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Robust Regression of General ReLUs with Queries
Ilias Diakonikolas, Daniel M. Kane, Mingchen Ma
We study the task of agnostically learning general (as opposed to homogeneous) ReLUs under the Gaussian distribution with respect to the squared loss. In the passive learning setti…
High-Dimensional Gaussian Mean Estimation under Realizable Contamination
Ilias Diakonikolas, Daniel M. Kane, Thanasis Pittas
We study mean estimation for a Gaussian distribution with identity covariance in under a missing data scheme termed realizable -contamination model. In this model…
Sample Complexity Bounds for Robust Mean Estimation with Mean-Shift Contamination
Ilias Diakonikolas, Giannis Iakovidis, Daniel M. Kane +1
We study the basic task of mean estimation in the presence of mean-shift contamination. In the mean-shift contamination model, an adversary is allowed to replace a small constant f…
Statistical Query Lower Bounds for Smoothed Agnostic Learning
Ilias Diakonikolas, Daniel M. Kane
We study the complexity of smoothed agnostic learning, recently introduced by~\cite{CKKMS24}, in which the learner competes with the best classifier in a target class under slight…
Replicable Distribution Testing
Ilias Diakonikolas, Jingyi Gao, Daniel Kane +2
We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probabili…
Algorithms and SQ Lower Bounds for Robustly Learning Real-valued Multi-index Models
Ilias Diakonikolas, Giannis Iakovidis, Daniel M. Kane +1
We study the complexity of learning real-valued Multi-Index Models (MIMs) under the Gaussian distribution. A -MIM is a function that depends only…
On Learning Parallel Pancakes with Mostly Uniform Weights
Ilias Diakonikolas, Daniel M. Kane, Sushrut Karmalkar +2
We study the complexity of learning -mixtures of Gaussians (-GMMs) on . This task is known to have complexity in full generality. To circumvent this…
Faster Algorithms for Agnostically Learning Disjunctions and their Implications
Ilias Diakonikolas, Daniel M. Kane, Lisheng Ren
We study the algorithmic task of learning Boolean disjunctions in the distribution-free agnostic PAC model. The best known agnostic learner for the class of disjunctions over $\{0,…
Batch List-Decodable Linear Regression via Higher Moments
Ilias Diakonikolas, Daniel M. Kane, Sushrut Karmalkar +2
We study the task of list-decodable linear regression using batches. A batch is called clean if it consists of i.i.d. samples from an unknown linear regression distribution. For a…
Robust Learning of Multi-index Models via Iterative Subspace Approximation
Ilias Diakonikolas, Giannis Iakovidis, Daniel M. Kane +1
We study the task of learning Multi-Index Models (MIMs) with label noise under the Gaussian distribution. A -MIM is any function that only depends on a -dimensional subsp…
Active Learning of General Halfspaces: Label Queries vs Membership Queries
Ilias Diakonikolas, Daniel M. Kane, Mingchen Ma
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces under the Gaussian distribution on in the presence of some form of query access. In th…
Efficient Testable Learning of General Halfspaces with Adversarial Label Noise
Ilias Diakonikolas, Daniel M. Kane, Sihan Liu +1
We study the task of testable learning of general -- not necessarily homogeneous -- halfspaces with adversarial label noise with respect to the Gaussian distribution. In the testab…
Robust Sparse Estimation for Gaussians with Optimal Error under Huber Contamination
Ilias Diakonikolas, Daniel M. Kane, Sushrut Karmalkar +2
We study Gaussian sparse estimation tasks in Huber's contamination model with a focus on mean estimation, PCA, and linear regression. For each of these tasks, we give the first sam…
SQ Lower Bounds for Non-Gaussian Component Analysis with Weaker Assumptions
Ilias Diakonikolas, Daniel Kane, Lisheng Ren +1
We study the complexity of Non-Gaussian Component Analysis (NGCA) in the Statistical Query (SQ) model. Prior work developed a general methodology to prove SQ lower bounds for this…
Agnostically Learning Multi-index Models with Queries
Ilias Diakonikolas, Daniel M. Kane, Vasilis Kontonis +2
We study the power of query access for the task of agnostic learning under the Gaussian distribution. In the agnostic model, no assumptions are made on the labels and the goal is t…
Clustering Mixtures of Bounded Covariance Distributions Under Optimal Separation
Ilias Diakonikolas, Daniel M. Kane, Jasper C. H. Lee +1
We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a -component mixtu…
Online Robust Mean Estimation
Daniel M. Kane, Ilias Diakonikolas, Hanshen Xiao +1
We study the problem of high-dimensional robust mean estimation in an online setting. Specifically, we consider a scenario where sensors are measuring some common, ongoing phen…