine learning. We provide an algorithm to train these networks in a supervised learning context and show that they overcome the limitations of regular tensor networks in higher dimensions, while keeping the computation efficient. A method to combine neural networks and tensor networks as part of a common deep learning architecture is also introduced. We benchmark our algorithm for several generalized tensor network architectures on the task of classifying images and sounds, and show that they outperform previously introduced tensor network algorithms. Some of the models we consider can be realized on a quantum computer and may guide the development of near-term quantum machine learning architectures.

In this paper, we provide two new stable online algorithms for the problem of prediction in reinforcement learning, \emph{i.e.}, estimating the value function of a model-free Markov reward process using the linear function approximation architecture and with memory and computation costs scaling quadratically in the size of the feature set. The algorithms employ the multi-timescale stochastic approximation variant of the very popular cross entropy (CE) optimization method which is a model based search method to find the global optimum of a real-valued function. A proof of convergence of the algorithms using the ODE method is provided. We supplement our theoretical results with experimental comparisons. The algorithms achieve good performance fairly consistently on many RL benchmark problems with regards to computational efficiency, accuracy and stability.

Variable clustering is important for explanatory analysis. However, only few dedicated methods for variable clustering with the Gaussian graphical model have been proposed. Even more severe, small insignificant partial correlations due to noise can dramatically change the clustering result when evaluating for example with the Bayesian Information Criteria (BIC). In this work, we try to address this issue by proposing a Bayesian model that accounts for negligible small, but not necessarily zero, partial correlations. Based on our model, we propose to evaluate a variable clustering result using the marginal likelihood. To address the intractable calculation of the marginal likelihood, we propose two solutions: one based on a variational approximation, and another based on MCMC. Experiments on simulated data shows that the proposed method is similarly accurate as BIC in the no noise setting, but considerably more accurate when there are noisy partial correlations. Furthermore, on real data the proposed method provides clustering results that are intuitively sensible, which is not always the case when using BIC or its extensions.

Indeed, the bulk of the empirical academic literature in finance takes this approach. However, practitioners' use of models, in particular for the pricing and risk management of derivative financial products relative to observed prices for liquidly traded market instruments, typically tends to depart from this ideal. Primacy is accorded to model "calibration" over empirical consistency, i.e., choosing a set of liquidly traded market instruments (which may include liquidly traded derivatives) as "calibration instruments", model parameters are determined so as to match model prices of these instruments as closely as possible to observed market prices at a given point in time. Once these market prices have changed, the model parameters (which were assumed to be constant, or at most time-varying in a known deterministic fashion) are recalibrated, thereby contradicting the model assumptions. "Legalising" these parameter changes by expanding the state space (e.g. via regime-switching or stochastic volatility models) shifts, rather than resolves, the problem: for example in the case of stochastic volatility, volatility becomes a state variable rather than a model parameter, and can evolve stochastically, but the parameters of the stochastic volatility process itself are assumed to be time-invariant.

Recently, deep neural network (DNN) has made a breakthrough in monaural source enhancement. Through a training step by using a large amount of data, DNN estimates a mapping between mixed signals and clean signals. At this time, we use an objective function that numerically expresses the quality of a mapping by DNN. In the conventional methods, L1 norm, L2 norm, and Itakura-Saito divergence are often used as objective functions. Recently, an objective function based on short-time objective intelligibility (STOI) has also been proposed. However, these functions only indicate similarity between the clean signal and the estimated signal by DNN. In other words, they do not show the quality of noise reduction or source enhancement. Motivated by the fact, this paper adopts signal-to-distortion ratio (SDR) as the objective function. Since SDR virtually shows signal-to-noise ratio (SNR), maximizing SDR solves the above problem. The experimental results revealed that the proposed method achieved better performance than the conventional methods.

This paper proposes a new method for solving the well-known rank aggregation problem from pairwise comparisons using the method of low-rank matrix completion. The partial and noisy data of pairwise comparisons is transformed into a matrix form. We then use tools from matrix completion, which has served as a major component in the low-rank completion solution of the Netflix challenge, to construct the preference of the different objects. In our approach, the data of multiple comparisons is used to create an estimate of the probability of object i to win (or be chosen) over object j, where only a partial set of comparisons between N objects is known. The data is then transformed into a matrix form for which the noiseless solution has a known rank of one. An alternating minimization algorithm, in which the target matrix takes a bilinear form, is then used in combination with maximum likelihood estimation for both factors. The reconstructed matrix is used to obtain the true underlying preference intensity. This work demonstrates the improvement of our proposed algorithm over the current state-of-the-art in both simulated scenarios and real data.

We introduce a new algorithm for reinforcement learning called Maximum aposteriori Policy Optimisation (MPO) based on coordinate ascent on a relative entropy objective. We show that several existing methods can directly be related to our derivation. We develop two off-policy algorithms and demonstrate that they are competitive with the state-of-the-art in deep reinforcement learning. In particular, for continuous control, our method outperforms existing methods with respect to sample efficiency, premature convergence and robustness to hyperparameter settings while achieving similar or better final performance.

Our goal is to synthesize controllers for robots that provably generalize well to novel environments given a dataset of example environments. The key technical idea behind our approach is to leverage tools from generalization theory in machine learning by exploiting a precise analogy (which we present in the form of a reduction) between robustness of controllers to novel environments and generalization of hypotheses in supervised learning. In particular, we utilize the Probably Approximately Correct (PAC)-Bayes framework, which allows us to obtain upper bounds (that hold with high probability) on the expected cost of (stochastic) controllers across novel environments. We propose control synthesis algorithms that explicitly seek to minimize this upper bound. The corresponding optimization problem can be solved using convex optimization (Relative Entropy Programming in particular) in the setting where we are optimizing over a finite control policy space. In the more general setting of continuously parameterized controllers, we minimize this upper bound using stochastic gradient descent. We present examples of our approach in the context of obstacle avoidance control with depth measurements. Our simulated examples demonstrate the potential of our approach to provide strong generalization guarantees on controllers for robotic systems with continuous state and action spaces, complicated (e.g., nonlinear) dynamics, and rich sensory inputs (e.g., depth measurements).

We propose a simple and easy to implement neural network compression algorithm that achieves results competitive with more complicated state-of-the-art methods. The key idea is to modify the original optimization problem by adding K independent Gaussian priors (corresponding to the k-means objective) over the network parameters to achieve parameter quantization, as well as an L1 penalty to achieve pruning. Unlike many existing quantization-based methods, our method uses hard clustering assignments of network parameters, which adds minimal change or overhead to standard network training. We also demonstrate experimentally that tying neural network parameters provides less gain in generalization performance than changing network architecture and connectivity patterns entirely.

Uncertainty computation in deep learning is essential to design robust and reliable systems. Variational inference (VI) is a promising approach for such computation, but requires more effort to implement and execute compared to maximum-likelihood methods. In this paper, we propose new natural-gradient algorithms to reduce such efforts for Gaussian mean-field VI. Our algorithms can be implemented within the Adam optimizer by perturbing the network weights during gradient evaluations, and uncertainty estimates can be cheaply obtained by using the vector that adapts the learning rate. This requires lower memory, computation, and implementation effort than existing VI methods, while obtaining uncertainty estimates of comparable quality. Our empirical results confirm this and further suggest that the weight-perturbation in our algorithm could be useful for exploration in reinforcement learning and stochastic optimization.