Using offline observational data for policy evaluation and learning allows decision-makers to evaluate and learn a policy that connects characteristics and interventions. Most existing literature has focused on either discrete treatment spaces or assumed no difference in the distributions between the policy-learning and policy-deployed environments. These restrict applications in many real-world scenarios where distribution shifts are present with continuous treatment. To overcome these challenges, this paper focuses on developing a distributionally robust policy under a continuous treatment setting. The proposed distributionally robust estimators are established using the Inverse Probability Weighting (IPW) method extended from the discrete one for policy evaluation and learning under continuous treatments. Specifically, we introduce a kernel function into the proposed IPW estimator to mitigate the exclusion of observations that can occur in the standard IPW method to continuous treatments. We then provide finite-sample analysis that guarantees the convergence of the proposed distributionally robust policy evaluation and learning estimators. The comprehensive experiments further verify the effectiveness of our approach when distribution shifts are present.

Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time series often suffer from temporal irregularities, including nonuniform intervals and misaligned variables, which pose significant challenges for accurate forecasting. To address these challenges, we propose an end-to-end framework that models temporal irregularities while capturing the joint distribution of variables at arbitrary continuous-time points. Specifically, we introduce a dynamic conditional continuous normalizing flow to model data distributions in a non-parametric manner, accommodating the complex, non-Gaussian characteristics commonly found in real-world datasets. Then, by leveraging a carefully factorized log-likelihood objective, our approach captures both temporal and cross-sectional dependencies efficiently. Extensive experiments on a range of real-world datasets demonstrate the superiority and adaptability of our method compared to existing approaches.

Consumer credit services offered by electronic commerce platforms provide customers with convenient loan access during shopping and have the potential to stimulate sales. To understand the causal impact of credit lines on spending, previous studies have employed causal estimators, (e.g., direct regression (DR), inverse propensity weighting (IPW), and double machine learning (DML)) to estimate the treatment effect. However, these estimators do not treat the spending of each individual as a distribution that can capture the range and pattern of amounts spent across different orders. By disregarding the outcome as a distribution, valuable insights embedded within the outcome distribution might be overlooked. This paper thus develops distribution valued estimators which extend from existing real valued DR, IPW, and DML estimators within Rubin’s causal framework. We establish their consistency and apply them to a real dataset from a large electronic commerce platform. Our findings reveal that credit lines generally have a positive impact on spending across all quantiles, but consumers would allocate more to luxuries (higher quantiles) than necessities (lower quantiles) as credit lines increase.

The growing demand for personalized decision-making has led to a surge of interest in estimating the Conditional Average Treatment Effect (CATE). Various types of CATE estimators have been developed with advancements in machine learning and causal inference. However, selecting the desirable CATE estimator through a conventional model validation procedure remains impractical due to the absence of counterfactual outcomes in observational data. Existing approaches for CATE estimator selection, such as plug-in and pseudo-outcome metrics, face two challenges. First, they must determine the metric form and the underlying machine learning models for fitting nuisance parameters (e.g., outcome function, propensity function, and plug-in learner). Second, they lack a specific focus on selecting a robust CATE estimator. To address these challenges, this paper introduces a Distributionally Robust Metric (DRM) for CATE estimator selection. The proposed DRM is nuisance-free, eliminating the need to fit models for nuisance parameters, and it effectively prioritizes the selection of a distributionally robust CATE estimator. The experimental results validate the effectiveness of the DRM method in selecting CATE estimators that are robust to the distribution shift incurred by covariate shift and hidden confounders.

Subset selection, i.e., finding a bunch of items from a collection to achieve specific goals, has wide applications in information retrieval, statistics, and machine learning. To implement an end-to-end learning framework, different relaxed differentiable operators of subset selection are proposed. Most existing work relies on either the regularization method or the perturbation method. In this work, we provide a probabilistic interpretation for regularization relaxation and unify two schemes. Besides, we build some concrete examples to show the generic connection between these two relaxations. Finally, we evaluate the perturbed selector as well as the regularized selector on two tasks: the maximum entropy sampling problem and the feature selection problem. The experimental results show that these two methods can achieve competitive performance against other benchmarks.

Time series forecasting is prevalent in various real-world applications. Despite the promising results of deep learning models in time series forecasting, especially the Recurrent Neural Networks (RNNs), the explanations of time series models, which are critical in high-stakes applications, have received little attention. In this paper, we propose a Decomposition-based Linear Explainable LSTM (DeLELSTM) to improve the interpretability of LSTM. Conventionally, the interpretability of RNNs only concentrates on the variable importance and time importance. We additionally distinguish between the instantaneous influence of new coming data and the long-term effects of historical data. Specifically, DeLELSTM consists of two components, i.e., standard LSTM and tensorized LSTM. The tensorized LSTM assigns each variable with a unique hidden state making up a matrix h(t), and the standard LSTM models all the variables with a shared hidden state H(t). By decomposing the H(t) into the linear combination of past information h(t-1) and the fresh information h(t)-h(t-1), we can get the instantaneous influence and the long-term effect of each feature. In addition, the advantage of linear regression also makes the explanation transparent and clear. We demonstrate the effectiveness and interpretability of DeLELSTM on three empirical datasets. Extensive experiments show that the proposed method achieves competitive performance against the baseline methods and provides a reliable explanation relative to domain knowledge.