Related papers: On sample complexity for computational pattern rec…
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…
In the problem of learning with label proportions, which we call LLP learning, the training data is unlabeled, and only the proportions of examples receiving each label are given. The goal is to learn a hypothesis that predicts the…
Contrastive learning is a highly successful technique for learning representations of data from labeled tuples, specifying the distance relations within the tuple. We study the sample complexity of contrastive learning, i.e. the minimum…
Biological and machine pattern recognition systems face a common challenge: Given sensory data about an unknown object, classify the object by comparing the sensory data with a library of internal representations stored in memory. In many…
We address the problem of communicating domain knowledge from a user to the designer of a clustering algorithm. We propose a protocol in which the user provides a clustering of a relatively small random sample of a data set. The algorithm…
In several applications, input samples are more naturally represented in terms of similarities between each other, rather than in terms of feature vectors. In these settings, machine-learning algorithms can become very computationally…
We provide several new results on the sample complexity of vector-valued linear predictors (parameterized by a matrix), and more generally neural networks. Focusing on size-independent bounds, where only the Frobenius norm distance of the…
Exemplar learning of visual similarities in an unsupervised manner is a problem of paramount importance to Computer Vision. In this context, however, the recent breakthrough in deep learning could not yet unfold its full potential. With…
Neural net classifiers trained on data with annotated class labels can also capture apparent visual similarity among categories without being directed to do so. We study whether this observation can be extended beyond the conventional…
We study the problem of learning an adversarially robust predictor to test time attacks in the semi-supervised PAC model. We address the question of how many labeled and unlabeled examples are required to ensure learning. We show that…
In lifelong learning, tasks (or classes) to be learned arrive sequentially over time in arbitrary order. During training, knowledge from previous tasks can be captured and transferred to subsequent ones to improve sample efficiency. We…
The increased availability of data in recent years has led several authors to ask whether it is possible to use data as a {\em computational} resource. That is, if more data is available, beyond the sample complexity limit, is it possible…
Due to the costliness of labelled data in real-world applications, semi-supervised learning, underpinned by pseudo labelling, is an appealing solution. However, handling confusing samples is nontrivial: discarding valuable confusing samples…
Approximate learning machines have become popular in the era of small devices, including quantised, factorised, hashed, or otherwise compressed predictors, and the quest to explain and guarantee good generalisation abilities for such…
We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this "learnability" even when given an amount of data that is too…
Sample compression schemes were defined by Littlestone and Warmuth (1986) as an abstraction of the structure underlying many learning algorithms. Roughly speaking, a sample compression scheme of size $k$ means that given an arbitrary list…
This work continues the study of the relationship between sample compression schemes and statistical learning, which has been mostly investigated within the framework of binary classification. The central theme of this work is establishing…
In this paper, we consider the problem of replicable realizable PAC learning. We construct a particularly hard learning problem and show a sample complexity lower bound with a close to $(\log|H|)^{3/2}$ dependence on the size of the…
Due to the costliness of labelled data in real-world applications, semi-supervised object detectors, underpinned by pseudo labelling, are appealing. However, handling confusing samples is nontrivial: discarding valuable confusing samples…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…