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Found 22 papers, 2 papers with code
The Sample Complexity of Simple Binary Hypothesis Testing
In this paper, we derive a formula that characterizes the sample complexity (up to multiplicative constants that are independent of $p$, $q$, and all error parameters) for: (i) all $0 \le \alpha, \beta \le 1/8$ in the prior-free setting; and (ii) all $\delta \le \alpha/4$ in the Bayesian setting.
Robust Sparse Estimation for Gaussians with Optimal Error under Huber Contamination
Concretely, for Gaussian robust $k$-sparse mean estimation on $\mathbb{R}^d$ with corruption rate $\epsilon>0$, our algorithm has sample complexity $(k^2/\epsilon^2)\mathrm{polylog}(d/\epsilon)$, runs in sample polynomial time, and approximates the target mean within $\ell_2$-error $O(\epsilon)$.
A Sub-Quadratic Time Algorithm for Robust Sparse Mean Estimation
We study the algorithmic problem of sparse mean estimation in the presence of adversarial outliers.
Black-Box $k$-to-$1$-PCA Reductions: Theory and Applications
The $k$-principal component analysis ($k$-PCA) problem is a fundamental algorithmic primitive that is widely-used in data analysis and dimensionality reduction applications.
Near-Optimal Algorithms for Gaussians with Huber Contamination: Mean Estimation and Linear Regression
We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination.
Nearly-Linear Time and Streaming Algorithms for Outlier-Robust PCA
Our main contribution is to develop a nearly-linear time algorithm for robust PCA with near-optimal error guarantees.
Simple Binary Hypothesis Testing under Local Differential Privacy and Communication Constraints
For the sample complexity of simple hypothesis testing under pure LDP constraints, we establish instance-optimal bounds for distributions with binary support; minimax-optimal bounds for general distributions; and (approximately) instance-optimal, computationally efficient algorithms for general distributions.
Outlier-Robust Sparse Mean Estimation for Heavy-Tailed Distributions
We study the fundamental task of outlier-robust mean estimation for heavy-tailed distributions in the presence of sparsity.
Gaussian Mean Testing Made Simple
Here we give an extremely simple algorithm for Gaussian mean testing with a one-page analysis.
List-Decodable Sparse Mean Estimation via Difference-of-Pairs Filtering
We study the problem of list-decodable sparse mean estimation.
Robust Sparse Mean Estimation via Sum of Squares
In this work, we develop the first efficient algorithms for robust sparse mean estimation without a priori knowledge of the covariance.
Communication-constrained hypothesis testing: Optimality, robustness, and reverse data processing inequalities
We show that the sample complexity of simple binary hypothesis testing under communication constraints is at most a logarithmic factor larger than in the unconstrained setting and this bound is tight.
Streaming Algorithms for High-Dimensional Robust Statistics
In this work, we develop the first efficient streaming algorithms for high-dimensional robust statistics with near-optimal memory requirements (up to logarithmic factors).
Statistical Query Lower Bounds for List-Decodable Linear Regression
We study the problem of list-decodable linear regression, where an adversary can corrupt a majority of the examples.
Optimal Lottery Tickets via Subset Sum: Logarithmic Over-Parameterization is Sufficient
We show that any target network of width $d$ and depth $l$ can be approximated by pruning a random network that is a factor $O(log(dl))$ wider and twice as deep.
Robust regression with covariate filtering: Heavy tails and adversarial contamination
We study the problem of linear regression where both covariates and responses are potentially (i) heavy-tailed and (ii) adversarially contaminated.
Outlier Robust Mean Estimation with Subgaussian Rates via Stability
We study the problem of outlier robust high-dimensional mean estimation under a finite covariance assumption, and more broadly under finite low-degree moment assumptions.
Optimal Lottery Tickets via SubsetSum: Logarithmic Over-Parameterization is Sufficient
We show that any target network of width $d$ and depth $l$ can be approximated by pruning a random network that is a factor $O(\log(dl))$ wider and twice as deep.
Extracting robust and accurate features via a robust information bottleneck
We propose a novel strategy for extracting features in supervised learning that can be used to construct a classifier which is more robust to small perturbations in the input space.
Estimating location parameters in entangled single-sample distributions
In the multivariate setting, we generalize our theory to mean estimation for mixtures of radially symmetric distributions, and derive minimax lower bounds on the expected error of any estimator that is agnostic to the scales of individual data points.
Deep Topic Models for Multi-label Learning
We present a probabilistic framework for multi-label learning based on a deep generative model for the binary label vector associated with each observation.
Generalization Error Bounds for Noisy, Iterative Algorithms
In statistical learning theory, generalization error is used to quantify the degree to which a supervised machine learning algorithm may overfit to training data.
