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Found 12 papers, 1 papers with code
Gradient-free optimization of highly smooth functions: improved analysis and a new algorithm
The first algorithm uses a gradient estimator based on randomization over the $\ell_2$ sphere due to Bach and Perchet (2016).
Estimating the minimizer and the minimum value of a regression function under passive design
We propose a new method for estimating the minimizer $\boldsymbol{x}^*$ and the minimum value $f^*$ of a smooth and strongly convex regression function $f$ from the observations contaminated by random noise.
Benign overfitting and adaptive nonparametric regression
In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older classes adaptively to the unknown smoothness.
A gradient estimator via L1-randomization for online zero-order optimization with two point feedback
We present a novel gradient estimator based on two function evaluations and randomization on the $\ell_1$-sphere.
Distributed Zero-Order Optimization under Adversarial Noise
We study the problem of distributed zero-order optimization for a class of strongly convex functions.
Optimization and Control Statistics Theory Statistics Theory
Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandits
The gradient is estimated by a randomized procedure involving two function evaluations and a smoothing kernel.
An alternative to synthetic control for models with many covariates under sparsity
The synthetic control method is a an econometric tool to evaluate causal effects when only one unit is treated.
Does data interpolation contradict statistical optimality?
We show that learning methods interpolating the training data can achieve optimal rates for the problems of nonparametric regression and prediction with square loss.
An $\{l_1,l_2,l_{\infty}\}$-Regularization Approach to High-Dimensional Errors-in-variables Models
Under the first assumption, the rates of convergence of the proposed estimators depend explicitly on $\bar \delta$, while the second assumption has been applied when an estimator for the second moment of the observational error is available.
Empirical entropy, minimax regret and minimax risk
Furthermore, for $p\in(0, 2)$, the excess risk rate matches the behavior of the minimax risk of function estimation in regression problems under the well-specified model.
Nuclear norm penalization and optimal rates for noisy low rank matrix completion
We show that the obtained rates are optimal up to logarithmic factors in a minimax sense and also derive, for any fixed matrix $A_0$, a non-minimax lower bound on the rate of convergence of our estimator, which coincides with the upper bound up to a constant factor.
Sparse recovery under matrix uncertainty
We consider the model {eqnarray*}y=X\theta^*+\xi, Z=X+\Xi,{eqnarray*} where the random vector $y\in\mathbb{R}^n$ and the random $n\times p$ matrix $Z$ are observed, the $n\times p$ matrix $X$ is unknown, $\Xi$ is an $n\times p$ random noise matrix, $\xi\in\mathbb{R}^n$ is a noise independent of $\Xi$, and $\theta^*$ is a vector of unknown parameters to be estimated.
Statistics Theory Statistics Theory
