Related papers: Unlabelled Sample Compression Schemes for Intersec…
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…
The Sauer-Shelah-Perles Lemma is a cornerstone of combinatorics and learning theory, bounding the size of a binary hypothesis class in terms of its Vapnik-Chervonenkis (VC) dimension. For classes of functions over a $k$-ary alphabet, namely…
Set systems of finite VC dimension are frequently used in applications relating to machine learning theory and statistics. Two simple types of VC classes which have been widely studied are the maximum classes (those which are extremal with…
Anomaly Detection is a relevant problem that arises in numerous real-world applications, especially when dealing with images. However, there has been little research for this task in the Continual Learning setting. In this work, we…
We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…
Semi-supervised learning (SSL) provides a powerful framework for leveraging unlabeled data when labels are limited or expensive to obtain. SSL algorithms based on deep neural networks have recently proven successful on standard benchmark…
One-class classification has been a prevailing method in building deep anomaly detection models under the assumption that a dataset consisting of normal samples is available. In practice, however, abnormal samples are often mixed in a…
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…
Unsupervised Deep Distance Metric Learning (UDML) aims to learn sample similarities in the embedding space from an unlabeled dataset. Traditional UDML methods usually use the triplet loss or pairwise loss which requires the mining of…
In response to a 1997 problem of M. Vidyasagar, we state a necessary and sufficient condition for distribution-free PAC learnability of a concept class $\mathscr C$ under the family of all non-atomic (diffuse) measures on the domain…
We introduce and study the spherical dimension, a natural topological relaxation of the VC dimension that unifies several results in learning theory where topology plays a key role in the proofs. The spherical dimension is defined by…
Metric learning is an important problem in machine learning. It aims to group similar examples together. Existing state-of-the-art metric learning approaches require class labels to learn a metric. As obtaining class labels in all…
Weakly Supervised Semantic Segmentation (WSSS) with image-level labels has gained attention for its cost-effectiveness. Most existing methods emphasize inter-class separation, often neglecting the shared semantics among related categories…
The Poisson-sampling technique eliminates dependencies among symbol appearances in a random sequence. It has been used to simplify the analysis and strengthen the performance guarantees of randomized algorithms. Applying this method to…
This paper studies quantum supervised learning for classical inference from quantum states. In this model, a learner has access to a set of labeled quantum samples as the training set. The objective is to find a quantum measurement that…
For any family of measurable sets in a probability space, we show that either (i) the family has infinite Vapnik-Chervonenkis (VC) dimension or (ii) for every epsilon > 0 there is a finite partition pi such the pi-boundary of each set has…
Learning curves plot the expected error of a learning algorithm as a function of the number of labeled samples it receives from a target distribution. They are widely used as a measure of an algorithm's performance, but classic PAC learning…
Multi-distribution learning is a natural generalization of PAC learning to settings with multiple data distributions. There remains a significant gap between the known upper and lower bounds for PAC-learnable classes. In particular, though…
With the advent of media streaming, video action recognition has become progressively important for various applications, yet at the high expense of requiring large-scale data labelling. To overcome the problem of expensive data labelling,…
Fix positive integers $k$ and $d$. We show that, as $n\to\infty$, any set system $\mathcal{A} \subset 2^{[n]}$ for which the VC dimension of $\{ \triangle_{i=1}^k S_i \mid S_i \in \mathcal{A}\}$ is at most $d$ has size at most…