Related papers: Classification in asymmetric spaces via sample com…

The goal of this presentation is to build an efficient non-parametric Bayes classifier in the presence of large numbers of predictors. When analyzing such data, parametric models are often too inflexible while non-parametric procedures tend…

Representation learning is a fundamental task in machine learning, aiming at uncovering structures from data to facilitate subsequent tasks. However, what is a good representation for planning and reasoning in a stochastic world remains an…

The problem of developing binary classifiers from positive and unlabeled data is often encountered in machine learning. A common requirement in this setting is to approximate posterior probabilities of positive and negative classes for a…

We study side-lengths of triangles in path metric spaces. We prove that unless such a space X is bounded, or quasi-isometric to line or half-line, every triple of real numbers satisfying the strict triangle inequalities, is realized by the…

Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…

We survey the recent developments in the theory of quasireg- ular mappings in metric spaces. In particular, we study the geometric porosity of the branch set of quasiregular mappings in general metric measure spaces, and then, introduce the…

Large-sample data became prevalent as data acquisition became cheaper and easier. While a large sample size has theoretical advantages for many statistical methods, it presents computational challenges. Sketching, or compression, is a…

In this paper we study critial isometric and minimal isometric embeddings of classes of Riemannian metrics which we call {\it quasi-$k$-curved metrics}. Quasi-$k$-curved metrics generalize the metrics of space forms. We construct explicit…

Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis),…

Quantum Computing and especially Quantum Machine Learning, in a short period of time, has gained a lot of interest through research groups around the world. This can be seen in the increasing number of proposed models for pattern…

In this note we study the problem of sampling and reconstructing signals which are assumed to lie on or close to one of several subspaces of a Hilbert space. Importantly, we here consider a very general setting in which we allow infinitely…

Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…

Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…

The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…

The class of quasisymmetric mappings on the real axis was first introduced by A. Beurling and L. V. Ahlfors in 1956. In 1980 P. Tukia and J. V\"{a}is\"{a}l\"{a} considered these mappings between general metric spaces. In our paper we…

Learning physical properties of high-dimensional states is crucial for developing quantum technologies but usually consumes an exceedingly large number of samples which are difficult to afford in practice. In this Letter, we use the…

We define thin and asymptotically scattered metric spaces as asymptotic counterparts of discrete and scattered metric spaces respectively. We characterize asymptotically scattered spaces in terms of prohibited subspaces, and classify thin…

Contrastive learning produces coherent semantic feature embeddings by encouraging positive samples to cluster closely while separating negative samples. However, existing contrastive learning methods lack principled guarantees on coverage…

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…

Few-shot image classification is a challenging problem that aims to achieve the human level of recognition based only on a small number of training images. One main solution to few-shot image classification is deep metric learning. These…