arXiv:2506. 01075v2 Announce Type: replace-cross Abstract: The Boolean Fourier representation has been widely used in learning theory, particularly for learning Disjunctive Normal Form (DNF) under uniform and product distributions.
arXiv:2609.08961v1 Announce Type: cross Abstract: For a finite set $O$ of Boolean functions, we consider the class of propositional formulas built using the functions in $O$ as connectives. We determ...
arXiv:2606. 19366v1 Announce Type: cross Abstract: Information lattice learning (ILL) learns interpretable rules of a signal by alternately projecting the signal onto a partition lattice that encodes a hierarchy of abstractions and lifting selected rules back to the signal domain.
arXiv:2608.31120v1 Announce Type: new Abstract: The motivation for this paper is the investigation of the trade-offs implicit in probabilistic models used in machine learning. Models are often used t...
arXiv:2607. 26357v1 Announce Type: new Abstract: The problem of learning the graphical Markov blanket (MB) of a variable from data has applications in many areas such as structure learning for Bayesian networks and Markov random fields, causal discovery, and feature selection.
arXiv:2602. 23006v2 Announce Type: replace-cross Abstract: Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations.
arXiv:2410. 02628v5 Announce Type: replace Abstract: Learning conditional distributions $\pi^*(\cdot|x)$ is a central problem in machine learning, which is typically approached via supervised methods with paired data $(x,y) \sim \pi^*$.
The paper extends the Generalized Naive Bayes (GNB) model to handle continuous explanatory variables. It shows that GNB structure learning depends only on pair copulas of bivariate marginals and can be framed as a matroid, enabling greedy algorithms that minimize Kullback–Leibler divergence. Three model variants are explored—joint Gaussian, Gaussian copula with arbitrary marginals, and fully arbitrary copula and marginals—along with a GNB forest-based model reduction method and empirical comparisons to classical glass‑box classifiers.
arXiv:2603. 07606v2 Announce Type: replace Abstract: Interpretable machine learning is essential in high-stakes domains where decision-making requires accountability, transparency, and trust.
arXiv:2602. 00511v3 Announce Type: replace Abstract: We introduce \emph{Partition of Unity Neural Networks} (PUNNs), a neural-network architecture for multiclass classification based on the classical mathematical notion of a partition of unity.
The paper introduces a new Monte Carlo algorithm for approximate counting of Disjunctive Normal Form (DNF) formulas, featuring an adaptive stopping rule and short‑circuit evaluation. It achieves PAC learning bounds and is asymptotically more efficient than existing methods, including classical Monte Carlo, hashing‑based, and neural‑network approaches. Experiments demonstrate that the algorithm outperforms prior techniques by orders of magnitude and scales to problems with millions of variables.
arXiv:2606. 15219v1 Announce Type: new Abstract: In this work, we tackle the following question: Can neural networks trained with gradient-based methods achieve the optimal computational-statistical tradeoff in learning Gaussian single-index models?
The paper presents a polynomial‑time algorithm for robustly learning Boolean concept classes with respect to a fixed distribution, achieving the optimal error rate of η + ε where η is the noise rate. It builds on Blanc’s earlier, computationally inefficient algorithm and introduces no‑regret learners to overcome the previous limitations. Additionally, the authors provide an efficient method that does not require an ERM oracle for any function class admitting sandwiching polynomials under hypercontractive distributions, including a first polynomial‑time solution for learning halfspaces with Gaussian marginals at error η + ε.