arXiv Statistics ML

On Large-Scale Multiple Testing Over Networks: A Non-Asymptotic Approach

arXiv Machine Learning
Sep 25

An Agnostic Sample Compression Scheme for Squared Loss of Near-Linear Size in the Fat-Shattering Dimension

arXiv:2609. 29696v1 Announce Type: new Abstract: We construct, for every function class $\mathcal{F}\subseteq[0,1]^{\mathcal{X}}$ and every accuracy $0<\alpha\le 1$, an agnostic sample compression scheme for the empirical squared loss: for every finite sample $S\in(\mathcal{X}\times[0,1])^m$ with arbitrary (noisy) labels, the scheme stores at most $O(\mathrm{fat}(\mathcal{F},c'\alpha)\cdot\log^3(2/\alpha))$ original labeled examples and auxiliary bits, independent of the sample size $m$, and reconstructs a function $\hat f$ with $L_2(\hat f,S)\le\inf_{f\in\mathcal{F}}L_2(f,S)+\alpha$.

By Guangjian Zhang
arXiv Machine Learning
Sep 25

The Impossible Trinity of Time-Series Validation: A Conservation Law among Training Sufficiency, Test Coverage, and Temporal Causality

The paper proves that in time‑series validation three desirable properties—training sufficiency, test coverage, and temporal causality—cannot all be satisfied simultaneously. It introduces quantitative bounds involving the smallest training fraction (α), test coverage (β), future training fraction (Λ), and distance to nearest future training point (δ), showing that exceeding the causal frontier α+β=1 requires training on future data that must lie within (1−α)T of a test point. The authors demonstrate that the impact of such future leakage depends on distance rather than amount, and compare different validation schemes (walk‑forward, k‑fold, purged k‑fold) in terms of their position on this Pareto frontier, illustrating the trade‑offs with empirical results on noise data.

By Jiayu Li