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Found 21 papers, 5 papers with code
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.
Outlier-Robust Learning of Ising Models Under Dobrushin's Condition
We study the problem of learning Ising models satisfying Dobrushin's condition in the outlier-robust setting where a constant fraction of the samples are adversarially corrupted.
Outlier-Robust High-Dimensional Sparse Estimation via Iterative Filtering
Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse PCA.
Testing for Families of Distributions via the Fourier Transform
We study the general problem of testing whether an unknown discrete distribution belongs to a specified family of distributions.
Efficient Algorithms and Lower Bounds for Robust Linear Regression
An error of $\Omega (\epsilon \sigma)$ is information-theoretically necessary, even with infinite sample size.
Sever: A Robust Meta-Algorithm for Stochastic Optimization
In high dimensions, most machine learning methods are brittle to even a small fraction of structured outliers.
Near-Optimal Sample Complexity Bounds for Maximum Likelihood Estimation of Multivariate Log-concave Densities
Prior to this work, no finite sample upper bound was known for this estimator in more than $3$ dimensions.
List-Decodable Robust Mean Estimation and Learning Mixtures of Spherical Gaussians
We give a learning algorithm for mixtures of spherical Gaussians that succeeds under significantly weaker separation assumptions compared to prior work.
Sharp Bounds for Generalized Uniformity Testing
We study the problem of generalized uniformity testing \cite{BC17} of a discrete probability distribution: Given samples from a probability distribution $p$ over an {\em unknown} discrete domain $\mathbf{\Omega}$, we want to distinguish, with probability at least $2/3$, between the case that $p$ is uniform on some {\em subset} of $\mathbf{\Omega}$ versus $\epsilon$-far, in total variation distance, from any such uniform distribution.
Learning Geometric Concepts with Nasty Noise
We give the first polynomial-time PAC learning algorithms for these concept classes with dimension-independent error guarantees in the presence of nasty noise under the Gaussian distribution.
Robustly Learning a Gaussian: Getting Optimal Error, Efficiently
We give robust estimators that achieve estimation error $O(\varepsilon)$ in the total variation distance, which is optimal up to a universal constant that is independent of the dimension.
Being Robust (in High Dimensions) Can Be Practical
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors.
Testing Bayesian Networks
This work initiates a systematic investigation of testing high-dimensional structured distributions by focusing on testing Bayesian networks -- the prototypical family of directed graphical models.
Statistical Query Lower Bounds for Robust Estimation of High-dimensional Gaussians and Gaussian Mixtures
For each of these problems, we show a {\em super-polynomial gap} between the (information-theoretic) sample complexity and the computational complexity of {\em any} Statistical Query algorithm for the problem.
Robust Learning of Fixed-Structure Bayesian Networks
We investigate the problem of learning Bayesian networks in a robust model where an $\epsilon$-fraction of the samples are adversarially corrupted.
Efficient Robust Proper Learning of Log-concave Distributions
We study the {\em robust proper learning} of univariate log-concave distributions (over continuous and discrete domains).
Learning Multivariate Log-concave Distributions
Prior to our work, no upper bound on the sample complexity of this learning problem was known for the case of $d>3$.
Robust Estimators in High Dimensions without the Computational Intractability
We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples.
Properly Learning Poisson Binomial Distributions in Almost Polynomial Time
Given $\widetilde{O}(1/\epsilon^2)$ samples from an unknown PBD $\mathbf{p}$, our algorithm runs in time $(1/\epsilon)^{O(\log \log (1/\epsilon))}$, and outputs a hypothesis PBD that is $\epsilon$-close to $\mathbf{p}$ in total variation distance.
The Fourier Transform of Poisson Multinomial Distributions and its Algorithmic Applications
An $(n, k)$-Poisson Multinomial Distribution (PMD) is a random variable of the form $X = \sum_{i=1}^n X_i$, where the $X_i$'s are independent random vectors supported on the set of standard basis vectors in $\mathbb{R}^k.$ In this paper, we obtain a refined structural understanding of PMDs by analyzing their Fourier transform.
Optimal Learning via the Fourier Transform for Sums of Independent Integer Random Variables
As one of our main structural contributions, we give an efficient algorithm to construct a sparse {\em proper} $\epsilon$-cover for ${\cal S}_{n, k},$ in total variation distance.
