Related papers: Chaining Bounds for Empirical Risk Minimization
We introduce a modified version of the excess risk, which can be used to obtain tighter, fast-rate PAC-Bayesian generalisation bounds. This modified excess risk leverages information about the relative hardness of data examples to reduce…
This paper proposes near-optimal algorithms for the pure-exploration linear bandit problem in the fixed confidence and fixed budget settings. Leveraging ideas from the theory of suprema of empirical processes, we provide an algorithm whose…
Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…
We study quantile trend filtering, a recently proposed method for nonparametric quantile regression with the goal of generalizing existing risk bounds known for the usual trend filtering estimators which perform mean regression. We study…
The paper considers the problem of global optimization in the setup of stochastic process bandits. We introduce an UCB algorithm which builds a cascade of discretization trees based on generic chaining in order to render possible his…
The radiological characterization of contaminated elements (walls, grounds, objects) from nuclear facilities often suffers from a too small number of measurements. In order to determine risk prediction bounds on the level of contamination,…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling…
We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes…
Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal…
We study the statistical properties of the least squares estimator in unimodal sequence estimation. Although closely related to isotonic regression, unimodal regression has not been as extensively studied. We show that the unimodal least…
We study estimation of a multivariate function $f:{\bf R}^d \to {\bf R}$ when the observations are available from function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are studied.…
Empirically it has been observed that the performance of deep neural networks steadily improves as we increase model size, contradicting the classical view on overfitting and generalization. Recently, the double descent phenomena has been…
Scenario decision making offers a flexible way of making decision in an uncertain environment while obtaining probabilistic guarantees on the risk of failure of the decision. The idea of this approach is to draw samples of the uncertainty…
Risk-sensitive control balances performance with resilience to unlikely events in uncertain systems. This paper introduces ergodic-risk criteria, which capture long-term cumulative risks through probabilistic limit theorems. By ensuring the…
We study the excess minimum risk in statistical inference, defined as the difference between the minimum expected loss in estimating a random variable from an observed feature vector and the minimum expected loss in estimating the same…
Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research. The prediction task may be given as…
We derive lower bounds on the Bayes risk in decentralized estimation, where the estimator does not have direct access to the random samples generated conditionally on the random parameter of interest, but only to the data received from…
We revisit the sequential variants of linear regression with the squared loss, classification problems with hinge loss, and logistic regression, all characterized by unbounded losses in the setup where no assumptions are made on the…