Top Two algorithms arose as an adaptation of Thompson sampling to best arm identification in multi-armed bandit models [38], for parametric families of arms. They select the next arm to sample from by randomizing among two candidate arms, a leader and a challenger. Despite their good empirical performance, theoretical guarantees for fixed-confidence best arm identification have only been obtained when the arms are Gaussian with known variances. In this paper, we provide a general analysis of Top Two methods, which identifies desirable properties of the leader, the challenger, and the (possibly non-parametric) distributions of the arms. As a result, we obtain theoretically supported Top Two algorithms for best arm identification with bounded distributions. Our proof method demonstrates in particular that the sampling step used to select the leader inherited from Thompson sampling can be replaced by other choices, like selecting the empirical best arm.

Lately, there has been a surge in interest surrounding generative modeling of time series data. Most existing approaches are designed either to process short sequences or to handle long-range sequences. This dichotomy can be attributed to gradient issues with recurrent networks, computational costs associated with transformers, and limited expressiveness of state space models. Towards a unified generative model for varying-length time series, we propose in this work to transform sequences into images. By employing invertible transforms such as the delay embedding and the short-time Fourier transform, we unlock three main advantages: i) We can exploit advanced diffusion vision models; ii) We can remarkably process short-and long-range inputs within the same framework; and iii) We can harness recent and established tools proposed in the time series to image literature.

Conformal prediction is a powerful tool for uncertainty quantification, but its application to time-series data is constrained by the violation of the exchangeability assumption. Current solutions for time-series prediction typically operate in the output space and rely on manually selected weights to address distribution drift, leading to overly conservative predictions. To enable dynamic weight learning in the semantically rich latent space, we introduce a novel approach called Conformalized Time Series with Semantic Features (CT-SSF). CT-SSF utilizes the inductive bias in deep representation learning to dynamically adjust weights, prioritizing semantic features relevant to the current prediction. Theoretically, we show that CT-SSF surpasses previous methods defined in the output space. Experiments on synthetic and benchmark datasets demonstrate that CT-SSF significantly outperforms existing state-of-the-art (SOTA) conformal prediction techniques in terms of prediction efficiency while maintaining a valid coverage guarantee.

Student cognitive modeling (SCM) is a fundamental task in intelligent education, with applications ranging from personalized learning to educational resource allocation. By exploiting students' response logs, SCM aims to predict their exercise performance as well as estimate knowledge proficiency in a subject. Data mining approaches such as matrix factorization can obtain high accuracy in predicting student performance on exercises, but the knowledge proficiency is unknown or poorly estimated. The situation is further exacerbated if only sparse interactions exist between exercises and students (or knowledge concepts). To solve this dilemma, we root monotonicity (a fundamental psychometric theory on educational assessments) in a co-factorization framework and present an autoencoder-like nonnegative matrix co-factorization (AE-NMCF), which improves the accuracy of estimating the student's knowledge proficiency via an encoder-decoder learning pipeline. The resulting estimation problem is nonconvex with nonnegative constraints. We introduce a projected gradient method based on block coordinate descent with Lipschitz constants and guarantee the method's theoretical convergence. Experiments on several real-world data sets demonstrate the efficacy of our approach in terms of both performance prediction accuracy and knowledge estimation ability, when compared with existing student cognitive models.