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We derive criteria for the selection of datapoints used for data-driven reduced-order modeling and other areas of supervised learning based on Gaussian process regression (GPR). While this is a well-studied area in the fields of active…

Restricted Isometry Property (RIP) is of fundamental importance in the theory of compressed sensing and forms the base of many exact and robust recovery guarantees in this field. A quantitative description of RIP involves bounding the…

Deep reinforcement learning (DRL) is one of the promising approaches for introducing robots into complicated environments. The recent remarkable progress of DRL stands on regularization of policy, which allows the policy to improve stably…

The class of direct preference optimization (DPO) algorithms has emerged as a promising approach for solving the alignment problem in foundation models. These algorithms work with very limited feedback in the form of pairwise preferences…

Motivated by the success of Sinkhorn's algorithm for entropic optimal transport, we study convergence properties of iterative proportional fitting procedures (IPFP) used to solve more general information projection problems. We establish…

The application of rough set theory in incomplete information systems is a key problem in practice since missing values almost always occur in knowledge acquisition due to the error of data measuring, the limitation of data collection, or…

Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…

This paper introduces a new property of estimators of the strength of statistical association, which helps characterize how well an estimator will perform in scenarios where dependencies between continuous and discrete random variables need…

The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…

Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this work, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating…

Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy that best fits observed sequences of states and actions implemented by an expert. Many algorithms for IRL have an inherently nested…

The safe application of reinforcement learning (RL) requires generalization from limited training data to unseen scenarios. Yet, fulfilling tasks under changing circumstances is a key challenge in RL. Current state-of-the-art approaches for…

Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…

Post-training with reinforcement learning (RL) has recently shown strong promise for advancing multimodal agents beyond supervised imitation. However, RL remains limited by poor data efficiency, particularly in settings where interaction…

Learning customer preferences from an observed behaviour is an important topic in the marketing literature. Structural models typically model forward-looking customers or firms as utility-maximizing agents whose utility is estimated using…

Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are…

We consider prophet inequalities under downward-closed constraints. In this problem, a decision-maker makes immediate and irrevocable choices on arriving elements, subject to constraints. Traditionally, performance is compared to the…

Group Relative Policy Optimization (GRPO), a prominent algorithm within the Reinforcement Learning from Verifiable Rewards (RLVR) framework, has achieved strong results in improving the reasoning capabilities of large language models…

Post-training LLMs with Reinforcement Learning, specifically Group Relative Policy Optimization (GRPO), has emerged as a paradigm for enhancing mathematical reasoning. However, standard GRPO relies on scalar correctness rewards that are…

This study reveals the inherent tolerance of contrastive learning (CL) towards sampling bias, wherein negative samples may encompass similar semantics (\eg labels). However, existing theories fall short in providing explanations for this…