Related papers: Learning Intersections of Two Margin Halfspaces un…

We revisit the problem of learning from untrusted batches introduced by Qiao and Valiant [QV17]. Recently, Jain and Orlitsky [JO19] gave a simple semidefinite programming approach based on the cut-norm that achieves essentially…

In a landmark result, Linial, Mansour and Nisan (J. ACM 1993) gave a quasipolynomial-time algorithm for learning constant-depth circuits given labeled i.i.d. samples under the uniform distribution. Their work has had a deep and lasting…

We study the efficient learnability of geometric concept classes - specifically, low-degree polynomial threshold functions (PTFs) and intersections of halfspaces - when a fraction of the data is adversarially corrupted. We give the first…

We study the problem of PAC learning one-hidden-layer ReLU networks with $k$ hidden units on $\mathbb{R}^d$ under Gaussian marginals in the presence of additive label noise. For the case of positive coefficients, we give the first…

Inspired by recent work on learning with distribution shift, we give a general outlier removal algorithm called iterative polynomial filtering and show a number of striking applications for supervised learning with contamination: (1) We…

We pose a fundamental question in computational learning theory: can we efficiently test whether a training set satisfies the assumptions of a given noise model? This question has remained unaddressed despite decades of research on learning…

We study the complexity of PAC learning halfspaces in the presence of Massart noise. In this problem, we are given i.i.d. labeled examples $(\mathbf{x}, y) \in \mathbb{R}^N \times \{ \pm 1\}$, where the distribution of $\mathbf{x}$ is…

We study active learning of homogeneous $s$-sparse halfspaces in $\mathbb{R}^d$ under the setting where the unlabeled data distribution is isotropic log-concave and each label is flipped with probability at most $\eta$ for a parameter $\eta…

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,…

Motivated by the recent empirical successes of deep generative models, we study the computational complexity of the following unsupervised learning problem. For an unknown neural network $F:\mathbb{R}^d\to\mathbb{R}^{d'}$, let $D$ be the…

This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…

We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex…

Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…

Distributed Principal Component Analysis (PCA) has been studied to deal with the case when data are stored across multiple machines and communication cost or privacy concerns prohibit the computation of PCA in a central location. However,…

We study the problem of computationally efficient proper agnostic learning of multidimensional concept classes under the Gaussian distribution. In this setting, given i.i.d. labeled samples from an unknown distribution over $\mathbb{R}^d…

We give a computationally-efficient PAC active learning algorithm for $d$-dimensional homogeneous halfspaces that can tolerate Massart noise (Massart and N\'ed\'elec, 2006) and Tsybakov noise (Tsybakov, 2004). Specialized to the…

Understanding noise tolerance of machine learning algorithms is a central quest in learning theory. In this work, we study the problem of computationally efficient PAC learning of halfspaces in the presence of malicious noise, where an…

Semi-supervised clustering is an very important topic in machine learning and computer vision. The key challenge of this problem is how to learn a metric, such that the instances sharing the same label are more likely close to each other on…

The class of quasiseparable matrices is defined by the property that any submatrix entirely below or above the main diagonal has small rank, namely below a bound called the order of quasiseparability. These matrices arise naturally in…

The success and generalisation of deep learning algorithms heavily depend on learning good feature representations. In medical imaging this entails representing anatomical information, as well as properties related to the specific imaging…