Related papers: Polynomial-Time Robust Multiclass Linear Classific…

Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension…

Most classification algorithms used in high energy physics fall under the category of supervised machine learning. Such methods require a training set containing both signal and background events and are prone to classification errors…

We study the problem of learning Bayesian networks where an $\epsilon$-fraction of the samples are adversarially corrupted. We focus on the fully-observable case where the underlying graph structure is known. In this work, we present the…

Via an overparameterized linear model with Gaussian features, we provide conditions for good generalization for multiclass classification of minimum-norm interpolating solutions in an asymptotic setting where both the number of underlying…

In traditional models of supervised learning, the goal of a learner -- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$ -- is to output a hypothesis that is competitive (to within $\epsilon$) of the…

We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper…

In contrast to multi-label learning, label distribution learning characterizes the polysemy of examples by a label distribution to represent richer semantics. In the learning process of label distribution, the training data is collected…

This work presents a new strategy for multi-class classification that requires no class-specific labels, but instead leverages pairwise similarity between examples, which is a weaker form of annotation. The proposed method, meta…

We establish finite-sample guarantees for a polynomial-time algorithm for learning a nonlinear, nonparametric directed acyclic graphical (DAG) model from data. The analysis is model-free and does not assume linearity, additivity,…

Linear and Quadratic Discriminant Analysis are well-known classical methods but can heavily suffer from non-Gaussian distributions and/or contaminated datasets, mainly because of the underlying Gaussian assumption that is not robust. To…

We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…

We consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. In the most basic form of this problem, we are given samples from a uniform mixture of…

We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical…

We show hardness of improperly learning halfspaces in the agnostic model, both in the distribution-independent as well as the distribution-specific setting, based on the assumption that worst-case lattice problems, such as GapSVP or SIVP,…

We give the first tester-learner for halfspaces that succeeds universally over a wide class of structured distributions. Our universal tester-learner runs in fully polynomial time and has the following guarantee: the learner achieves error…

We consider the problem of spherical Gaussian Mixture models with $k \geq 3$ components when the components are well separated. A fundamental previous result established that separation of $\Omega(\sqrt{\log k})$ is necessary and sufficient…

Modern machine learning classifiers often exhibit vanishing classification error on the training set. They achieve this by learning nonlinear representations of the inputs that maps the data into linearly separable classes. Motivated by…

Generative Adversarial Networks (GANs) can successfully approximate a probability distribution and produce realistic samples. However, open questions such as sufficient convergence conditions and mode collapse still persist. In this paper,…

We give a $2^{\tilde{O}(\sqrt{n}/\epsilon)}$-time algorithm for properly learning monotone Boolean functions under the uniform distribution over $\{0,1\}^n$. Our algorithm is robust to adversarial label noise and has a running time nearly…

We study the complexity of learning $k$-mixtures of Gaussians ($k$-GMMs) on $\mathbb{R}^d$. This task is known to have complexity $d^{\Omega(k)}$ in full generality. To circumvent this exponential lower bound on the number of components,…