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This paper studies the problem of {\em learning} the probability distribution $P_X$ of a discrete random variable $X$ using indirect and sequential samples. At each time step, we choose one of the possible $K$ functions, $g_1, \ldots, g_K$…

Due to the significant increase in the size of spatial data, it is essential to use distributed parallel processing systems to efficiently analyze spatial data. In this paper, we first study learned spatial data partitioning, which…

In this paper, we present a novel algorithm for piecewise linear regression which can learn continuous as well as discontinuous piecewise linear functions. The main idea is to repeatedly partition the data and learn a liner model in in each…

In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution…

Probabilistic mixture models have been widely used for different machine learning and pattern recognition tasks such as clustering, dimensionality reduction, and classification. In this paper, we focus on trying to solve the most common…

Inspired by a recent classical distribution-free junta tester by Chen, Liu, Serverdio, Sheng, and Xie (STOC'18), we construct a quantum tester for the same problem with complexity $O(k/\varepsilon)$, which constitutes a quadratic…

We study the interplay between the data distribution and Q-learning-based algorithms with function approximation. We provide a unified theoretical and empirical analysis as to how different properties of the data distribution influence the…

At the interface of machine learning and quantum computing, an important question is what distributions can be learned provably with optimal sample complexities and with quantum-accelerated time complexities. In the classical case, Klivans…

Curriculum learning (CL) - training using samples that are generated and presented in a meaningful order - was introduced in the machine learning context around a decade ago. While CL has been extensively used and analysed empirically,…

Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…

We consider the problem of distributed learning, where a network of agents collectively aim to agree on a hypothesis that best explains a set of distributed observations of conditionally independent random processes. We propose a…

We give an algorithm for learning $O(\log n)$ juntas in polynomial-time with respect to Markov Random Fields (MRFs) in a smoothed analysis framework where only the external field has been randomly perturbed. This is a broad generalization…

In a recent breakthrough, [Bshouty et al., 2005] obtained the first passive-learning algorithm for DNFs under the uniform distribution. They showed that DNFs are learnable in the Random Walk and Noise Sensitivity models. We extend their…

This paper introduces distribution-based prediction, a novel approach to using Large Language Models (LLMs) as predictive tools by interpreting output token probabilities as distributions representing the models' learned representation of…

The $K$-nearest neighbors is a basic problem in machine learning with numerous applications. In this problem, given a (training) set of $n$ data points with labels and a query point $p$, we want to assign a label to $p$ based on the labels…

We propose statistically robust and computationally efficient linear learning methods in the high-dimensional batch setting, where the number of features $d$ may exceed the sample size $n$. We employ, in a generic learning setting, two…

We prove hardness-of-learning results under a well-studied assumption on the existence of local pseudorandom generators. As we show, this assumption allows us to surpass the current state of the art, and prove hardness of various basic…

Neural networks (NN) perform well in diverse tasks, but sometimes produce nonsensical results to humans. Most NN models "solely" learn from (input, output) pairs, occasionally conflicting with human knowledge. Many studies indicate…

Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $\Vert \cdot \Vert_*$. However, despite the assortment of computational methods for such problems,…

Learning joint probability distributions on n random variables requires exponential sample size in the generic case. Here we consider the case that a temporal (or causal) order of the variables is known and that the (unknown) graph of…