Related papers: Agnostic Online Learning and Excellent Sets
Szemer\'edi's regularity lemma is a powerful tool in graph theory. It states that for every large enough graph, there exists a partition of the edge set with bounded size such that most induced subgraphs are quasirandom. When the graph is a…
Agnostic online learning is classically solved via a reduction to the realizable setting, utilizing Littlestone's Standard Optimal Algorithm (SOA) as a base learner. However, the SOA is computationally intractable to execute even for a…
We present online prediction methods for time series that let us explicitly handle nonstationary artifacts (e.g. trend and seasonality) present in most real time series. Specifically, we show that applying appropriate transformations to…
The arithmetic regularity lemma for $\mathbb{F}_p^n$, proved by Green in 2005, states that given a subset $A\subseteq \mathbb{F}_p^n$, there exists a subspace $H\leq \mathbb{F}_p^n$ of bounded codimension such that $A$ is Fourier-uniform…
In order to develop practical and efficient algorithms while circumventing overly pessimistic computational lower bounds, recent work has been interested in developing oracle-efficient algorithms in a variety of learning settings. Two such…
We prove that every online learnable class of functions of Littlestone dimension $d$ admits a learning algorithm with finite information complexity. Towards this end, we use the notion of a globally stable algorithm. Generally, the…
Which classes can be learned properly in the online model? -- that is, by an algorithm that at each round uses a predictor from the concept class. While there are simple and natural cases where improper learning is necessary, it is natural…
We study a theoretical and algorithmic framework for structured prediction in the online learning setting. The problem of structured prediction, i.e. estimating function where the output space lacks a vectorial structure, is well studied in…
We introduce a model of online algorithms subject to strict constraints on data retention. An online learning algorithm encounters a stream of data points, one per round, generated by some stationary process. Crucially, each data point can…
This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…
Frei et al. [6] showed that the problem to decide whether a graph is stable with respect to some graph parameter under adding or removing either edges or vertices is $\Theta_2^{\text{P}}$-complete. They studied the common graph parameters…
We initiate the study of numerical linear algebra in the sliding window model, where only the most recent $W$ updates in a stream form the underlying data set. We first introduce a unified row-sampling based framework that gives randomized…
Online learning with expert advice is widely used in various machine learning tasks. It considers the problem where a learner chooses one from a set of experts to take advice and make a decision. In many learning problems, experts may be…
Ensemble learning of $K$ nonlinear perceptrons, which determine their outputs by sign functions, is discussed within the framework of online learning and statistical mechanics. One purpose of statistical learning theory is to theoretically…
This paper deals with order identification for nested models in the i.i.d. framework. We study the asymptotic efficiency of two generalized likelihood ratio tests of the order. They are based on two estimators which are proved to be…
Ensemble learning is a process by which multiple base learners are strategically generated and combined into one composite learner. There are two features that are essential to an ensemble's performance, the individual accuracies of the…
Strongly stable monomial ideals are important in algebraic geometry, commutative algebra, and combinatorics. Prompted, for example, by combinatorial approaches for studying Hilbert schemes and the existence of maximal total Betti numbers…
Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…
We propose a new hierarchy of semidefinite programming relaxations for inference problems. As test cases, we consider the problem of community detection in block models. The vertices are partitioned into $k$ communities, and a graph is…
In many quantum tasks, there is an unknown quantum object that one wishes to learn. An online strategy for this task involves adaptively refining a hypothesis to reproduce such an object or its measurement statistics. A common evaluation…