相关论文: Agnostic learning in (almost) optimal time via Gau…

We provide a convergence analysis of gradient descent for the problem of agnostically learning a single ReLU function with moderate bias under Gaussian distributions. Unlike prior work that studies the setting of zero bias, we consider the…

We consider the problem of learning an arbitrarily-biased ReLU activation (or neuron) over Gaussian marginals with the squared loss objective. Despite the ReLU neuron being the basic building block of modern neural networks, we still do not…

We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…

We study the computational complexity of adversarially robust proper learning of halfspaces in the distribution-independent agnostic PAC model, with a focus on $L_p$ perturbations. We give a computationally efficient learning algorithm and…

We investigate approximation guarantees provided by logistic regression for the fundamental problem of agnostic learning of homogeneous halfspaces. Previously, for a certain broad class of "well-behaved" distributions on the examples,…

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…

We study the problem of learning a low-degree spherical polynomial of degree $k_0 = \Theta(1) \ge 1$ defined on the unit sphere in $\RR^d$ by training an over-parameterized two-layer neural network with augmented feature in this paper. Our…

We study the problem of learning mixtures of Gaussians with approximate differential privacy. We prove that roughly $kd^2 + k^{1.5} d^{1.75} + k^2 d$ samples suffice to learn a mixture of $k$ arbitrary $d$-dimensional Gaussians up to low…

We consider the problem of private density estimation for mixtures of unrestricted high dimensional Gaussians in the agnostic setting. We prove the first upper bound on the sample complexity of this problem. Previously, private learnability…

We derive approximation bounds for learning single neuron models using thresholded gradient descent when both the labels and the covariates are possibly corrupted adversarially. We assume the data follows the model $y =…

We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…

Rubinfeld & Vasilyan recently introduced the framework of testable learning as an extension of the classical agnostic model. It relaxes distributional assumptions which are difficult to verify by conditions that can be checked efficiently…

The exploration-exploitation trade-off is among the central challenges of reinforcement learning. The optimal Bayesian solution is intractable in general. This paper studies to what extent analytic statements about optimal learning are…

Multi-distribution learning extends agnostic Probably Approximately Correct (PAC) learning to the setting in which a family of $k$ distributions, $\{D_i\}_{i\in[k]}$, is considered and a classifier's performance is measured by its error…

Algorithmic machine teaching has been studied under the linear setting where exact teaching is possible. However, little is known for teaching nonlinear learners. Here, we establish the sample complexity of teaching, aka teaching dimension,…

The approximate degree of a Boolean function is the minimum degree of real polynomial that approximates it pointwise. For any Boolean function, its approximate degree serves as a lower bound on its quantum query complexity, and generically…

There have been many recent advances on provably efficient Reinforcement Learning (RL) in problems with rich observation spaces. However, all these works share a strong realizability assumption about the optimal value function of the true…

We consider the problem of computing the best-fitting ReLU with respect to square-loss on a training set when the examples have been drawn according to a spherical Gaussian distribution (the labels can be arbitrary). Let $\mathsf{opt} < 1$…

We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary…

We consider PAC learning of probability distributions (a.k.a. density estimation), where we are given an i.i.d. sample generated from an unknown target distribution, and want to output a distribution that is close to the target in total…