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Found 25 papers, 1 papers with code
Learning bounded-degree polytrees with known skeleton
We establish finite-sample guarantees for efficient proper learning of bounded-degree polytrees, a rich class of high-dimensional probability distributions and a subclass of Bayesian networks, a widely-studied type of graphical model.
Tight Bounds for Machine Unlearning via Differential Privacy
We consider the formulation of "machine unlearning" of Sekhari, Acharya, Kamath, and Suresh (NeurIPS 2021), which formalizes the so-called "right to be forgotten" by requiring that a trained model, upon request, should be able to "unlearn" a number of points from the training data, as if they had never been included in the first place.
Near-Optimal Degree Testing for Bayes Nets
This paper considers the problem of testing the maximum in-degree of the Bayes net underlying an unknown probability distribution $P$ over $\{0, 1\}^n$, given sample access to $P$.
Concentration Bounds for Discrete Distribution Estimation in KL Divergence
We study the problem of discrete distribution estimation in KL divergence and provide concentration bounds for the Laplace estimator.
Near-Optimal Bounds for Testing Histogram Distributions
We investigate the problem of testing whether a discrete probability distribution over an ordered domain is a histogram on a specified number of bins.
Private independence testing across two parties
We introduce $\pi$-test, a privacy-preserving algorithm for testing statistical independence between data distributed across multiple parties.
Robust Testing in High-Dimensional Sparse Models
Our results show that the complexity of testing in these two settings significantly increases under robustness constraints.
Independence Testing for Bounded Degree Bayesian Network
We study the following independence testing problem: given access to samples from a distribution $P$ over $\{0, 1\}^n$, decide whether $P$ is a product distribution or whether it is $\varepsilon$-far in total variation distance from any product distribution.
The Role of Interactivity in Structured Estimation
Without sparsity assumptions, it has been established that interactivity cannot improve the minimax rates of estimation under these information constraints.
Uniformity Testing in the Shuffle Model: Simpler, Better, Faster
Uniformity testing, or testing whether independent observations are uniformly distributed, is the prototypical question in distribution testing.
The Price of Tolerance in Distribution Testing
Specifically, we show the sample complexity to be \[\tilde \Theta\left(\frac{\sqrt{n}}{\varepsilon_2^{2}} + \frac{n}{\log n} \cdot \max \left\{\frac{\varepsilon_1}{\varepsilon_2^2},\left(\frac{\varepsilon_1}{\varepsilon_2^2}\right)^{\!\! 2}\right\}\right),\] providing a smooth tradeoff between the two previously known cases.
Interactive Inference under Information Constraints
We study the role of interactivity in distributed statistical inference under information constraints, e. g., communication constraints and local differential privacy.
The Discrete Gaussian for Differential Privacy
Specifically, we theoretically and experimentally show that adding discrete Gaussian noise provides essentially the same privacy and accuracy guarantees as the addition of continuous Gaussian noise.
Random Restrictions of High-Dimensional Distributions and Uniformity Testing with Subcube Conditioning
We give a nearly-optimal algorithm for testing uniformity of distributions supported on $\{-1, 1\}^n$, which makes $\tilde O (\sqrt{n}/\varepsilon^2)$ queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)).
Domain Compression and its Application to Randomness-Optimal Distributed Goodness-of-Fit
We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints.
Learning from satisfying assignments under continuous distributions
We give a range of efficient algorithms and hardness results for this problem, focusing on the case when $f$ is a low-degree polynomial threshold function (PTF).
Private Identity Testing for High-Dimensional Distributions
In this work we present novel differentially private identity (goodness-of-fit) testers for natural and widely studied classes of multivariate product distributions: Gaussians in $\mathbb{R}^d$ with known covariance and product distributions over $\{\pm 1\}^{d}$.
Inference under Information Constraints II: Communication Constraints and Shared Randomness
We propose a general-purpose simulate-and-infer strategy that uses only private-coin communication protocols and is sample-optimal for distribution learning.
Inference under Information Constraints I: Lower Bounds from Chi-Square Contraction
Underlying our bounds is a characterization of the contraction in chi-square distances between the observed distributions of the samples when information constraints are placed.
The Structure of Optimal Private Tests for Simple Hypotheses
Specifically, we characterize this sample complexity up to constant factors in terms of the structure of $P$ and $Q$ and the privacy level $\varepsilon$, and show that this sample complexity is achieved by a certain randomized and clamped variant of the log-likelihood ratio test.
Test without Trust: Optimal Locally Private Distribution Testing
We are concerned with two settings: First, when we insist on using an already deployed, general-purpose locally differentially private mechanism such as the popular RAPPOR or the recently introduced Hadamard Response for collecting data, and must build our tests based on the data collected via this mechanism; and second, when no such restriction is imposed, and we can design a bespoke mechanism specifically for testing.
Distributed Simulation and Distributed Inference
Nonetheless, we present a Las Vegas algorithm that simulates a single sample from the unknown distribution using $O(k/2^\ell)$ samples in expectation.
Testing $k$-Monotonicity
Our results include the following: - We demonstrate a separation between testing $k$-monotonicity and testing monotonicity, on the hypercube domain $\{0, 1\}^d$, for $k\geq 3$; - We demonstrate a separation between testing and learning on $\{0, 1\}^d$, for $k=\omega(\log d)$: testing $k$-monotonicity can be performed with $2^{O(\sqrt d \cdot \log d\cdot \log{1/\varepsilon})}$ queries, while learning $k$-monotone functions requires $2^{\Omega(k\cdot \sqrt d\cdot{1/\varepsilon})}$ queries (Blais et al. (RANDOM 2015)).
A Chasm Between Identity and Equivalence Testing with Conditional Queries
We answer a question of Chakraborty et al. (ITCS 2013) showing that non-adaptive uniformity testing indeed requires $\Omega(\log n)$ queries in the conditional model.
Learning circuits with few negations
In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and the class of all functions.
