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Statistical Relational Learning (SRL) methods for anomaly detection are introduced via a security-related application. Operational requirements for online learning stability are outlined and compared to mathematical definitions as applied…
We consider online similarity prediction problems over networked data. We begin by relating this task to the more standard class prediction problem, showing that, given an arbitrary algorithm for class prediction, we can construct an…
Offset Rademacher complexities have been shown to provide tight upper bounds for the square loss in a broad class of problems including improper statistical learning and online learning. We show that the offset complexity can be generalized…
Learning from non-independent and non-identically distributed data poses a persistent challenge in statistical learning. In this study, we introduce data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert…
Online sparse linear regression is an online problem where an algorithm repeatedly chooses a subset of coordinates to observe in an adversarially chosen feature vector, makes a real-valued prediction, receives the true label, and incurs the…
The Statistical Learning Theory (SLT) provides the theoretical guarantees for supervised machine learning based on the Empirical Risk Minimization Principle (ERMP). Such principle defines an upper bound to ensure the uniform convergence of…
This paper describes a family of probabilistic architectures designed for online learning under the logarithmic loss. Rather than relying on non-linear transfer functions, our method gains representational power by the use of data…
We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert space, where the target lies in a vector-valued reproducing kernel Hilbert space induced by an…
We study the online learnability of hypothesis classes with respect to arbitrary, but bounded loss functions. No characterization of online learnability is known at this level of generality. We give a new scale-sensitive combinatorial…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a "leading prediction strategy", which not only…
We study a generalization of the problem of online learning in adversarial linear contextual bandits by incorporating loss functions that belong to a reproducing kernel Hilbert space, which allows for a more flexible modeling of complex…
We study Online Convex Optimization in the unbounded setting where neither predictions nor gradient are constrained. The goal is to simultaneously adapt to both the sequence of gradients and the comparator. We first develop parameter-free…
In this paper, we demonstrate how to learn the objective function of a decision-maker while only observing the problem input data and the decision-maker's corresponding decisions over multiple rounds. We present exact algorithms for this…
In online learning, the data is provided in a sequential order, and the goal of the learner is to make online decisions to minimize overall regrets. This note is concerned with continuous-time models and algorithms for several online…
We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our…
We study the problem of reconstructing solutions of inverse problems when only noisy measurements are available. We assume that the problem can be modeled with an infinite-dimensional forward operator that is not continuously invertible.…
In this paper, we describe families of those bounded linear operators on a separable Hilbert space that are simultaneously unitarily equivalent to integral operators on $L_2(R)$ with bounded and arbitrarily smooth Carleman kernels. The main…
Online linear programming plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…