Related papers: Risk bounds when learning infinitely many response…
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…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…
Deep learning methods minimise the empirical risk using loss functions such as the cross entropy loss. When minimising the empirical risk, the generalisation of the learnt function still depends on the performance on the training data, the…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
In many applications of relational learning, the available data can be seen as a sample from a larger relational structure (e.g. we may be given a small fragment from some social network). In this paper we are particularly concerned with…
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 present a framework to derive risk bounds for vector-valued learning with a broad class of feature maps and loss functions. Multi-task learning and one-vs-all multi-category learning are treated as examples. We discuss in detail…
We prove risk bounds for binary classification in high-dimensional settings when the sample size is allowed to be smaller than the dimensionality of the training set observations. In particular, we prove upper bounds for both 'compressive…
The paper focuses on mean-field type multi-agent control problems with finite state and action spaces where the dynamics and cost structures are symmetric and homogeneous, and are affected by the distribution of the agents. A standard…
We derive bounds for a notion of adversarial risk, designed to characterize the robustness of linear and neural network classifiers to adversarial perturbations. Specifically, we introduce a new class of function transformations with the…
In this paper, we consider the problem of minimizing a linear functional subject to uncertain linear and bilinear matrix inequalities, which depend in a possibly nonlinear way on a vector of uncertain parameters. Motivated by recent results…
This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…
This work studies the problem of learning under both large datasets and large-dimensional feature space scenarios. The feature information is assumed to be spread across agents in a network, where each agent observes some of the features.…
Trace norm regularization is a popular method of multitask learning. We give excess risk bounds with explicit dependence on the number of tasks, the number of examples per task and properties of the data distribution. The bounds are…
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. When the input…
Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…
This work studies discrete-time discounted Markov decision processes with continuous state and action spaces and addresses the inverse problem of inferring a cost function from observed optimal behavior. We first consider the case in which…
Directed and undirected graphical models, also called Bayesian networks and Markov random fields, respectively, are important statistical tools in a wide variety of fields, ranging from computational biology to probabilistic artificial…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
High-dimensional data is common in multiple areas, such as health care and genomics, where the number of features can be tens of thousands. In such scenarios, the large number of features often leads to inefficient learning. Constraint…