Monotonicity Testing of High-Dimensional Distributions with Subcube Conditioning

• URL: http://arxiv.org/abs/2502.16355v1
• Date: Sat, 22 Feb 2025 21:04:22 GMT
• Title: Monotonicity Testing of High-Dimensional Distributions with Subcube Conditioning
• Authors: Deeparnab Chakrabarty, Xi Chen, Simeon Ristic, C. Seshadhri, Erik Waingarten,
• Abstract summary: We study monotonicity testing of high-dimensional distributions on $-1,1n$ in the model of subcube conditioning.<n>Our work is the first to use directed isoperimetric inequalities (developed for function monotonicity testing) for analyzing a distribution testing algorithm.
• Score: 10.903818216004703
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study monotonicity testing of high-dimensional distributions on $\{-1,1\}^n$ in the model of subcube conditioning, suggested and studied by Canonne, Ron, and Servedio~\cite{CRS15} and Bhattacharyya and Chakraborty~\cite{BC18}. Previous work shows that the \emph{sample complexity} of monotonicity testing must be exponential in $n$ (Rubinfeld, Vasilian~\cite{RV20}, and Aliakbarpour, Gouleakis, Peebles, Rubinfeld, Yodpinyanee~\cite{AGPRY19}). We show that the subcube \emph{query complexity} is $\tilde{\Theta}(n/\varepsilon^2)$, by proving nearly matching upper and lower bounds. Our work is the first to use directed isoperimetric inequalities (developed for function monotonicity testing) for analyzing a distribution testing algorithm. Along the way, we generalize an inequality of Khot, Minzer, and Safra~\cite{KMS18} to real-valued functions on $\{-1,1\}^n$. We also study uniformity testing of distributions that are promised to be monotone, a problem introduced by Rubinfeld, Servedio~\cite{RS09} , using subcube conditioning. We show that the query complexity is $\tilde{\Theta}(\sqrt{n}/\varepsilon^2)$. Our work proves the lower bound, which matches (up to poly-logarithmic factors) the uniformity testing upper bound for general distributions (Canonne, Chen, Kamath, Levi, Waingarten~\cite{CCKLW21}). Hence, we show that monotonicity does not help, beyond logarithmic factors, in testing uniformity of distributions with subcube conditional queries.

Related papers

• Replicable Uniformity Testing [1.5883812630616523]
  This work revisits uniformity testing under the framework of algorithmic replicability. We obtain a replicable tester using only $tildeO(sqrtn varepsilon-2 rho-1)$ samples.
  arXiv  Detail & Related papers  (2024-10-12T02:55:17Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• Statistical Learning under Heterogeneous Distribution Shift [71.8393170225794]
  Ground-truth predictor is additive $mathbbE[mathbfz mid mathbfx,mathbfy] = f_star(mathbfx) +g_star(mathbfy)$.
  arXiv  Detail & Related papers  (2023-02-27T16:34:21Z)
• Randomized Greedy Learning for Non-monotone Stochastic Submodular Maximization Under Full-bandit Feedback [98.29086113546045]
  We investigate the problem of unconstrained multi-armed bandits with full-bandit feedback and rewards for submodularity. We show that RGL empirically outperforms other full-bandit variants in submodular and non-submodular settings.
  arXiv  Detail & Related papers  (2023-02-02T18:52:14Z)
• Sharp Constants in Uniformity Testing via the Huber Statistic [16.384142529375435]
  Uniformity testing is one of the most well-studied problems in property testing. It is known that the optimal sample complexity to distinguish the uniform distribution on $m$ elements from any $epsilon$-far distribution with $1-delta probability is $n. We show that the collisions tester achieves a sharp maximal constant in the number of standard deviations of separation between uniform and non-uniform inputs.
  arXiv  Detail & Related papers  (2022-06-21T20:43:53Z)
• Polyak-Ruppert Averaged Q-Leaning is Statistically Efficient [90.14768299744792]
  We study synchronous Q-learning with Polyak-Ruppert averaging (a.k.a., averaged Q-leaning) in a $gamma$-discounted MDP. We establish normality for the iteration averaged $barboldsymbolQ_T$. In short, our theoretical analysis shows averaged Q-Leaning is statistically efficient.
  arXiv  Detail & Related papers  (2021-12-29T14:47:56Z)
• The Sample Complexity of Robust Covariance Testing [56.98280399449707]
  We are given i.i.d. samples from a distribution of the form $Z = (1-epsilon) X + epsilon B$, where $X$ is a zero-mean and unknown covariance Gaussian $mathcalN(0, Sigma)$. In the absence of contamination, prior work gave a simple tester for this hypothesis testing task that uses $O(d)$ samples. We prove a sample complexity lower bound of $Omega(d2)$ for $epsilon$ an arbitrarily small constant and $gamma
  arXiv  Detail & Related papers  (2020-12-31T18:24:41Z)
• Optimal Testing of Discrete Distributions with High Probability [49.19942805582874]
  We study the problem of testing discrete distributions with a focus on the high probability regime. We provide the first algorithms for closeness and independence testing that are sample-optimal, within constant factors.
  arXiv  Detail & Related papers  (2020-09-14T16:09:17Z)
• Learning and Testing Junta Distributions with Subcube Conditioning [11.464622619555222]
  We study the problems of learning and testing junta distributions on $-1,1n$ with respect to the uniform distribution. The main contribution is an algorithm for finding relevant coordinates in a $k$-junta distribution with subcube conditioning.
  arXiv  Detail & Related papers  (2020-04-26T22:52:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.