Timezone: »
Given samples from an unknown distribution, p, is it possible to distinguish whether p belongs to some class of distributions C versus p being far from every distribution in C? This fundamental question has receivedtremendous attention in Statistics, albeit focusing onasymptotic analysis, as well as in Computer Science, wherethe emphasis has been on small sample size and computationalcomplexity. Nevertheless, even for basic classes ofdistributions such as monotone, log-concave, unimodal, and monotone hazard rate, the optimal sample complexity is unknown.We provide a general approach via which we obtain sample-optimal and computationally efficient testers for all these distribution families. At the core of our approach is an algorithm which solves the following problem:Given samplesfrom an unknown distribution p, and a known distribution q, are p and q close in Chi^2-distance, or far in total variation distance?The optimality of all testers is established by providing matching lower bounds. Finally, a necessary building block for our tester and important byproduct of our work are the first known computationally efficient proper learners for discretelog-concave and monotone hazard rate distributions. We exhibit the efficacy of our testers via experimental analysis.
Author Information
Jayadev Acharya (Massachusetts Institute of Technology)
Constantinos Daskalakis (MIT)
Gautam Kamath (MIT)
More from the Same Authors
-
2021 : Estimation of Standard Asymmetric Auction Models »
Yeshwanth Cherapanamjeri · Constantinos Daskalakis · Andrew Ilyas · Emmanouil Zampetakis -
2021 : Near-Optimal No-Regret Learning in General Games »
Constantinos Daskalakis · Maxwell Fishelson · Noah Golowich -
2021 : Estimation of Standard Asymmetric Auction Models »
Yeshwanth Cherapanamjeri · Constantinos Daskalakis · Andrew Ilyas · Emmanouil Zampetakis -
2021 : Near-Optimal No-Regret Learning in General Games »
Constantinos Daskalakis · Maxwell Fishelson · Noah Golowich -
2022 : Choosing Public Datasets for Private Machine Learning via Gradient Subspace Distance »
Xin Gu · Gautam Kamath · Steven Wu -
2022 : Hidden Poison: Machine Unlearning Enables Camouflaged Poisoning Attacks »
Jimmy Di · Jack Douglas · Jayadev Acharya · Gautam Kamath · Ayush Sekhari -
2022 : Indiscriminate Data Poisoning Attacks on Neural Networks »
Yiwei Lu · Gautam Kamath · Yaoliang Yu -
2022 : Indiscriminate Data Poisoning Attacks on Neural Networks »
Yiwei Lu · Gautam Kamath · Yaoliang Yu -
2022 : Hidden Poison: Machine unlearning enables camouflaged poisoning attacks »
Jimmy Di · Jack Douglas · Jayadev Acharya · Gautam Kamath · Ayush Sekhari -
2023 Poster: Private Distribution Learning with Public Data: The View from Sample Compression »
Shai Ben-David · Alex Bie · Clément L Canonne · Gautam Kamath · Vikrant Singhal -
2023 Poster: Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistent »
Giannis Daras · Yuval Dagan · Alex Dimakis · Constantinos Daskalakis -
2023 Poster: Distribution Learnability and Robustness »
Shai Ben-David · Alex Bie · Gautam Kamath · Tosca Lechner -
2023 Poster: Hidden Poison: Machine Unlearning Enables Camouflaged Poisoning Attacks »
Jimmy Di · Jack Douglas · Jayadev Acharya · Gautam Kamath · Ayush Sekhari -
2022 : Private GANs, Revisited »
Alex Bie · Gautam Kamath · Guojun Zhang -
2022 Poster: New Lower Bounds for Private Estimation and a Generalized Fingerprinting Lemma »
Gautam Kamath · Argyris Mouzakis · Vikrant Singhal -
2022 Poster: Private Estimation with Public Data »
Alex Bie · Gautam Kamath · Vikrant Singhal -
2021 : Spotlight 4: Estimation of Standard Asymmetric Auction Models »
Yeshwanth Cherapanamjeri · Constantinos Daskalakis · Andrew Ilyas · Emmanouil Zampetakis -
2021 Poster: Near-Optimal No-Regret Learning in General Games »
Constantinos Daskalakis · Maxwell Fishelson · Noah Golowich -
2021 Poster: Enabling Fast Differentially Private SGD via Just-in-Time Compilation and Vectorization »
Pranav Subramani · Nicholas Vadivelu · Gautam Kamath -
2021 Poster: Efficient Truncated Linear Regression with Unknown Noise Variance »
Constantinos Daskalakis · Patroklos Stefanou · Rui Yao · Emmanouil Zampetakis -
2021 Poster: Remember What You Want to Forget: Algorithms for Machine Unlearning »
Ayush Sekhari · Jayadev Acharya · Gautam Kamath · Ananda Theertha Suresh -
2021 Oral: Near-Optimal No-Regret Learning in General Games »
Constantinos Daskalakis · Maxwell Fishelson · Noah Golowich -
2020 Poster: Tight last-iterate convergence rates for no-regret learning in multi-player games »
Noah Golowich · Sarath Pattathil · Constantinos Daskalakis -
2020 Poster: Truncated Linear Regression in High Dimensions »
Constantinos Daskalakis · Dhruv Rohatgi · Emmanouil Zampetakis -
2020 Poster: The Discrete Gaussian for Differential Privacy »
Clément L Canonne · Gautam Kamath · Thomas Steinke -
2020 Social: Data Privacy: Academia, Industry, Policy, and Society »
Gautam Kamath -
2020 Poster: CoinPress: Practical Private Mean and Covariance Estimation »
Sourav Biswas · Yihe Dong · Gautam Kamath · Jonathan Ullman -
2020 Poster: Private Identity Testing for High-Dimensional Distributions »
Clément L Canonne · Gautam Kamath · Audra McMillan · Jonathan Ullman · Lydia Zakynthinou -
2020 Poster: Constant-Expansion Suffices for Compressed Sensing with Generative Priors »
Constantinos Daskalakis · Dhruv Rohatgi · Emmanouil Zampetakis -
2020 Spotlight: Constant-Expansion Suffices for Compressed Sensing with Generative Priors »
Constantinos Daskalakis · Dhruv Rohatgi · Emmanouil Zampetakis -
2020 Spotlight: Private Identity Testing for High-Dimensional Distributions »
Clément L Canonne · Gautam Kamath · Audra McMillan · Jonathan Ullman · Lydia Zakynthinou -
2020 Poster: Independent Policy Gradient Methods for Competitive Reinforcement Learning »
Constantinos Daskalakis · Dylan Foster · Noah Golowich -
2019 Poster: Private Hypothesis Selection »
Mark Bun · Gautam Kamath · Thomas Steinke · Steven Wu -
2019 Poster: Differentially Private Algorithms for Learning Mixtures of Separated Gaussians »
Gautam Kamath · Or Sheffet · Vikrant Singhal · Jonathan Ullman -
2018 : Improving Generative Adversarial Networks using Game Theory and Statistics »
Constantinos Daskalakis -
2018 Poster: Learning and Testing Causal Models with Interventions »
Jayadev Acharya · Arnab Bhattacharyya · Constantinos Daskalakis · Saravanan Kandasamy -
2018 Poster: Smoothed Analysis of Discrete Tensor Decomposition and Assemblies of Neurons »
Nima Anari · Constantinos Daskalakis · Wolfgang Maass · Christos Papadimitriou · Amin Saberi · Santosh Vempala -
2018 Poster: HOGWILD!-Gibbs can be PanAccurate »
Constantinos Daskalakis · Nishanth Dikkala · Siddhartha Jayanti -
2018 Poster: The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization »
Constantinos Daskalakis · Ioannis Panageas -
2017 Poster: Concentration of Multilinear Functions of the Ising Model with Applications to Network Data »
Constantinos Daskalakis · Nishanth Dikkala · Gautam Kamath -
2015 Poster: Optimal Testing for Properties of Distributions »
Jayadev Acharya · Constantinos Daskalakis · Gautam Kamath -
2014 Poster: Near-Optimal-Sample Estimators for Spherical Gaussian Mixtures »
Ananda Theertha Suresh · Alon Orlitsky · Jayadev Acharya · Ashkan Jafarpour -
2012 Poster: Tight Bounds on Redundancy and Distinguishability of Label-Invariant Distributions »
Jayadev Acharya · Hirakendu Das · Alon Orlitsky