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Found 15 papers, 0 papers with code
Privately Estimating a Gaussian: Efficient, Robust and Optimal
We prove a new lower bound on differentially private covariance estimation to show that the dependence on the condition number $\kappa$ in the above sample bound is also tight.
A Moment-Matching Approach to Testable Learning and a New Characterization of Rademacher Complexity
A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of \emph{testable learning}, where the goal is to replace hard-to-verify distributional assumptions (such as Gaussianity) with efficiently testable ones and to require that the learner succeed whenever the unknown distribution passes the corresponding test.
List-Decodable Covariance Estimation
For any $\alpha > 0$, our algorithm takes input a sample $Y \subseteq \mathbb{R}^d$ of size $n\geq d^{\mathsf{poly}(1/\alpha)}$ obtained by adversarially corrupting an $(1-\alpha)n$ points in an i. i. d.
Private Robust Estimation by Stabilizing Convex Relaxations
Prior works obtained private robust algorithms for mean estimation of subgaussian distributions with bounded covariance.
Memory-Sample Lower Bounds for Learning Parity with Noise
We show that any learning algorithm for the learning problem corresponding to $M$, with error, requires either a memory of size at least $\Omega\left(\frac{k \cdot \ell}{\varepsilon} \right)$, or at least $2^{\Omega(r)}$ samples.
Robustly Learning Mixtures of $k$ Arbitrary Gaussians
We give a polynomial-time algorithm for the problem of robustly estimating a mixture of $k$ arbitrary Gaussians in $\mathbb{R}^d$, for any fixed $k$, in the presence of a constant fraction of arbitrary corruptions.
Sparse PCA: Algorithms, Adversarial Perturbations and Certificates
Despite a long history of prior works, including explicit studies of perturbation resilience, the best known algorithmic guarantees for Sparse PCA are fragile and break down under small adversarial perturbations.
List-Decodable Subspace Recovery: Dimension Independent Error in Polynomial Time
As a result, in addition to Gaussians, our algorithm applies to the uniform distribution on the hypercube and $q$-ary cubes and arbitrary product distributions with subgaussian marginals.
List-Decodable Linear Regression
To complement our result, we prove that the anti-concentration assumption on the inliers is information-theoretically necessary.
On the Expressive Power of Kernel Methods and the Efficiency of Kernel Learning by Association Schemes
We study the expressive power of kernel methods and the algorithmic feasibility of multiple kernel learning for a special rich class of kernels.
Efficient Algorithms for Outlier-Robust Regression
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels.
An Analysis of the t-SNE Algorithm for Data Visualization
A first line of attack in exploratory data analysis is data visualization, i. e., generating a 2-dimensional representation of data that makes clusters of similar points visually identifiable.
Outlier-robust moment-estimation via sum-of-squares
We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers.
Better Agnostic Clustering Via Relaxed Tensor Norms
As an immediate corollary, for any $\gamma > 0$, we obtain an efficient algorithm for learning the means of a mixture of $k$ arbitrary \Poincare distributions in $\mathbb{R}^d$ in time $d^{O(1/\gamma)}$ so long as the means have separation $\Omega(k^{\gamma})$.
Agnostic Learning by Refuting
We introduce \emph{refutation complexity}, a natural computational analog of Rademacher complexity of a Boolean concept class and show that it exactly characterizes the sample complexity of \emph{efficient} agnostic learning.
