Related papers: Localization of VC Classes: Beyond Local Rademache…
This paper provides a general result on controlling local Rademacher complexities, which captures in an elegant form to relate the complexities with constraint on the expected norm to the corresponding ones with constraint on the empirical…
We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type…
We present a novel notion of complexity that interpolates between and generalizes some classic existing complexity notions in learning theory: for estimators like empirical risk minimization (ERM) with arbitrary bounded losses, it is upper…
The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…
We propose Very Simple Classifier (VSC) a novel method designed to incorporate the concepts of subsampling and locality in the definition of features to be used as the input of a perceptron. The rationale is that locality theoretically…
We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense…
We analyze the local Rademacher complexity of empirical risk minimization (ERM)-based multi-label learning algorithms, and in doing so propose a new algorithm for multi-label learning. Rather than using the trace norm to regularize the…
Machine learning models provide statistically impressive results which might be individually unreliable. To provide reliability, we propose an Epistemic Classifier (EC) that can provide justification of its belief using support from the…
A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. Based on weak…
This guide provides a reference for high-probability regret bounds in empirical risk minimization (ERM). The presentation is modular: we begin with intuition and general proof strategies, then state broadly applicable guarantees under…
We show two novel concentration inequalities for suprema of empirical processes when sampling without replacement, which both take the variance of the functions into account. While these inequalities may potentially have broad applications…
We introduce a novel Entropy-driven Monte Carlo (EdMC) strategy to efficiently sample solutions of random Constraint Satisfaction Problems (CSPs). First, we extend a recent result that, using a large-deviation analysis, shows that the…
We propose a new embedding method which is particularly well-suited for settings where the sample size greatly exceeds the ambient dimension. Our technique consists of partitioning the space into simplices and then embedding the data points…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
We consider robust empirical risk minimization (ERM), where model parameters are chosen to minimize the worst-case empirical loss when each data point varies over a given convex uncertainty set. In some simple cases, such problems can be…
One of the main open problems in the theory of multi-category margin classification is the form of the optimal dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter gamma. From a practical…
We address binary classification using neural ordinary differential equations from the perspective of simultaneous control of $N$ data points. We consider a single-neuron architecture with parameters fixed as piecewise constant functions of…
We derive an upper bound on the local Rademacher complexity of $\ell_p$-norm multiple kernel learning, which yields a tighter excess risk bound than global approaches. Previous local approaches aimed at analyzed the case $p=1$ only while…
This paper considers the design of a minimax test for two hypotheses where the actual probability densities of the observations are located in neighborhoods obtained by placing a bound on the relative entropy between actual and nominal…
We introduce a notion of a point-wise entropy of measures (i.e local entropy) called neutralized local entropy, and compare it with the Brin-Katok local entropy. We show that the neutralized local entropy coincides with Brin-Katok local…