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math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? 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for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models Direct Estimation of Schrödinger Bridge Time-Series Drifts: Finite-Sample, Asymptotic, and Adaptive Guarantees Information-theoretic Limits of Learning and Estimation Adaptivity Under Realizability Constraints: Comparing In-Context and Agentic Learning Multiscale Euclidean Network Trajectories: Second-Moment Geometry, Attribution, and Change Points Causal discovery under mean independence and linearity Perturbation is All You Need for Extrapolating Language Models Realizable Bayes-Consistency for General Metric Losses Vanishing L2 regularization for the softmax Multi Armed Bandit Imbalanced Classification under Capacity Constraints Intrinsic effective sample size for manifold-valued Markov chain Monte Carlo via kernel discrepancy On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization Extrapolation in Statistical Learning 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Towards a theory of negative dependence
Robin Pemantle · 2004-04-05 · via math.ST updates on arXiv.org

The FKG theorem says that the POSITIVE LATTICE CONDITION, an easily checkable hypothesis which holds for many natural families of events, implies POSITIVE ASSOCIATION, a very useful property. Thus there is a natural and useful theory of positively dependent events. There is, as yet, no corresponding theory of negatively dependent events. There is, however, a need for such a theory. This paper, unfortunately, contains no substantial theorems. Its purpose is to present examples that motivate a need for such a theory, give plausibility arguments for the existence of such a theory, outline a few possible directions such a theory might take, and state a number of specific conjectures which pertain to the examples and to a wish list of theorems.

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