Unified Sample-Optimal Property Estimation in Near-Linear Time

Authors: Yi Hao, Alon Orlitsky

NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sampleand time-efficient estimators for all sufficiently smooth, symmetric and non-symmetric, additive properties. This technique yields near-linear-time computable estimators whose approximation values are asymptotically optimal and highly-concentrated, resulting in the first: 1) estimators achieving the O(k/(ε2 log k)) min-max ε-error sample complexity for all k-symbol Lipschitz properties; 2) unified near-optimal differentially private estimators for a variety of properties; 3) unified estimator achieving optimal bias and near-optimal variance for five important properties; 4) near-optimal sample-complexity estimators for several important symmetric properties over both domain sizes and confidence levels.
Researcher Affiliation Academia Yi Hao Dept. of Electrical and Computer Engineering University of California, San Diego yih179@ucsd.edu Alon Orlitsky Dept. of Electrical and Computer Engineering University of California, San Diego alon@ucsd.edu
Pseudocode No The paper describes the methodology conceptually and mathematically but does not include explicit pseudocode or algorithm blocks.
Open Source Code No The paper does not contain any statement about releasing source code for the described methodology.
Open Datasets No This is a theoretical paper presenting a methodology and its properties, not empirical work involving training on datasets. Therefore, there is no mention of publicly available datasets for training.
Dataset Splits No This is a theoretical paper presenting a methodology and its properties, not empirical work involving data splits for validation. Therefore, there is no mention of training/validation/test splits.
Hardware Specification No This is a theoretical paper. No specific hardware used for experiments is mentioned.
Software Dependencies No The paper mentions the 'Remez algorithm' as a computational tool for approximating polynomials, but does not list specific software dependencies with version numbers.
Experiment Setup No This is a theoretical paper describing an estimation methodology. It does not provide details of an experimental setup such as hyperparameters or training configurations.