We prove new concentration inequalities for random variables.
problem Concentration of random variables in nonlinear functions.
method Efron-Stein inequalities and PAC-Bayesian approach.
result User-friendly concentration bounds for various applications.
A new method for evaluating and selecting policies in contextual bandits improves confidence intervals and policy quality.
problem Evaluating and selecting policies in contextual bandits with logged data.
method Self-normalized Importance Weighting (SN) estimator with Efron-Stein tail inequality and multiplicative bias control.
result The method provides tighter confidence intervals and better policy selection compared to competitors.
New algorithms for hypothesis testing in high-dimensional data are shown to be effective under various noisy conditions.
problem Testing high-dimensional probability measures under noisy conditions.
method Low coordinate degree functions (LCDF) using Efron-Stein decomposition.
result LCDF can effectively test high-dimensional probability measures under noisy channels, with efficacy depending on scalar Fisher information.
New method TLC improves transductive learning bounds.
problem Sharp generalization bounds for transductive learning.
method Transductive Local Complexity (TLC) framework.
result Nearly sharp bounds consistent with inductive results.
Bagging is a device intended for reducing the prediction error of learning algorithms. In its simplest form, bagging draws bootstrap samples from the training sample, applies the learning algorithm to each bootstrap sample, and then averages the resulting prediction rules. We extend the definition of bagging from stati…
The network jackknife provides conservative variance estimates for network statistics.
problem Estimating the variance of network statistics.
method Leave-node-out jackknife procedure for network data under the sparse graphon model.
result The network jackknife leads to conservative estimates of the variance for network functionals invariant to node permutation.
We consider a priori generalization bounds developed in terms of cross-validation estimates and the stability of learners. In particular, we first derive an exponential Efron-Stein type tail inequality for the concentration of a general function of n independent random variables. Next, under some reasonable notion of s…
New measure of robustness for estimators, with tight bounds for Gaussian mean estimation.
problem Developing robust statistical estimators for datasets with noise or outliers.
method Introducing empirical sensitivity as a new robustness measure and proving lower bounds for Gaussian mean estimation.
result Empirical sensitivity bounds for optimal estimators are tight, showing obstructions on mean and variance.
There is accumulating evidence in the literature that stability of learning algorithms is a key characteristic that permits a learning algorithm to generalize. Despite various insightful results in this direction, there seems to be an overlooked dichotomy in the type of stability-based generalization bounds we have in …
Study of asymmetric rank-one tensor models with non-Gaussian noise.
problem Analyzing maximum-likelihood estimators for asymmetric rank-one tensor models.
method Spectrally separated branch analysis, resolvent methods, cumulant expansions, Efron-Stein-type variance bounds.
result Asymptotic singular value and mode-wise alignments are robust to non-Gaussian noise.
New tools in nonlinear random matrices improve understanding of the Sum of Squares hierarchy.
problem Improving the Sum of Squares (SoS) hierarchy's performance on average-case problems.
method Developed new tools in nonlinear random matrices and applied them to analyze the SoS hierarchy.
result Subexponential-time SoS lower bounds for various problems, offering evidence for the low-degree likelihood ratio hypothesis.