Learning optimal dynamic treatment rules, or sequential policies for taking actions, is important, although often only observational data is available. Many recent works in offline reinforcement learning develop methodology to evaluate and optimize sequential decision rules, without the ability to conduct online exploration. An extensive literature on causal inference and machine learning establishes methodologies for learning causal contrasts, such as the conditional average treatment effect (CATE) (Wager and Athey, 2018; Foster and Syrgkanis, 2019; Künzel et al., 2019; Kennedy, 2020), which is sufficient for making optimal decisions. Methods that specifically estimate causal contrasts (such as the CATE), can better adapt to potentially smoother or more structured contrast functions, while methods that instead contrast estimates (by taking the difference of outcome regressions or Q functions) can not. Additionally, estimation of causal contrasts can be improved via orthogonalization or double machine learning (Kennedy, 2022; Chernozhukov et al., 2018). Estimating the causal contrast is both sufficient for optimal decisions and statistically favorable.

Multi-task learning (MTL) is a powerful machine learning paradigm designed to leverage shared knowledge across tasks to improve generalization and performance. Previous works have proposed approaches to MTL that can be divided into feature learning, focused on the identification of a common feature representation, and task clustering, where similar tasks are grouped together. In this paper, we propose an MTL approach at the intersection between task clustering and feature transformation based on a two-phase iterative aggregation of targets and features. First, we propose a bias-variance analysis for regression models with additive Gaussian noise, where we provide a general expression of the asymptotic bias and variance of a task, considering a linear regression trained on aggregated input features and an aggregated target. Then, we exploit this analysis to provide a two-phase MTL algorithm (NonLinCTFA). Firstly, this method partitions the tasks into clusters and aggregates each obtained group of targets with their mean. Then, for each aggregated task, it aggregates subsets of features with their mean in a dimensionality reduction fashion. In both phases, a key aspect is to preserve the interpretability of the reduced targets and features through the aggregation with the mean, which is further motivated by applications to Earth science. Finally, we validate the algorithms on synthetic data, showing the effect of different parameters and real-world datasets, exploring the validity of the proposed methodology on classical datasets, recent baselines, and Earth science applications.

Within the field of optimal transport (OT), the choice of ground cost is crucial to ensuring that the optimality of a transport map corresponds to usefulness in real-world applications. It is therefore desirable to use known information to tailor cost functions and hence learn OT maps which are adapted to the problem at hand. By considering a class of neural ground costs whose Monge maps have a known form, we construct a differentiable Monge map estimator which can be optimized to be consistent with known information about an OT map. In doing so, we simultaneously learn both an OT map estimator and a corresponding adapted cost function. Through suitable choices of loss function, our method provides a general approach for incorporating prior information about the Monge map itself when learning adapted OT maps and cost functions.

While it is commonly observed in practice that pruning networks to a certain level of sparsity can improve the quality of the features, a theoretical explanation of this phenomenon remains elusive. In this work, we investigate this by demonstrating that a broad class of statistical models can be optimally learned using pruned neural networks trained with gradient descent, in high-dimensions. We consider learning both single-index and multi-index models of the form $y = \sigma^*(\boldsymbol{V}^{\top} \boldsymbol{x}) + \epsilon$, where $\sigma^*$ is a degree-$p$ polynomial, and $\boldsymbol{V} \in \mathbbm{R}^{d \times r}$ with $r \ll d$, is the matrix containing relevant model directions. We assume that $\boldsymbol{V}$ satisfies a certain $\ell_q$-sparsity condition for matrices and show that pruning neural networks proportional to the sparsity level of $\boldsymbol{V}$ improves their sample complexity compared to unpruned networks. Furthermore, we establish Correlational Statistical Query (CSQ) lower bounds in this setting, which take the sparsity level of $\boldsymbol{V}$ into account. We show that if the sparsity level of $\boldsymbol{V}$ exceeds a certain threshold, training pruned networks with a gradient descent algorithm achieves the sample complexity suggested by the CSQ lower bound. In the same scenario, however, our results imply that basis-independent methods such as models trained via standard gradient descent initialized with rotationally invariant random weights can provably achieve only suboptimal sample complexity.

A client device which has access to $n$ training data samples needs to obtain a statistical hypothesis or model $W$ and then to send it to a remote server. The client and the server devices share some common randomness sequence as well as a prior on the hypothesis space. In this problem a suitable hypothesis or model $W$ should meet two distinct design criteria simultaneously: (i) small (population) risk during the inference phase and (ii) small 'complexity' for it to be conveyed to the server with minimum communication cost. In this paper, we propose a joint training and source coding scheme with provable in-expectation guarantees, where the expectation is over the encoder's output message. Specifically, we show that by imposing a constraint on a suitable Kullback-Leibler divergence between the conditional distribution induced by a compressed learning model $\widehat{W}$ given $W$ and the prior, one guarantees simultaneously small average empirical risk (aka training loss), small average generalization error and small average communication cost. We also consider a one-shot scenario in which the guarantees on the empirical risk and generalization error are obtained for every encoder's output message.

Monte Carlo methods, Variational Inference, and their combinations play a pivotal role in sampling from intractable probability distributions. However, current studies lack a unified evaluation framework, relying on disparate performance measures and limited method comparisons across diverse tasks, complicating the assessment of progress and hindering the decision-making of practitioners. In response to these challenges, our work introduces a benchmark that evaluates sampling methods using a standardized task suite and a broad range of performance criteria. Moreover, we study existing metrics for quantifying mode collapse and introduce novel metrics for this purpose. Our findings provide insights into strengths and weaknesses of existing sampling methods, serving as a valuable reference for future developments. The code is publicly available here.

This paper reviews our previous trials of Nudge-XAI, an approach that introduces automatic biases into explanations from explainable AIs (XAIs) with the aim of leading users to better decisions, and it discusses the benefits and challenges. Nudge-XAI uses a user model that predicts the influence of providing an explanation or emphasizing it and attempts to guide users toward AI-suggested decisions without coercion. The nudge design is expected to enhance the autonomy of users, reduce the risk associated with an AI making decisions without users' full agreement, and enable users to avoid AI failures. To discuss the potential of Nudge-XAI, this paper reports a post-hoc investigation of previous experimental results using cluster analysis. The results demonstrate the diversity of user behavior in response to Nudge-XAI, which supports our aim of enhancing user autonomy. However, it also highlights the challenge of users who distrust AI and falsely make decisions contrary to AI suggestions, suggesting the need for personalized adjustment of the strength of nudges to make this approach work more generally.

In this paper, we study cascading failures in power grids through the lens of information diffusion models. Similar to the spread of rumors or influence in an online social network, it has been observed that failures (outages) in a power grid can spread contagiously, driven by viral spread mechanisms. We employ a stochastic diffusion model that is Markovian (memoryless) and local (the activation of one node, i.e., transmission line, can only be caused by its neighbors). Our model integrates viral diffusion principles with physics-based concepts, by correlating the diffusion weights (contagion probabilities between transmission lines) with the hyperparametric Information Cascades (IC) model. We show that this diffusion model can be learned from traces of cascading failures, enabling accurate modeling and prediction of failure propagation. This approach facilitates actionable information through well-understood and efficient graph analysis methods and graph diffusion simulations. Furthermore, by leveraging the hyperparametric model, we can predict diffusion and mitigate the risks of cascading failures even in unseen grid configurations, whereas existing methods falter due to a lack of training data. Extensive experiments based on a benchmark power grid and simulations therein show that our approach effectively captures the failure diffusion phenomena and guides decisions to strengthen the grid, reducing the risk of large-scale cascading failures. Additionally, we characterize our model's sample complexity, improving upon the existing bound.

This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce the notion of unreliability in regression, i.e., when the output of the regressor exceeds a specified discrepancy (or error). Then, using powerful tools for probabilistic modeling, we estimate the discrepancy density, and we measure its statistical diversity using our proposed metric for statistical dissimilarity. In turn, this allows us to derive a data-driven score that expresses the uncertainty of the regression outcome. We show empirical improvements in error detection for multiple regression tasks, consistently outperforming popular baseline approaches, and contributing to the broader field of uncertainty quantification and safe machine learning systems. Our code is available at https://zenodo.org/records/11281964.

Writing mathematical proofs has been identified as an important [1-3] and yet challenging topic [4] in computing education and mathematics education. A large body of research has shown that timely feedback is crucial to student learning [5, 6]. However, students are largely unable to receive timely feedback on written proofs due to the need to have proofs collected and hand-graded by instructors or teaching assistants. The ability to grade student proofs fully automatically with natural language processing (NLP) alleviates this need by allowing us to give students instant feedback on their proofs to let students iteratively enhance the quality of their proofs. In this paper, we propose a novel set of training methods and models capable of autograding freeform mathematical proofs, a problem at the intersection of mathematical proof education and Automatic Short Answer Grading (ASAG), by using existing NLP models and other machine learning techniques. Our proof autograder enables the development of grading systems that provide instant feedback to students without needing attention from instructors. It can also be deployed in large-scale educational platforms, allowing for more access for students. The main contributions of this paper are: Introducing the first pipeline of machine learning models capable of autograding mathematical proofs with similar accuracy to human graders Quantifying the amount of training data needed to achieve a satisfactory performance from the grading models Publishing an anonymized and labeled mathematical proof dataset that can be used in future model developments [7] Creating a set of autograded problems using the grading pipeline, and performing a user study that answers the following research questions: - Are students able to write better proofs by interacting with the autograder and the feedback it generates?