February 2026

arXiv:2408.12175v3 Announce Type: replace-cross Abstract: Aleatoric (data) and epistemic (knowledge) uncertainty are textbook components of Uncertainty Quantification. Jointly estimating these components has been shown to be problematic and non-trivial. As a result, there are multiple ways to disentangle these uncertainties, but current methods to evaluate them are insufficient. We propose that aleatoric and epistemic uncertainty estimates should be orthogonally disentangled – meaning that each uncertainty is not affected by the other – a necessary condition that is often […]

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arXiv:2405.16828v4 Announce Type: replace-cross Abstract: In this work, we present a novel conformal prediction method for time-series, which we call Kernel-based Optimally Weighted Conformal Prediction Intervals (KOWCPI). Specifically, KOWCPI adapts the classic Reweighted Nadaraya-Watson (RNW) estimator for quantile regression on dependent data and learns optimal data-adaptive weights. Theoretically, we tackle the challenge of establishing a conditional coverage guarantee for non-exchangeable data under strong mixing conditions on the non-conformity scores. We demonstrate the superior performance of KOWCPI on real […]

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arXiv:2402.03991v3 Announce Type: replace-cross Abstract: We present a unified theoretical framework connecting the first property of Deep Neural Collapse (DNC1) to the emergence of implicit low-rank bias in nonlinear networks trained with $L^2$ weight decay regularization. Our main contributions are threefold. First, we derive a quantitative relation between the Total Cluster Variation (TCV) of intermediate embeddings and the numerical rank of stationary weight matrices. In particular, we establish that, at any critical point, the distance from a weight […]

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arXiv:2304.04724v3 Announce Type: replace-cross Abstract: We analyze the mixing time of Metropolized Hamiltonian Monte Carlo (HMC) with the leapfrog integrator to sample from a distribution on $mathbb{R}^d$ whose log-density is smooth, has Lipschitz Hessian in Frobenius norm and satisfies isoperimetry. We bound the gradient complexity to reach $epsilon$ error in total variation distance from a warm start by $tilde O(d^{1/4}text{polylog}(1/epsilon))$ and demonstrate the benefit of choosing the number of leapfrog steps to be larger than 1. To surpass […]

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arXiv:2601.21014v2 Announce Type: replace Abstract: Learning causal structures from observational data remains a fundamental yet computationally intensive task, particularly in high-dimensional settings where existing methods face challenges such as the super-exponential growth of the search space and increasing computational demands. To address this, we introduce VISTA (Voting-based Integration of Subgraph Topologies for Acyclicity), a modular framework that decomposes the global causal structure learning problem into local subgraphs based on Markov Blankets. The global integration is achieved through a […]

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arXiv:2511.18141v2 Announce Type: replace Abstract: Dirichlet regression models are suitable for compositional data, in which the response variable represents proportions that sum to one. However, there are still no well-established methods for constructing valid prediction sets in this context, especially considering the geometry of the compositional space. In this work, we investigate conformal prediction-based strategies for constructing valid predictive regions in Dirichlet regression models. We evaluate three distinct approaches: a method based on quantile residuals, an approximate construction […]

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arXiv:2503.02437v2 Announce Type: replace Abstract: This paper addresses the challenge of allocating heterogeneous resources among multiple agents in a decentralized manner. Our proposed method, Liquid-Graph-Time Clustering-IPPO, builds upon Independent Proximal Policy Optimization (IPPO) by integrating dynamic cluster consensus, a mechanism that allows agents to form and adapt local sub-teams based on resource demands. This decentralized coordination strategy reduces reliance on global information and enhances scalability. We evaluate LGTC-IPPO against standard multi-agent reinforcement learning baselines and a centralized expert […]

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arXiv:2502.14121v2 Announce Type: replace Abstract: Designing modern industrial systems requires balancing several competing objectives, such as profitability, resilience, and sustainability, while accounting for complex interactions between technological, economic, and environmental factors. Multi-objective optimization (MOO) methods are commonly used to navigate these tradeoffs, but selecting the appropriate algorithm to tackle these problems is often unclear, particularly when system representations vary from fully equation-based (white-box) to entirely data-driven (black-box) models. While grey-box MOO methods attempt to bridge this gap, they […]

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arXiv:2406.01552v2 Announce Type: replace Abstract: Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address problems in these domains. In this paper, we show how to exploit the underlying symmetries of functions that map tensors to tensors. More concretely, we develop universally expressive equivariant machine learning architectures on tensors that exploit that, in […]

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arXiv:2404.07593v3 Announce Type: replace Abstract: Identifying the parameters of a non-linear model that best explain observed data is a core task across scientific fields. When such models rely on complex simulators, evaluating the likelihood is typically intractable, making traditional inference methods such as MCMC inapplicable. Simulation-based inference (SBI) addresses this by training deep generative models to approximate the posterior distribution over parameters using simulated data. In this work, we consider the tall data setting, where multiple independent observations […]

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