January 2026

arXiv:2601.21478v1 Announce Type: cross Abstract: Pathophysiolpgical modelling of brain systems from microscale to macroscale remains difficult in group comparisons partly because of the infeasibility of modelling the interactions of thousands of neurons at the scales involved. Here, to address the challenge, we present a novel approach to construct differential causal networks directly from electroencephalogram (EEG) data. The proposed network is based on conditionally coupled neuronal circuits which describe the average behaviour of interacting neuron populations that contribute to […]

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arXiv:2601.21471v1 Announce Type: cross Abstract: We study fixed-confidence best-arm identification (BAI) where a cheap but potentially biased proxy (e.g., LLM judge) is available for every sample, while an expensive ground-truth label can only be acquired selectively when using a human for auditing. Unlike classical multi-fidelity BAI, the proxy is biased (arm- and context-dependent) and ground truth is selectively observed. Consequently, standard multi-fidelity methods can mis-select the best arm, and uniform auditing, though accurate, wastes scarce resources and is […]

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arXiv:2601.21470v1 Announce Type: cross Abstract: We study semi-supervised stochastic optimization when labeled data is scarce but predictions from pre-trained models are available. PPI and SVRG both reduce variance through control variates — PPI uses predictions, SVRG uses reference gradients. We show they are mathematically equivalent and develop PPI-SVRG, which combines both. Our convergence bound decomposes into the standard SVRG rate plus an error floor from prediction uncertainty. The rate depends only on loss geometry; predictions affect only the […]

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arXiv:2601.21301v1 Announce Type: cross Abstract: We present the convergence rates of synchronous and asynchronous Q-learning for average-reward Markov decision processes, where the absence of contraction poses a fundamental challenge. Existing non-asymptotic results overcome this challenge by either imposing strong assumptions to enforce seminorm contraction or relying on discounted or episodic Markov decision processes as successive approximations, which either require unknown parameters or result in suboptimal sample complexity. In this work, under a reachability assumption, we establish optimal $widetilde{O}(varepsilon^{-2})$ […]

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arXiv:2601.21294v1 Announce Type: cross Abstract: Partial Least Squares (PLS) learns shared structure from paired data via the top singular vectors of the empirical cross-covariance (PLS-SVD), but multimodal datasets often have missing entries in both views. We study PLS-SVD under independent entry-wise missing-completely-at-random masking in a proportional high-dimensional spiked model. After appropriate normalization, the masked cross-covariance behaves like a spiked rectangular random matrix whose effective signal strength is attenuated by $sqrt{rho}$, where $rho$ is the joint entry retention probability. […]

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arXiv:2601.21131v1 Announce Type: cross Abstract: Adaptive sampling schemes are well known to create complex dependence that may invalidate conventional inference methods. A recent line of work shows that this need not be the case for UCB-type algorithms in multi-armed bandits. A central emerging theme is a `stability’ property with asymptotically deterministic arm-pull counts in these algorithms, making inference as easy as in the i.i.d. setting. In this paper, we study the precise arm-pull dynamics in another canonical class […]

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arXiv:2601.21061v1 Announce Type: cross Abstract: Generative Flow Networks (GFlowNets; GFNs) are a class of generative models that learn to sample compositional objects proportionally to their a priori unknown value, their reward. We focus on the case where the reward has a specified, actionable structure, namely that it is submodular. We show submodularity can be harnessed to retrieve upper bounds on the reward of compositional objects that have not yet been observed. We provide in-depth analyses of the probability […]

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arXiv:2601.20961v1 Announce Type: cross Abstract: We provide a complete theory of optimal universal rates for binary classification in the agnostic setting. This extends the realizable-case theory of Bousquet, Hanneke, Moran, van Handel, and Yehudayoff (2021) by removing the realizability assumption on the distribution. We identify a fundamental tetrachotomy of optimal rates: for every concept class, the optimal universal rate of convergence of the excess error rate is one of $e^{-n}$, $e^{-o(n)}$, $o(n^{-1/2})$, or arbitrarily slow. We further identify […]

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arXiv:2601.20875v1 Announce Type: cross Abstract: The achievement of the 2030 Sustainable Development Goals (SDGs) is dependent upon strategic resource distribution. We propose a causal discovery framework using Panel Vector Autoregression, along with both country-specific fixed effects and PCMCI+ conditional independence testing on 168 countries (2000-2025) to develop the first complete causal architecture of SDG dependencies. Utilizing 8 strategically chosen SDGs, we identify a distributed causal network (i.e., no single ‘hub’ SDG), with 10 statistically significant Granger-causal relationships identified […]

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arXiv:2601.20756v1 Announce Type: cross Abstract: Score-based diffusion models have recently been extended to infinite-dimensional function spaces, with uses such as inverse problems arising from partial differential equations. In the Bayesian formulation of inverse problems, the aim is to sample from a posterior distribution over functions obtained by conditioning a prior on noisy observations. While diffusion models provide expressive priors in function space, the theory of conditioning them to sample from the posterior remains open. We address this, assuming […]

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