March 2026

arXiv:2602.08998v4 Announce Type: replace-cross Abstract: We study homology of ample groupoids via the compactly supported Moore complex of the nerve. Let $A$ be a topological abelian group. For $nge 0$ set $C_n(mathcal G;A) := C_c(mathcal G_n,A)$ and define $partial_n^A=sum_{i=0}^n(-1)^i(d_i)_*$. This defines $H_n(mathcal G;A)$. The theory is functorial for continuous ‘etale homomorphisms. It is compatible with standard reductions, including restriction to saturated clopen subsets. In the ample setting it is invariant under Kakutani equivalence. We reprove Matui type long […]

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arXiv:2602.07098v2 Announce Type: replace-cross Abstract: Modern Bayesian inference involves a mixture of computational methods for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows. An overarching motif of many Bayesian methods is that they are relatively slow, which often becomes prohibitive when fitting complex models to large data sets. Amortized Bayesian inference (ABI) offers a path to solving the computational challenges of Bayes. ABI trains neural networks on model simulations, rewarding users with rapid […]

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arXiv:2601.22481v2 Announce Type: replace-cross Abstract: This dissertation presents a general framework for changepoint detection based on L0 model selection. The core method, Iteratively Reweighted Fused Lasso (IRFL), improves upon the generalized lasso by adaptively reweighting penalties to enhance support recovery and minimize criteria such as the Bayesian Information Criterion (BIC). The approach allows for flexible modeling of seasonal patterns, linear and quadratic trends, and autoregressive dependence in the presence of changepoints. Simulation studies demonstrate that IRFL achieves accurate […]

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arXiv:2511.01137v2 Announce Type: replace-cross Abstract: We use geometric invariant theory (GIT) to study the deep linear network (DLN). The Kempf-Ness theorem is used to establish that the $L^2$ regularizer is minimized on the balanced manifold. We introduce related balancing flows using the Riemannian geometry of fibers. The balancing flow defined by the $L^2$ regularizer is shown to converge to the balanced manifold at a uniform exponential rate. The balancing flow defined by the squared moment map is computed […]

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arXiv:2510.03798v2 Announce Type: replace-cross Abstract: The batched multi-armed bandit (MAB) problem, in which rewards are collected in batches, is crucial for applications such as clinical trials. Existing research predominantly assumes light-tailed reward distributions, yet many real-world scenarios, including clinical outcomes, exhibit heavy-tailed characteristics. This paper bridges this gap by proposing robust batched bandit algorithms designed for heavy-tailed rewards, within both finite-arm and Lipschitz-continuous settings. We reveal a surprising phenomenon: in the instance-independent regime, as well as in the […]

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arXiv:2509.20721v2 Announce Type: replace-cross Abstract: Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive. In this work, we show that scaling laws can be formally explained as redundancy laws. Using kernel regression, we show that a polynomial tail in the data covariance spectrum yields an excess risk power law with exponent alpha = 2s […]

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arXiv:2508.14936v2 Announce Type: replace-cross Abstract: Synthetic data holds substantial potential to address practical challenges in epidemiology due to restricted data access and privacy concerns. However, many current methods suffer from limited quality, high computational demands, and complexity for non-experts. Furthermore, common evaluation strategies for synthetic data often fail to directly reflect statistical utility and measure privacy risks sufficiently. Against this background, a critical underexplored question is whether synthetic data can reliably reproduce key findings from epidemiological research while […]

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arXiv:2508.07392v3 Announce Type: replace-cross Abstract: Modern methods of generative modelling and unpaired data translation based on Schr”odinger bridges and stochastic optimal control theory aim to transform an initial density to a target one in an optimal way. In the present paper, we assume that we only have access to i.i.d. samples from the initial and final distributions. This makes our setup suitable for both generative modelling and unpaired data translation. Relying on the stochastic optimal control approach, we […]

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arXiv:2507.16749v3 Announce Type: replace-cross Abstract: Monitoring for changes in a predictive relationship represented by a fitted supervised learning model (i.e., concept drift detection) is a widespread problem in modern data-driven applications. A general and powerful Fisher score-based concept drift approach was recently proposed, in which detecting concept drift reduces to detecting changes in the mean of the model’s score vector using a multivariate exponentially weighted moving average (MEWMA). To implement the approach, the initial data must be split […]

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arXiv:2504.09396v2 Announce Type: replace-cross Abstract: We develop a reinforcement learning (RL) framework for insurance loss reserving that formulates reserve setting as a finite-horizon sequential decision problem under claim development uncertainty, macroeconomic stress, and solvency governance. The reserving process is modeled as a Markov Decision Process (MDP) in which reserve adjustments influence future reserve adequacy, capital efficiency, and solvency outcomes. A Proximal Policy Optimization (PPO) agent is trained using a risk-sensitive reward that penalizes reserve shortfall, capital inefficiency, and […]

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