March 2026

arXiv:2603.05317v1 Announce Type: new Abstract: In clinical prediction settings the importance of a high-dimensional feature like genomics is often assessed by evaluating the change in predictive performance when adding it to a set of traditional clinical variables. This approach is questionable, because it does not account for collinearity nor known directionality of dependencies between variables. We suggest to use asymmetric Shapley values as a more suitable alternative to quantify feature importance in the context of a mixed-dimensional prediction […]

Ver mais

arXiv:2603.05288v1 Announce Type: new Abstract: Finding patient subgroups with similar characteristics is crucial for personalized decision-making in various disciplines such as healthcare and policy evaluation. While most existing approaches rely on unsupervised clustering methods, there is a growing trend toward using supervised clustering methods that identify operationalizable subgroups in the context of a specific outcome of interest. We propose Bayesian Supervised Causal Clustering (BSCC), with treatment effect as outcome to guide the clustering process. BSCC identifies homogenous subgroups […]

Ver mais

arXiv:2603.05226v1 Announce Type: new Abstract: Individualized decision rules (IDRs) have become increasingly prevalent in societal applications such as personalized marketing, healthcare, and public policy design. However, a critical ethical concern arises from the potential discriminatory effects of IDRs trained on biased data. These algorithms may disproportionately harm individuals from minority subgroups defined by sensitive attributes like gender, race, or language. To address this issue, we propose a novel framework that incorporates demographic parity (DP) and conditional demographic parity […]

Ver mais

arXiv:2603.04895v1 Announce Type: new Abstract: Overparameterized ML models, including neural networks, typically induce underdetermined training objectives with multiple global minima. The implicit bias refers to the limiting global minimum that is attained by a common optimization algorithm, such as gradient descent (GD). In this paper, we characterize the implicit bias of GD for training a shallow ReLU model with the squared loss on high-dimensional random features. Prior work showed that the implicit bias does not exist in the […]

Ver mais

arXiv:2603.04807v1 Announce Type: new Abstract: We study how architectural inductive bias reshapes the implicit regularization induced by the edge-of-stability phenomenon in gradient descent. Prior work has established that for fully connected networks, the strength of this regularization is governed solely by the global input geometry; consequently, it is insufficient to prevent overfitting on difficult distributions such as the high-dimensional sphere. In this paper, we show that locality and weight sharing fundamentally change this picture. Specifically, we prove that […]

Ver mais

arXiv:2603.04635v1 Announce Type: new Abstract: Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $epsilon$-far from all product distributions in total variation distance. In the non-parametric finite-sample regime, this task is notoriously expensive, as the minimax sample complexity scales polynomially with the support size. In this work, we move beyond these worst-case limitations by […]

Ver mais

arXiv:2603.04525v1 Announce Type: new Abstract: Modern approaches for learning from non-Markovian time series, such as recurrent neural networks, neural controlled differential equations or transformers, typically rely on implicit memory mechanisms that can be difficult to interpret or to train over long horizons. We propose the Volterra signature $mathrm{VSig}(x;K)$ as a principled, explicit feature representation for history-dependent systems. By developing the input path $x$ weighted by a temporal kernel $K$ into the tensor algebra, we leverage the associated Volterra–Chen […]

Ver mais

arXiv:2603.04479v1 Announce Type: new Abstract: We study the Collatz total stopping time $tau(n)$ over $nle 10^7$ from a probabilistic machine learning viewpoint. Empirically, $tau(n)$ is a skewed and heavily overdispersed count with pronounced arithmetic heterogeneity. We develop two complementary models. First, a Bayesian hierarchical Negative Binomial regression (NB2-GLM) predicts $tau(n)$ from simple covariates ($log n$ and residue class $n bmod 8$), quantifying uncertainty via posterior and posterior predictive distributions. Second, we propose a mechanistic generative approximation based on […]

Ver mais

arXiv:2603.04473v1 Announce Type: new Abstract: Discovering causal direction from temporal observational data is particularly challenging for symbolic sequences, where functional models and noise assumptions are often unavailable. We propose a novel emph{Dictionary Based Pattern Entropy ($DPE$)} framework that infers both the direction of causation and the specific subpatterns driving changes in the effect variable. The framework integrates emph{Algorithmic Information Theory} (AIT) and emph{Shannon Information Theory}. Causation is interpreted as the emergence of compact, rule based patterns in the […]

Ver mais

arXiv:2603.03388v2 Announce Type: new Abstract: Recent neural solvers have achieved strong performance on vehicle routing problems (VRPs), yet they mainly assume symmetric Euclidean distances, restricting applicability to real-world scenarios. A core challenge is encoding the relational features in asymmetric distance matrices of VRPs. Early attempts directly encoded these matrices but often failed to produce compact embeddings and generalized poorly at scale. In this paper, we propose RADAR, a scalable neural framework that augments existing neural VRP solvers with […]

Ver mais