9 accepted papers
We study the complexity of learning real-valued Multi-Index Models (MIMs) under the Gaussian distribution. A $K$-MIM is a function $f:\mathbb{R}^d\to \mathbb{R}$ that depends only on the projection of its input onto a $K$-dimensional subspace. We give a general algorithm for PAC learning a broad c…
We study the task of Multiclass Linear Classification (MLC) in the distribution-free PAC model with Random Classification Noise (RCN). Specifically, the learner is given a set of labeled examples $(x, y)$, where $x$ is drawn from an unknown distribution on $R^d$ and the labels are generated by…
Co-training is a classical semi-supervised learning method which only requires a small number of labeled examples for learning, under reasonable assumptions. Despite extensive literature on the topic, very few hypothesis classes are known to be provably efficiently learnable via co-training, even un…
We study the problem of PAC learning halfspaces in the reliable agnostic model of Kalai et al. (2012). The reliable PAC model captures learning scenarios where one type of error is costlier than the others. Our main positive result is a new algorithm for reliable learning of Gaussian halfspace…
We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples $(\\mathbf{x},y)$ from an unknown distribution on $\\mathbb{R}^n \\times \\{\pm 1 \\}$, whose marginal distribution on $\\mathbf{x}$ is the standard Gaussian and the labels $y$…
We study the complexity of Non-Gaussian Component Analysis (NGCA) in the Statistical Query (SQ) model. Prior work developed a methodology to prove SQ lower bounds for NGCA that have been applicable to a wide range of contexts. In particular, it was known that for any univariate distribution $A$ sati…
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 arbitrary and the label $y$ is a Massart corruption of $f(\mathbf…
We study the problem of distribution-free learning of a single neuron under adversarial label noise with respect to the squared loss. For a wide range of activation functions, including ReLUs and sigmoids, we prove hardness of learning results in the Statistical Query model and under a well-studied…
We study the problem of PAC learning a single neuron in the presence of Massart noise. Specifically, for a known activation function $f: \mathbb{R}\to \mathbb{R}$, the learner is given access to labeled examples $(\mathbf{x}, y) \in \mathbb{R}^d \times \mathbb{R}$, where the marginal distribution of…