Prediction sets can wrap around any ML model to cover unknown test outcomes with a guaranteed probability. Yet, it remains unclear how to use them optimally for downstream decision-making. Here, we propose a decision-theoretic framework that seeks to minimize the expected loss (risk) against a worst-case distribution consistent with the prediction set's coverage guarantee. We first characterize the minimax optimal policy for a fixed prediction set, showing that it balances the worst-case loss inside the set with a penalty for potential losses outside the set. Building on this, we derive the optimal prediction set construction that minimizes the resulting robust risk subject to a coverage constraint. Finally, we introduce Risk-Optimal Conformal Prediction (ROCP), a practical algorithm that targets these risk-minimizing sets while maintaining finite-sample distribution-free marginal coverage. Empirical evaluations on medical diagnosis and safety-critical decision-making tasks demonstrate that ROCP reduces critical mistakes compared to baselines, particularly when out-of-set errors are costly.

Semi-supervised learning (SSL) addresses the critical challenge of training accurate models when labeled data is scarce but unlabeled data is abundant. Graph-based SSL (GSSL) has emerged as a popular framework that captures data structure through graph representations. Classic graph SSL methods, such as Label Propagation and Label Spreading, aim to compute low-dimensional representations where points with the same labels are close in representation space. Although often effective, these methods can be suboptimal on data with complex label distributions. In our work, we develop AUC-spec, a graph approach that computes a low-dimensional representation that maximizes class separation. We compute this representation by optimizing the Area Under the ROC Curve (AUC) as estimated via the labeled points. We provide a detailed analysis of our approach under a product-of-manifold model, and show that the required number of labeled points for AUC-spec is polynomial in the model parameters. Empirically, we show that AUC-spec balances class separation with graph smoothness. It demonstrates competitive results on synthetic and real-world datasets while maintaining computational efficiency comparable to the field's classic and state-of-the-art methods.

Causal discovery is essential for advancing data-driven fields such as scientific AI and data analysis, yet existing approaches face significant time- and space-efficiency bottlenecks when scaling to large graphs. To address this challenge, we present CauScale, a neural architecture designed for efficient causal discovery that scales inference to graphs with up to 1000 nodes. CauScale improves time efficiency via a reduction unit that compresses data embeddings and improves space efficiency by adopting tied attention weights to avoid maintaining axis-specific attention maps. To keep high causal discovery accuracy, CauScale adopts a two-stream design: a data stream extracts relational evidence from high-dimensional observations, while a graph stream integrates statistical graph priors and preserves key structural signals. CauScale successfully scales to 500-node graphs during training, where prior work fails due to space limitations. Across testing data with varying graph scales and causal mechanisms, CauScale achieves 99.6% mAP on in-distribution data and 84.4% on out-of-distribution data, while delivering 4-13,000 times inference speedups over prior methods. Our project page is at https://github.com/OpenCausaLab/CauScale.

Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schrödinger bridge (SB) provide principled solutions, efficient SOC solvers like adjoint matching (AM), which excel in continuous domains, remain unexplored for discrete spaces. We bridge this gap by revealing that the core mechanism of AM is $\mathit{state}\text{-}\mathit{space~agnostic}$, and introduce $\mathbf{discrete~ASBS}$, a unified framework that extends AM and adjoint Schrödinger bridge sampler (ASBS) to discrete spaces. Theoretically, we analyze the optimality conditions of the discrete SB problem and its connection to SOC, identifying a necessary cyclic group structure on the state space to enable this extension. Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability.

Causal discovery from time series is a fundamental task in machine learning. However, its widespread adoption is hindered by a reliance on untestable causal assumptions and by the lack of robustness-oriented evaluation in existing benchmarks. To address these challenges, we propose CausalCompass, a flexible and extensible benchmark suite designed to assess the robustness of time-series causal discovery (TSCD) methods under violations of modeling assumptions. To demonstrate the practical utility of CausalCompass, we conduct extensive benchmarking of representative TSCD algorithms across eight assumption-violation scenarios. Our experimental results indicate that no single method consistently attains optimal performance across all settings. Nevertheless, the methods exhibiting superior overall performance across diverse scenarios are almost invariably deep learning-based approaches. We further provide hyperparameter sensitivity analyses to deepen the understanding of these findings. We also find, somewhat surprisingly, that NTS-NOTEARS relies heavily on standardized preprocessing in practice, performing poorly in the vanilla setting but exhibiting strong performance after standardization. Finally, our work aims to provide a comprehensive and systematic evaluation of TSCD methods under assumption violations, thereby facilitating their broader adoption in real-world applications. The code and datasets are available at https://github.com/huiyang-yi/CausalCompass.

Zero-shot diffusion posterior sampling offers a flexible framework for inverse problems by accommodating arbitrary degradation operators at test time, but incurs high computational cost due to repeated likelihood-guided updates. In contrast, previous amortized diffusion approaches enable fast inference by replacing likelihood-based sampling with implicit inference models, but at the expense of robustness to unseen degradations. We introduce an amortization strategy for diffusion posterior sampling that preserves explicit likelihood guidance by amortizing the inner optimization problems arising in variational diffusion posterior sampling. This accelerates inference for in-distribution degradations while maintaining robustness to previously unseen operators, thereby improving the trade-off between efficiency and flexibility in diffusion-based inverse problems.

Inference on the conditional mean function (CMF) is central to tasks from adaptive experimentation to optimal treatment assignment and algorithmic fairness auditing. In this work, we provide a novel asymptotic anytime-valid test for a CMF global null (e.g., that all conditional means are zero) and contrasts between CMFs, enabling experimenters to make high confidence decisions at any time during the experiment beyond a minimum sample size. We provide mild conditions under which our tests achieve (i) asymptotic type-I error guarantees, (i) power one, and, unlike past tests, (iii) optimal sample complexity relative to a Gaussian location testing. By inverting our tests, we show how to construct function-valued asymptotic confidence sequences for the CMF and contrasts thereof. Experiments on both synthetic and real-world data show our method is well-powered across various distributions while preserving the nominal error rate under continuous monitoring.

Recent research shows that Preference Alignment (PA) objectives act as divergence estimators between aligned (chosen) and unaligned (rejected) response distributions. In this work, we extend this divergence-based perspective to general alignment settings, such as reinforcement learning with verifiable rewards (RLVR), where only environmental rewards are available. Within this unified framework, we propose f-Group Relative Policy Optimization (f-GRPO), a class of on-policy reinforcement learning, and f-Hybrid Alignment Loss (f-HAL), a hybrid on/off policy objectives, for general LLM alignment based on variational representation of f-divergences. We provide theoretical guarantees that these classes of objectives improve the average reward after alignment. Empirically, we validate our framework on both RLVR (Math Reasoning) and PA tasks (Safety Alignment), demonstrating superior performance and flexibility compared to current methods.

ABSTRACT Subjective ratings contain inherent noise that limits the model-human correlation, but this reliability issue is rarely quantified. In this paper, we present ρ-Perfect, a practical estimation of the highest achievable correlation of a model on subjectively rated datasets. We define ρ-Perfect to be the correlation between a perfect predictor and human ratings, and derive an estimate of the value based on heteroscedastic noise scenarios, a common occurrence in subjectively rated datasets. We show that ρ-Perfect squared estimates test-retest correlation and use this to validate the estimate. We demonstrate the use of ρ-Perfect on a speech quality dataset and show how the measure can distinguish between model limitations and data quality issues.

We consider the problem of prediction with expert advice for ``easy'' sequences. We show that a variant of NormalHedge enjoys a second-order $ε$-quantile regret bound of $O\big(\sqrt{V_T \log(V_T/ε)}\big) $ when $V_T > \log N$, where $V_T$ is the cumulative second moment of instantaneous per-expert regret averaged with respect to a natural distribution determined by the algorithm. The algorithm is motivated by a continuous time limit using Stochastic Differential Equations. The discrete time analysis uses self-concordance techniques.