arXiv Machine Learning
Jul 21
Tight Sample Bounds for Renyi and Min-Entropy Estimation
arXiv:2607. 16966v1 Announce Type: cross Abstract: Estimating entropy from samples is fundamental in information theory and property testing.
Learning CNF Formulas from Uniform Random Solutions: Near-Tight Sample Complexity for Valiant's Algorithm
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arXiv Machine Learning
Sep 25
Bandit Multiclass PAC Learning: Corrected Lower Bounds, Exact Families, and a Confidence Direct-Sum Phenomenon
The paper revisits realizable multiclass PAC learning with bandit feedback, correcting a previously claimed lower bound on sample complexity. It introduces a new anchored dimension, “aBDS,” and establishes a constant‑free three‑part lower bound, while also providing tighter upper bounds that eliminate dependence on the total label count. The authors demonstrate that the optimal sample complexity can vary dramatically even among classes with identical dimensional profiles, revealing a confidence direct‑sum phenomenon and a rank‑saturation phase transition.
arXiv Machine Learning
Sep 10
Smoothed Picard Hamiltonian Monte Carlo
arXiv:2609.06906v1 Announce Type: cross Abstract: We develop a new low-accuracy sampler, called \emph{smoothed Picard Hamiltonian Monte Carlo}, which combines Gaussian smoothing, Picard iteration, an...
arXiv AI
Sep 15
Gap Entropy and Almost Instance-Wise Optimal Best-Arm Identification
arXiv:2609.13703v1 Announce Type: cross Abstract: In the best-arm identification problem, we are given $n$ stochastic arms with unknown means and wish to identify the arm with the largest mean with p...
arXiv Machine Learning
Jun 18
How fast can you find a good hypothesis?
arXiv:2509. 03734v3 Announce Type: replace-cross Abstract: In the hypothesis selection problem, we are given sample and query access to finite set of candidate distributions (hypotheses), $\mathcal{H} = \{H_1, \ldots, H_n\}$, and samples from an unknown distribution $P$, both over a domain $\mathcal{X}$.
arXiv Machine Learning
Oct 15
Hypothesis Selection via Weighted Medians
arXiv:2610.20375v1 Announce Type: cross Abstract: Given $n$ distributions (hypotheses) $\mathcal H=\{H_1,\ldots,H_n\}$ and samples from an unknown target distribution $P$, proper hypothesis selection...
arXiv Machine Learning
Sep 14
Tight Sampling Complexity with stochastic gradient oracles in Fixed Dimensions
arXiv:2609. 12590v1 Announce Type: cross Abstract: We investigate the stochastic-gradient query complexity of sampling smooth strongly log-concave distributions in any fixed Euclidean dimension.
arXiv Statistics ML
Oct 26
Strictly Replicable Realizable Learning: Unknown Marginals, Finite-Class Interpolation, and the Cost of Shared Randomness
arXiv:2610. 26944v2 Announce Type: replace Abstract: Strict replicability requires two independent training samples, processed with the same random seed, to produce exactly the same hypothesis.
arXiv Machine Learning
Aug 7
Optimal Rates for Learning with Monotone Adversaries
arXiv:2608. 06337v1 Announce Type: cross Abstract: A monotone adversary observes an i.
arXiv Machine Learning
Jul 2
Fast Score-Based Sampling via Log-Concave Reductions
arXiv:2512. 24152v2 Announce Type: replace-cross Abstract: Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities.
arXiv Statistics ML
Oct 2
Sharp Non-Asymptotic Analysis of the Penalized Challenger in $\beta$-EB-TCI for Bernoulli Bandits
arXiv:2610.01951v1 Announce Type: cross Abstract: Top-two algorithms are simple and effective for fixed-confidence best-arm identification, but their sharp non-asymptotic behavior is still not well u...
arXiv Machine Learning
Oct 12
Learning by Compression: Risk Estimates Attain the Law-of-Large-Numbers Rate
The paper shows that for learning algorithms based on preferential compression, the risk can be bounded by the compression complexity term λk/N plus an O(1/√N) term, eliminating the previously assumed logarithmic factor. This bound holds uniformly over all possible values of λk and matches the law‑of‑large‑numbers rate of empirical risk estimation. The authors also demonstrate that the leading λk/N term is necessary and analyze when empirical risk converges at O(1/√N) versus slower or inconsistent rates, while the complexity‑based estimator retains the O(1/√N) rate.