Related papers: On Statistical Learning of Simplices: Unmixing Pro…

This study presents PRISM, a probabilistic simplex component analysis approach to identifying the vertices of a data-circumscribing simplex from data. The problem has a rich variety of applications, the most notable being hyperspectral…

We study the tradeoff between sample complexity and round complexity in on-demand sampling, where the learning algorithm adaptively samples from $k$ distributions over a limited number of rounds. In the realizable setting of…

In learning theory, a standard assumption is that the data is generated from a finite mixture model. But what happens when the number of components is not known in advance? The problem of estimating the number of components, also called…

Sample complexity of bias estimation is a lower bound on the runtime of any bias detection method. Many regulatory frameworks require the bias to be tested for all subgroups, whose number grows exponentially with the number of protected…

In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of distributions, given one \emph{single} sample from each distribution. We study mean estimation and linear…

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…

We propose a method of reduction of experimental noise in single-pixel imaging by expressing the subsets of sampling patterns as linear combinations of vertices of a multidimensional regular simplex. This method may be also directly…

Stabilizing an unknown dynamical system is one of the central problems in control theory. In this paper, we study the sample complexity of the learn-to-stabilize problem in Linear Time-Invariant (LTI) systems on a single trajectory. Current…

We study the task of learning Multi-Index Models (MIMs) with label noise under the Gaussian distribution. A $K$-MIM is any function $f$ that only depends on a $K$-dimensional subspace. We focus on well-behaved MIMs with finite ranges that…

We provide high-probability sample complexity guarantees for exact structure recovery and accurate predictive learning using noise-corrupted samples from an acyclic (tree-shaped) graphical model. The hidden variables follow a…

Binary classification from positive-only samples is a variant of PAC learning where the learner receives i.i.d. positive samples and aims to learn a classifier with low error. Previous work by Natarajan, Gereb-Graus, and Shvaytser…

We show that $n$-variable tree-structured Ising models can be learned computationally-efficiently to within total variation distance $\epsilon$ from an optimal $O(n \ln n/\epsilon^2)$ samples, where $O(\cdot)$ hides an absolute constant…

We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…

We consider a learning problem of identifying a dictionary matrix D (M times N dimension) from a sample set of M dimensional vectors Y = N^{-1/2} DX, where X is a sparse matrix (N times P dimension) in which the density of non-zero entries…

Transfer learning is an essential technique for many machine learning/AI models of complex structures such as large language models and generative AI. The essence of transfer learning is to leverage knowledge from resolved source tasks for…

Simplicial complexes form an important class of topological spaces that are frequently used in many application areas such as computer-aided design, computer graphics, and simulation. Representation learning on graphs, which are just 1-d…

Sample weighting is widely used in deep learning. A large number of weighting methods essentially utilize the learning difficulty of training samples to calculate their weights. In this study, this scheme is called difficulty-based…

Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…

We study the problem of PAC learning $\gamma$-margin halfspaces in the presence of Massart noise. Without computational considerations, the sample complexity of this learning problem is known to be $\widetilde{\Theta}(1/(\gamma^2…

Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on…