arXiv subjects

Maciej Skórski

Publications and source records attributed to Maciej Skórski.

3 recordsLinked to original sources

arXiv2026

Birthday Estimators Are Uniformly Optimal for Renyi Entropy

Collisions are a basic probe of unknown distributions, used for testing and for counting substructures in graphs, and they underlie Rényi entropy, a fundamental measure of uncertainty with applications in cryptography, machine learning, physics, and biology. Motivated by this, we study the natural birthday estimator. We prove Bernstein-type concentration for it and show that it is minimax optimal, uniformly and jointly in alphabet size, order, accuracy, and confidence, with no sample splitting, clipping, or median aggregation. This, in particular, settles the sample complexity of integer-order Rényi entropy estimation up to absolute constants in all regimes, closing the gap between the best known upper and lower bounds. Our concentration bound rests on a sensitivity analysis of collision count, and the matching lower bound on a sharp analysis of detecting a hidden spike in a plateau distribution.

cs.IT↗

arXiv2024

Accurate Analysis of Sparse Random Projections

There has been recently a lot of research on sparse variants of random projections, faster adaptations of the state-of-the-art dimensionality reduction technique originally due to Johsnon and Lindenstrauss. Although the construction is very simple, its analyses are notoriously complicated. Meeting the demand for both simplicity and accuracy, this work establishes sharp sub-poissonian tail bounds for the distribution of sparse random projections. Compared to other works, this analysis provide superior numerical guarantees (exactly matching impossibility results) while being arguably less complicated (the technique resembles Bennet's Inequality and is of independent interest).

cs.DS↗

arXiv2013

A Convex Analysis Approach to Computational Entropy

This paper studies the notion of computational entropy. Using techniques from convex optimization, we investigate the following problems: (a) Can we derandomize the computational entropy? More precisely, for the computational entropy, what is the real difference in security defined using the three important classes of circuits: deterministic boolean, deterministic real valued, or (the most powerful) randomized ones? (b) How large the difference in the computational entropy for an unbounded versus efficient adversary can be? (c) Can we obtain useful, simpler characterizations for the computational entropy?

cs.IT↗