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In this paper, we consider several efficient data structures for the problem of sampling from a dynamically changing discrete probability distribution, where some prior information is known on the distribution of the rates, in particular the maximum and minimum rate, and where the number of possible outcomes N is large. We consider three basic data structures, the Acceptance-Rejection method, the Complete Binary Tree and the Alias method. These can be used as building blocks in a multi-level data structure, where at each of the levels, one of the basic data structures can be used, with the top level selecting a group of events, and the bottom level selecting an element from a group. Depending on assumptions on the distribution of the rates of outcomes, different combinations of the basic structures can be used. We prove that for particular data structures the expected time of sampling and update is constant when the rate distribution follows certain conditions. We show that for any distribution, combining a tree structure with the Acceptance-Rejection method, we have an expected time of sampling and update of $O\left(\log\log{r_{max}}/{r_{min}}\right)$ is possible, where $r_{max}$ is the maximum rate and $r_{min}$ the minimum rate. We also discuss an implementation of a Two Levels Acceptance-Rejection data structure, that allows expected constant time for sampling, and amortized constant time for updates, assuming that $r_{max}$ and $r_{min}$ are known and the number of events is sufficiently large. We also present an experimental verification, highlighting the limits given by the constraints of a real-life setting.

Prescriptive process monitoring is a family of techniques to optimize the performance of a business process by triggering interventions at runtime. Existing prescriptive process monitoring techniques assume that the number of interventions that may be triggered is unbounded. In practice, though, specific interventions consume resources with finite capacity. For example, in a loan origination process, an intervention may consist of preparing an alternative loan offer to increase the applicant's chances of taking a loan. This intervention requires a certain amount of time from a credit officer, and thus, it is not possible to trigger this intervention in all cases. This paper proposes a prescriptive process monitoring technique that triggers interventions to optimize a cost function under fixed resource constraints. The proposed technique relies on predictive modeling to identify cases that are likely to lead to a negative outcome, in combination with causal inference to estimate the effect of an intervention on the outcome of the case. These outputs are then used to allocate resources to interventions to maximize a cost function. A preliminary empirical evaluation suggests that the proposed approach produces a higher net gain than a purely predictive (non-causal) baseline.

This paper revisits the temporal difference (TD) learning algorithm for the policy evaluation tasks in reinforcement learning. Typically, the performance of TD(0) and TD($\lambda$) is very sensitive to the choice of stepsizes. Oftentimes, TD(0) suffers from slow convergence. Motivated by the tight link between the TD(0) learning algorithm and the stochastic gradient methods, we develop a provably convergent adaptive projected variant of the TD(0) learning algorithm with linear function approximation that we term AdaTD(0). In contrast to the TD(0), AdaTD(0) is robust or less sensitive to the choice of stepsizes. Analytically, we establish that to reach an $\epsilon$ accuracy, the number of iterations needed is $\tilde{O}(\epsilon^{-2}\ln^4\frac{1}{\epsilon}/\ln^4\frac{1}{\rho})$ in the general case, where $\rho$ represents the speed of the underlying Markov chain converges to the stationary distribution. This implies that the iteration complexity of AdaTD(0) is no worse than that of TD(0) in the worst case. When the stochastic semi-gradients are sparse, we provide theoretical acceleration of AdaTD(0). Going beyond TD(0), we develop an adaptive variant of TD($\lambda$), which is referred to as AdaTD($\lambda$). Empirically, we evaluate the performance of AdaTD(0) and AdaTD($\lambda$) on several standard reinforcement learning tasks, which demonstrate the effectiveness of our new approaches.

Approximating complex probability densities is a core problem in modern statistics. In this paper, we introduce the concept of Variational Inference (VI), a popular method in machine learning that uses optimization techniques to estimate complex probability densities. This property allows VI to converge faster than classical methods, such as, Markov Chain Monte Carlo sampling. Conceptually, VI works by choosing a family of probability density functions and then finding the one closest to the actual probability density -- often using the Kullback-Leibler (KL) divergence as the optimization metric. We introduce the Evidence Lower Bound to tractably compute the approximated probability density and we review the ideas behind mean-field variational inference. Finally, we discuss the applications of VI to variational auto-encoders (VAE) and VAE-Generative Adversarial Network (VAE-GAN). With this paper, we aim to explain the concept of VI and assist in future research with this approach.

We develop a post-selective Bayesian framework to jointly and consistently estimate parameters in group-sparse linear regression models. After selection with the Group LASSO (or generalized variants such as the overlapping, sparse, or standardized Group LASSO), uncertainty estimates for the selected parameters are unreliable in the absence of adjustments for selection bias. Existing post-selective approaches are limited to uncertainty estimation for (i) real-valued projections onto very specific selected subspaces for the group-sparse problem, (ii) selection events categorized broadly as polyhedral events that are expressible as linear inequalities in the data variables. Our Bayesian methods address these gaps by deriving a likelihood adjustment factor, and an approximation thereof, that eliminates bias from selection. Paying a very nominal price for this adjustment, experiments on simulated data, and data from the Human Connectome Project demonstrate the efficacy of our methods for a joint estimation of group-sparse parameters and their uncertainties post selection.

A fundamental goal of scientific research is to learn about causal relationships. However, despite its critical role in the life and social sciences, causality has not had the same importance in Natural Language Processing (NLP), which has traditionally placed more emphasis on predictive tasks. This distinction is beginning to fade, with an emerging area of interdisciplinary research at the convergence of causal inference and language processing. Still, research on causality in NLP remains scattered across domains without unified definitions, benchmark datasets and clear articulations of the remaining challenges. In this survey, we consolidate research across academic areas and situate it in the broader NLP landscape. We introduce the statistical challenge of estimating causal effects, encompassing settings where text is used as an outcome, treatment, or as a means to address confounding. In addition, we explore potential uses of causal inference to improve the performance, robustness, fairness, and interpretability of NLP models. We thus provide a unified overview of causal inference for the computational linguistics community.

Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale datasets. Among the possible strategies to alleviate this issue, practitioners can rely on computing estimates of these distances over subsets of data, {\em i.e.} minibatches. While computationally appealing, we highlight in this paper some limits of this strategy, arguing it can lead to undesirable smoothing effects. As an alternative, we suggest that the same minibatch strategy coupled with unbalanced optimal transport can yield more robust behavior. We discuss the associated theoretical properties, such as unbiased estimators, existence of gradients and concentration bounds. Our experimental study shows that in challenging problems associated to domain adaptation, the use of unbalanced optimal transport leads to significantly better results, competing with or surpassing recent baselines.

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.

We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.

In this paper, we propose to tackle the problem of reducing discrepancies between multiple domains referred to as multi-source domain adaptation and consider it under the target shift assumption: in all domains we aim to solve a classification problem with the same output classes, but with labels' proportions differing across them. We design a method based on optimal transport, a theory that is gaining momentum to tackle adaptation problems in machine learning due to its efficiency in aligning probability distributions. Our method performs multi-source adaptation and target shift correction simultaneously by learning the class probabilities of the unlabeled target sample and the coupling allowing to align two (or more) probability distributions. Experiments on both synthetic and real-world data related to satellite image segmentation task show the superiority of the proposed method over the state-of-the-art.