February 2026

arXiv:2510.13868v2 Announce Type: replace-cross Abstract: We propose textit{DeepMartingale}, a deep-learning framework for the dual formulation of discrete-monitoring optimal stopping problems under continuous-time models. Leveraging a martingale representation, our method implements a emph{pure-dual} procedure that directly optimizes over a parameterized class of martingales, producing computable and tight emph{dual upper bounds} for the value function in high-dimensional settings without requiring any primal information or Snell-envelope approximation. We prove convergence of the resulting upper bounds under mild assumptions for both first- […]

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arXiv:2510.07128v4 Announce Type: replace-cross Abstract: Conventional joint modeling approaches generally characterize the relationship between longitudinal biomarkers and discrete event occurrences within terminal, recurring or competing risk settings, thereby offering a limited representation of complex, multi-state trajectories. We propose a general multi-state joint modeling framework that unifies longitudinal biomarker dynamics with multi-state time-to-event processes defined on arbitrary directed graphs. The proposed framework also accomodates nonlinear longitudinal submodels and scalable inference via stochastic gradient descent. This formulation encompasses both Markovian […]

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arXiv:2509.12051v2 Announce Type: replace-cross Abstract: Ambient air pollution poses significant health and environmental challenges. Exposure to high concentrations of PM$_{2.5}$ have been linked to increased respiratory and cardiovascular hospital admissions, more emergency department visits and deaths. Traditional air quality monitoring systems such as EPA-certified stations provide limited spatial and temporal data. The advent of low-cost sensors has dramatically improved the granularity of air quality data, enabling real-time, high-resolution monitoring. This study exploits the extensive data from PurpleAir sensors […]

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arXiv:2507.03772v3 Announce Type: replace-cross Abstract: The evaluation of large language model (LLM) outputs is increasingly performed by other LLMs, a setup commonly known as “LLM-as-a-judge”, or autograders. While autograders offer a scalable alternative to human evaluation, they have shown mixed reliability and may exhibit systematic biases, depending on response type, scoring methodology, domain specificity, or other factors. Here we propose a statistical framework based on Bayesian generalised linear models (GLMs) that enables researchers to simultaneously assess their autograders […]

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arXiv:2505.08371v4 Announce Type: replace-cross Abstract: We address the problem of inferring the causal direction between a continuous variable $X$ and a discrete variable $Y$ from observational data. For the model $X to Y$, we adopt the threshold model used in prior work. For the model $Y to X$, we consider two cases: (1) the conditional distributions of $X$ given different values of $Y$ form a location-shift family, and (2) they are mixtures of generalized normal distributions with independently […]

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arXiv:2503.19874v2 Announce Type: replace-cross Abstract: We consider the problem of selecting a subset of points from a dataset of $n$ unlabeled examples for labeling, with the goal of training a multiclass classifier. To address this, we build upon the regret minimization framework introduced by Allen-Zhu et al. in “Near-optimal design of experiments via regret minimization” (ICML, 2017). We propose an alternative regularization scheme within this framework, which leads to a new sample selection objective along with a provable […]

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arXiv:2502.12108v3 Announce Type: replace-cross Abstract: Integrated Gradients (IG), a widely used axiomatic path-based attribution method, assigns importance scores to input features by integrating model gradients along a straight path from a baseline to the input. While effective in some cases, we show that straight paths can lead to flawed attributions. In this paper, we identify the cause of these misattributions and propose an alternative approach that equips the input space with a model-induced Riemannian metric (derived from the […]

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arXiv:2502.06051v3 Announce Type: replace-cross Abstract: Many offline reinforcement learning algorithms are underpinned by $f$-divergence regularization, but their sample complexity *defined with respect to regularized objectives* still lacks tight analyses, especially in terms of concrete data coverage conditions. In this paper, we study the exact concentrability requirements to achieve the $tilde{Theta}(epsilon^{-1})$ sample complexity for offline $f$-divergence-regularized contextual bandits. For reverse Kullback-Leibler (KL) divergence, arguably the most commonly used one, we achieve an $tilde{O}(epsilon^{-1})$ sample complexity under single-policy concentrability for […]

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arXiv:2602.21160v2 Announce Type: replace Abstract: In safety-critical classification, the cost of failure is often asymmetric, yet Bayesian deep learning summarises epistemic uncertainty with a single scalar, mutual information (MI), that cannot distinguish whether a model’s ignorance involves a benign or safety-critical class. We decompose MI into a per-class vector $C_k(x)=sigma_k^{2}/(2mu_k)$, with $mu_k{=}mathbb{E}[p_k]$ and $sigma_k^2{=}mathrm{Var}[p_k]$ across posterior samples. The decomposition follows from a second-order Taylor expansion of the entropy; the $1/mu_k$ weighting corrects boundary suppression and makes $C_k$ comparable […]

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arXiv:2602.19241v2 Announce Type: replace Abstract: Low-precision training is critical for optimizing the trade-off between model quality and training costs, necessitating the joint allocation of model size, dataset size, and numerical precision. While empirical scaling laws suggest that quantization impacts effective model and data capacities or acts as an additive error, the theoretical mechanisms governing these effects remain largely unexplored. In this work, we initiate a theoretical study of scaling laws for low-precision training within a high-dimensional sketched linear […]

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