The design of symbol detectors in digital communication systems has traditionally relied on statistical channel models that describe the relation between the transmitted symbols and the observed signal at the receiver. Here we review a data-driven framework to symbol detection design which combines machine learning (ML) and model-based algorithms. In this hybrid approach, well-known channelmodel-based algorithms such as the Viterbi method, BCJR detection, and multiple-input multiple-output (MIMO) soft interference cancellation (SIC) are augmented with MLbased algorithms to remove their channel-model-dependence, allowing the receiver to learn to implement these algorithms solely from data. The resulting data-driven receivers are most suitable for systems where the underlying channel models are poorly understood, highly complex, or do not well-capture the underlying physics. Our approach is unique in that it only replaces the channel-model-based computations with dedicated neural networks that can be trained from a small amount of data, while keeping the general algorithm intact. Our results demonstrate that these techniques can yield near-optimal performance of model-based algorithms without knowing the exact channel input-output statistical relationship and in the presence of channel state information uncertainty. I. INTRODUCTION In digital communication systems, the receiver is required to reliably recover the transmitted symbols from the observed channel output. This task is commonly referred to as symbol detection. Conventional symbol detection algorithms, such as those based on the maximum a-posteriori probability (MAP) rule, require complete knowledge of the underlying channel model and its parameters [1], [2]. This work was supported in part by the US - Israel Binational Science Foundation under grant No. 2026094, by the Israel Science Foundation under grant No. 0100101, and by the Office of the Naval Research under grant No. 18-1-2191. N. Shlezinger and Y. C. Eldar are with the Faculty of Math and CS, Weizmann Institute of Science, Rehovot, Israel (email: nirshlezinger1@gmail.com; yonina@weizmann.ac.il). Furthermore, when the channel models are known, many detection algorithms rely on channel state information (CSI), i.e., the instantaneous parameters of the channel model, for detection. Therefore, conventional channel-model-based techniques require the instantaneous CSI to be estimated.

We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model's log-density. We estimate the Stein discrepancy between the data density p(x) and the model density q(x) defined by a vector function of the data. We parameterize this function with a neural network and fit its parameters to maximize the discrepancy. This yields a novel goodness-of-fit test which outperforms existing methods on high dimensional data. Furthermore, optimizing $q(x)$ to minimize this discrepancy produces a novel method for training unnormalized models which scales more gracefully than existing methods. The ability to both learn and compare models is a unique feature of the proposed method.

This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions. We assume that the number of components $k$ is bounded and that the centers lie in a ball of bounded radius, while allowing the dimension $d$ to be as large as the sample size $n$. Extending the one-dimensional result of Heinrich and Kahn \cite{HK2015}, we show that the minimax rate of estimating the mixing distribution in Wasserstein distance is $\Theta((d/n)^{1/4} + n^{-1/(4k-2)})$, achieved by an estimator computable in time $O(nd^2+n^{5/4})$. Furthermore, we show that the mixture density can be estimated at the optimal parametric rate $\Theta(\sqrt{d/n})$ in Hellinger distance; however, no computationally efficient algorithm is known to achieve the optimal rate. Both the theoretical and methodological development rely on a careful application of the method of moments. Central to our results is the observation that the information geometry of finite Gaussian mixtures is characterized by the moment tensors of the mixing distribution, whose low-rank structure can be exploited to obtain a sharp local entropy bound.

In this paper, we study the problem of sampling from distributions of the form p(x) \propto e^{-\beta f(x)} for some function f whose values and gradients we can query. This mode of access to f is natural in the scenarios in which such problems arise, for instance sampling from posteriors in parametric Bayesian models. Classical results show that a natural random walk, Langevin diffusion, mixes rapidly when f is convex. Unfortunately, even in simple examples, the applications listed above will entail working with functions f that are nonconvex -- for which sampling from p may in general require an exponential number of queries. In this paper, we study one aspect of nonconvexity relevant for modern machine learning applications: existence of invariances (symmetries) in the function f, as a result of which the distribution p will have manifolds of points with equal probability. We give a recipe for proving mixing time bounds of Langevin dynamics in order to sample from manifolds of local optima of the function f in settings where the distribution is well-concentrated around them. We specialize our arguments to classic matrix factorization-like Bayesian inference problems where we get noisy measurements A(XX^T), X \in R^{d \times k} of a low-rank matrix, i.e. f(X) = \|A(XX^T) - b\|^2_2, X \in R^{d \times k}, and \beta the inverse of the variance of the noise. Such functions f are invariant under orthogonal transformations, and include problems like matrix factorization, sensing, completion. Beyond sampling, Langevin dynamics is a popular toy model for studying stochastic gradient descent. Along these lines, we believe that our work is an important first step towards understanding how SGD behaves when there is a high degree of symmetry in the space of parameters the produce the same output.

Meta-learning can successfully acquire useful inductive biases from data, especially when a large number of meta-tasks are available. Yet, its generalization properties to unseen tasks are poorly understood. Particularly if the number of meta-tasks is small, this raises concerns for potential overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning with unbounded loss functions and Bayesian base learners. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-regularization. When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes as base learners, the resulting approach consistently outperforms several popular meta-learning methods, both in terms of predictive accuracy and the quality of its uncertainty estimates.

Companies may be achieving only a third of the value they could be getting from data science in industry applications. In this paper, we propose a methodology for categorizing and answering 'The Big Three' questions (what is going on, what is causing it, and what actions can I take that will optimize what I care about) using data science. The applications of data science seem to be nearly endless in today's modern landscape, with each company jockeying for position in the new data and insights economy. Yet, data scientists seem to be solely focused on using classification, regression, and clustering methods to answer the question 'what is going on'. Answering questions about why things are happening or how to take optimal actions to improve metrics are relegated to niche fields of research and generally neglected in industry data science analysis. We survey technical methods to answer these other important questions, describe areas in which some of these methods are being applied, and provide a practical example of how to apply our methodology and selected methods to a real business use case.

Causal models could increase interpretability, robustness to distributional shift and sample efficiency of RL agents. In this vein, we address the question of learning a causal model of an RL environment. This problem is known to be difficult due to spurious correlations. We overcome this difficulty by rewarding an RL agent for designing and executing interventions to discover the true model. We compare rewarding the agent for disproving uncertain edges in the causal graph, rewarding the agent for activating a certain node, or rewarding the agent for increasing the causal graph loss. We show that our methods result in a better causal graph than one generated by following the random policy, or a policy trained on the environment's reward. We find that rewarding for the causal graph loss works the best.

Effective decision making requires understanding the uncertainty inherent in a prediction. To estimate uncertainty in regression, one could modify a deep neural network to predict coverage intervals, such as by predicting the mean and standard deviation. Unfortunately, in our empirical evaluations the predicted coverage from existing approaches is either overconfident or lacks sharpness (gives imprecise intervals). To address this challenge, we propose a novel method to estimate uncertainty based on two distinct neural networks with two distinct loss functions in a similar vein to Generative Adversarial Networks. Specifically, one network tries to learn the cumulative distribution function, and the second network tries to learn its inverse. Theoretical analysis demonstrates that the idealized solution is a fixed point and that under certain conditions the approach is asymptotically consistent to ground truth. We benchmark the approach on one synthetic and five real-world datasets, including forecasting A1c values in diabetic patients from electronic health records, where uncertainty is critical. In synthetic data, the proposed approach essentially matches the theoretically optimal solution in all aspects. In the real datasets, the proposed approach is empirically more faithful in its coverage estimates and typically gives sharper intervals than competing methods.

In this work, we propose learnable Bernoulli dropout (LBD), a new model-agnostic dropout scheme that considers the dropout rates as parameters jointly optimized with other model parameters. By probabilistic modeling of Bernoulli dropout, our method enables more robust prediction and uncertainty quantification in deep models. Especially, when combined with variational auto-encoders (VAEs), LBD enables flexible semi-implicit posterior representations, leading to new semi-implicit VAE~(SIVAE) models. We solve the optimization for training with respect to the dropout parameters using Augment-REINFORCE-Merge (ARM), an unbiased and low-variance gradient estimator. Our experiments on a range of tasks show the superior performance of our approach compared with other commonly used dropout schemes. Overall, LBD leads to improved accuracy and uncertainty estimates in image classification and semantic segmentation. Moreover, using SIVAE, we can achieve state-of-the-art performance on collaborative filtering for implicit feedback on several public datasets.

Network congestion games are a well-understood model of multi-agent strategic interactions. Despite their ubiquitous applications, it is not clear whether it is possible to design information structures to ameliorate the overall experience of the network users. We focus on Bayesian games with atomic players, where network vagaries are modeled via a (random) state of nature which determines the costs incurred by the players. A third-party entity---the sender---can observe the realized state of the network and exploit this additional information to send a signal to each player. A natural question is the following: is it possible for an informed sender to reduce the overall social cost via the strategic provision of information to players who update their beliefs rationally? The paper focuses on the problem of computing optimal ex ante persuasive signaling schemes, showing that symmetry is a crucial property for its solution. Indeed, we show that an optimal ex ante persuasive signaling scheme can be computed in polynomial time when players are symmetric and have affine cost functions. Moreover, the problem becomes NP-hard when players are asymmetric, even in non-Bayesian settings.