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Found 14 papers, 0 papers with code
Fitting an ellipsoid to a quadratic number of random points
We consider the problem $(\mathrm{P})$ of fitting $n$ standard Gaussian random vectors in $\mathbb{R}^d$ to the boundary of a centered ellipsoid, as $n, d \to \infty$.
Multivariate mean estimation with direction-dependent accuracy
We consider the problem of estimating the mean of a random vector based on $N$ independent, identically distributed observations.
Learning bounded subsets of $L_p$
We study learning problems in which the underlying class is a bounded subset of $L_p$ and the target $Y$ belongs to $L_p$.
Mean estimation and regression under heavy-tailed distributions--a survey
We dedicate a section on statistical learning problems--in particular, regression function estimation--in the presence of possibly heavy-tailed data.
Approximating the covariance ellipsoid
The slabs are generated using $X_1,..., X_N$, and under minimal assumptions on $X$ (e. g., $X$ can be heavy-tailed) it suffices that $N = c_1d \eta^{-4}\log(2/\eta)$ to ensure that $(1-\eta) {\cal K} \subset {\cal B} \subset (1+\eta){\cal K}$.
Extending the scope of the small-ball method
The small-ball method was introduced as a way of obtaining a high probability, isomorphic lower bound on the quadratic empirical process, under weak assumptions on the indexing class.
An optimal unrestricted learning procedure
We study learning problems involving arbitrary classes of functions $F$, distributions $X$ and targets $Y$.
Column normalization of a random measurement matrix
In this note we answer a question of G. Lecu\'{e}, by showing that column normalization of a random matrix with iid entries need not lead to good sparse recovery properties, even if the generating random variable has a reasonable moment growth.
Sub-Gaussian estimators of the mean of a random vector
We study the problem of estimating the mean of a random vector $X$ given a sample of $N$ independent, identically distributed points.
Regularization, sparse recovery, and median-of-means tournaments
A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables.
`local' vs. `global' parameters -- breaking the gaussian complexity barrier
We show that if $F$ is a convex class of functions that is $L$-subgaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by `local' covering estimates of the class, rather than by the gaussian averages.
On aggregation for heavy-tailed classes
We introduce an alternative to the notion of `fast rate' in Learning Theory, which coincides with the optimal error rate when the given class happens to be convex and regular in some sense.
Learning without Concentration for General Loss Functions
We study prediction and estimation problems using empirical risk minimization, relative to a general convex loss function.
Learning without Concentration
We obtain sharp bounds on the performance of Empirical Risk Minimization performed in a convex class and with respect to the squared loss, without assuming that class members and the target are bounded functions or have rapidly decaying tails.
