Concurrently advances in causal modelling has led to a better understanding of how to predict complex systems when these are subjected to control. A major breakthrough then occurred about 20 years ago when it was then discovered that causal and graphical modelling could be combined. This paper reports on how the combination of these two technologies are being applied to give more insights concerning causal hypotheses that relate specially to reliability and system safety. Of course causal ideas have been embedded within reliability theory for a long time, both to explore the reasons behind a failure and to also estimate the efficacy of various interventions in the system that might ameliorate adverse outcomes. However, the graphical frameworks around which these ideas appear have been tree like - for example fault trees or event chains (Leverson 2011) - rather than the most common graphical framework for analyzing causation: the BN. Only recently have graphical causal methods emerged for methodologies and algorithms to exist for causal discovery and causal reasoning on such tree structures. The primary such graph is the chain event graph (CEG), see Thwaites, Smith and Riccomagno (2010), Barclay, Hutton and Smith (2013) and Collazo et.

This paper is concerned with data-driven unsupervised domain adaptation, where it is unknown in advance how the joint distribution changes across domains, i.e., what factors or modules of the data distribution remain invariant or change across domains. To develop an automated way of domain adaptation with multiple source domains, we propose to use a graphical model as a compact way to encode the change property of the joint distribution, which can be learned from data, and then view domain adaptation as a problem of Bayesian inference on the graphical models. Such a graphical model distinguishes between constant and varied modules of the distribution and specifies the properties of the changes across domains, which serves as prior knowledge of the changing modules for the purpose of deriving the posterior of the target variable $Y$ in the target domain. This provides an end-to-end framework of domain adaptation, in which additional knowledge about how the joint distribution changes, if available, can be directly incorporated to improve the graphical representation. We discuss how causality-based domain adaptation can be put under this umbrella. Experimental results on both synthetic and real data demonstrate the efficacy of the proposed framework for domain adaptation.

According to the goal-gradient hypothesis, people increase their efforts toward a reward as they close in on the reward. This hypothesis has recently been used to explain users' behavior in online communities that use badges as rewards for completing specific activities. In such settings, users exhibit a "steering effect," a dramatic increase in activity as the users approach a badge threshold, thereby following the predictions made by the goal-gradient hypothesis. This paper provides a new probabilistic model of users' behavior, which captures users who exhibit different levels of steering. We apply this model to data from the popular Q&A site, Stack Overflow, and study users who achieve one of the badges available on this platform. Our results show that only a fraction (20%) of all users strongly experience steering, whereas the activity of more than 40% of badge achievers appears not to be affected by the badge. In particular, we find that for some of the population, an increased activity in and around the badge acquisition date may reflect a statistical artifact rather than steering, as was previously thought in prior work. These results are important for system designers who hope to motivate and guide their users towards certain actions. We have highlighted the need for further studies which investigate what motivations drive the non-steered users to contribute to online communities.

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.

Most work in algorithmic fairness to date has focused on discrete outcomes, such as deciding whether to grant someone a loan or not. In these classification settings, group fairness criteria such as independence, separation and sufficiency can be measured directly by comparing rates of outcomes between subpopulations. Many important problems however require the prediction of a real-valued outcome, such as a risk score or insurance premium. In such regression settings, measuring group fairness criteria is computationally challenging, as it requires estimating information-theoretic divergences between conditional probability density functions. This paper introduces fast approximations of the independence, separation and sufficiency group fairness criteria for regression models from their (conditional) mutual information definitions, and uses such approximations as regularisers to enforce fairness within a regularised risk minimisation framework. Experiments in real-world datasets indicate that in spite of its superior computational efficiency our algorithm still displays state-of-the-art accuracy/fairness tradeoffs.

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.

In recent years there has been a push to integrate symbolic AI and deep learning, as it is argued that the strengths and weaknesses of these approaches are complementary. One such trend in the literature are weakly supervised learning techniques that use operators from fuzzy logics. They employ prior background knowledge described in logic to benefit the training of a neural network from unlabeled and noisy data. By interpreting logical symbols using neural networks, this background knowledge can be added to regular loss functions used in deep learning to integrate reasoning and learning. In this paper, we analyze how a large collection of logical operators from the fuzzy logic literature behave in a differentiable setting. We find large differences between the formal properties of these operators that are of crucial importance in a differentiable learning setting. We show that many of these operators, including some of the best known, are highly unsuitable for use in a differentiable learning setting. A further finding concerns the treatment of implication in these fuzzy logics, with a strong imbalance between gradients driven by the antecedent and the consequent of the implication. Finally, we empirically show that it is possible to use Differentiable Fuzzy Logics for semi-supervised learning. However, to achieve the most significant performance improvement over a supervised baseline, we have to resort to non-standard combinations of logical operators which perform well in learning, but which no longer satisfy the usual logical laws. We end with a discussion on extensions to large-scale problems.

The continuous expansion of the urban traffic sensing infrastructure has led to a surge in the volume of widely available road related data. Consequently, increasing effort is being dedicated to the creation of intelligent transportation systems, where decisions on issues ranging from city-wide road maintenance planning to improving the commuting experience are informed by computational models of urban traffic instead of being left entirely to humans. The automation of traffic management has received substantial attention from the research community, however, most approaches target highways, produce predictions valid for a limited time window or require expensive retraining of available models in order to accurately forecast traffic at a new location. In this article, we propose a novel and accurate traffic flow prediction method based on symbolic regression enhanced with a lag operator. Our approach produces robust models suitable for the intricacies of urban roads, much more difficult to predict than highways. Additionally, there is no need to retrain the model for a period of up to 9 weeks. Furthermore, the proposed method generates models that are transferable to other segments of the road network, similar to, yet geographically distinct from the ones they were initially trained on. We demonstrate the achievement of these claims by conducting extensive experiments on data collected from the Darmstadt urban infrastructure.

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.