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Found 8 papers, 1 papers with code
Efficient Minimax Optimal Estimators For Multivariate Convex Regression
We present the first computationally efficient minimax optimal (up to logarithmic factors) estimators for the tasks of (i) $L$-Lipschitz convex regression (ii) $\Gamma$-bounded convex regression under polytopal support.
On the Minimal Error of Empirical Risk Minimization
We study the minimal error of the Empirical Risk Minimization (ERM) procedure in the task of regression, both in the random and the fixed design settings.
A bounded-noise mechanism for differential privacy
We present an asymptotically optimal $(\epsilon,\delta)$ differentially private mechanism for answering multiple, adaptively asked, $\Delta$-sensitive queries, settling the conjecture of Steinke and Ullman [2020].
On Suboptimality of Least Squares with Application to Estimation of Convex Bodies
We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions.
Convex Regression in Multidimensions: Suboptimality of Least Squares Estimators
The least squares estimator (LSE) is shown to be suboptimal in squared error loss in the usual nonparametric regression model with Gaussian errors for $d \geq 5$ for each of the following families of functions: (i) convex functions supported on a polytope (in fixed design), (ii) bounded convex functions supported on a polytope (in random design), and (iii) convex Lipschitz functions supported on any convex domain (in random design).
Double descent in the condition number
In solving a system of $n$ linear equations in $d$ variables $Ax=b$, the condition number of the $n, d$ matrix $A$ measures how much errors in the data $b$ affect the solution $x$.
Optimality of Maximum Likelihood for Log-Concave Density Estimation and Bounded Convex Regression
In this paper, we study two problems: (1) estimation of a $d$-dimensional log-concave distribution and (2) bounded multivariate convex regression with random design with an underlying log-concave density or a compactly supported distribution with a continuous density.
Space lower bounds for linear prediction in the streaming model
We show that fundamental learning tasks, such as finding an approximate linear separator or linear regression, require memory at least \emph{quadratic} in the dimension, in a natural streaming setting.
