Related papers: The Learning and Communication Complexity of Subse…

In statistical setting of the pattern recognition problem the number of examples required to approximate an unknown labelling function is linear in the VC dimension of the target learning class. In this work we consider the question whether…

Alice and Bob are given $n$-bit integer pairs $(x,y)$ and $(a,b)$, respectively, and they must decide if $y=ax+b$. We prove that the randomised communication complexity of this Point--Line Incidence problem is $\Theta(\log n)$. This…

Gathering training data is a key step of any supervised learning task, and it is both critical and expensive. Critical, because the quantity and quality of the training data has a high impact on the performance of the learned function.…

This paper resolves two open problems from a recent paper, arXiv:2403.16981, concerning the sample complexity of distributed simple binary hypothesis testing under information constraints. The first open problem asks whether interaction…

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…

We study the problem of identifying correlations in multivariate data, under information constraints: Either on the amount of memory that can be used by the algorithm, or the amount of communication when the data is distributed across…

In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…

Communication complexity is the amount of communication needed to compute a function when the function inputs are distributed over multiple parties. In its simplest form, one-way communication complexity, Alice and Bob compute a function…

We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection $\{(S_i,l_i)\}_{i=1}^n$, where each $S_i$ is a sample drawn from the probability distribution of $X_i…

Modern computing and communication technologies can make data collection procedures very efficient. However, our ability to analyze large data sets and/or to extract information out from them is hard-pressed to keep up with our capacities…

We investigate the problem of approximating the product $a^TBc$, where $a,c\in S^{n-1}$ and $B\in O_n$, in models of communication complexity and streaming algorithms. The worst meaningful approximation is to simply decide whether the…

Most self-supervised learning (SSL) methods learn continuous visual representations by aligning different views of the same input, offering limited control over how information is structured across representation dimensions. In this work,…

Classification is an important task in many fields including biomedical research and machine learning. Traditionally, a classification rule is constructed based a bunch of labeled data. Recently, due to technological innovation and…

Contrastive learning has achieved remarkable success in learning effective representations, with supervised contrastive learning often outperforming self-supervised approaches. However, in real-world scenarios, data annotations are often…

In communication complexity the input of a function $f:X\times Y\rightarrow Z$ is distributed between two players Alice and Bob. If Alice knows only $x\in X$ and Bob only $y\in Y$, how much information must Alice and Bob share to be able to…

We investigate certain word-construction games with variable turn orders. In these games, Alice and Bob take turns on choosing consecutive letters of a word of fixed length, with Alice winning if the result lies in a predetermined target…

The problem of statistical learning is to construct a predictor of a random variable $Y$ as a function of a related random variable $X$ on the basis of an i.i.d. training sample from the joint distribution of $(X,Y)$. Allowable predictors…

We consider a binary supervised learning classification problem where instead of having data in a finite-dimensional Euclidean space, we observe measures on a compact space $\mathcal{X}$. Formally, we observe data $D_N = (\mu_1, Y_1),…

Why are classifiers in high dimension vulnerable to "adversarial" perturbations? We show that it is likely not due to information theoretic limitations, but rather it could be due to computational constraints. First we prove that, for a…

Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…