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Recent works on 3D scene understanding leverage 2D masks from visual foundation models (VFMs) to supervise radiance fields, enabling instance-level 3D segmentation. However, the supervision signals from foundation models are not…

We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue…

In this paper, we propose a new, simplified high probability analysis of AdaGrad for smooth, non-convex problems. More specifically, we focus on a particular accelerated gradient (AGD) template (Lan, 2020), through which we recover the…

We study in this paper the rate of convergence for learning densities under the Generative Adversarial Networks (GAN) framework, borrowing insights from nonparametric statistics. We introduce an improved GAN estimator that achieves a faster…

The sample complexity of learning a Boolean-valued function class is precisely characterized by its Rademacher complexity. This has little bearing, however, on the sample complexity of \emph{efficient} agnostic learning. We introduce…

Let $V$ be any vector space of multivariate degree-$d$ homogeneous polynomials with co-dimension at most $k$, and $S$ be the set of points where all polynomials in $V$ {\em nearly} vanish. We establish a qualitatively optimal upper bound on…

We study agnostic active learning, where the goal is to learn a classifier in a pre-specified hypothesis class interactively with as few label queries as possible, while making no assumptions on the true function generating the labels. The…

Statistical and machine-learning algorithms are frequently applied to high-dimensional data. In many of these applications data is scarce, and often much more costly than computation time. We provide the first sample-efficient…

Approximating convex bodies is a fundamental problem in geometry. Given a convex body $K$ in $\mathbb{R}^d$ for a fixed dimension $d$, the objective is to minimize the number of facets of an approximating polytope for a given Hausdorff…

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…

This paper is concerned with computationally efficient learning of homogeneous sparse halfspaces in $\mathbb{R}^d$ under noise. Though recent works have established attribute-efficient learning algorithms under various types of label noise…

For high-dimensional Gaussian data, we investigate theoretically how the features of a two-layer neural network adapt to the structure of the target function through a few large batch gradient descent steps, leading to an improvement in the…

We demonstrate a compactness result holding broadly across supervised learning with a general class of loss functions: Any hypothesis class $H$ is learnable with transductive sample complexity $m$ precisely when all of its finite…

Adaptive gradient methods, such as AdaGrad, are among the most successful optimization algorithms for neural network training. While these methods are known to achieve better dimensional dependence than stochastic gradient descent (SGD) for…

We introduce a new technique for reducing the dimension of the ambient space of low-degree polynomials in the Gaussian space while preserving their relative correlation structure, analogous to the Johnson-Lindenstrauss lemma. As…

The information exponent ([BAGJ21]) and its extensions -- which are equivalent to the lowest degree in the Hermite expansion of the link function (after a potential label transform) for Gaussian single-index models -- have played an…

We consider the basic problem of learning Single-Index Models with respect to the square loss under the Gaussian distribution in the presence of adversarial label noise. Our main contribution is the first computationally efficient algorithm…

For the problem of task-agnostic reinforcement learning (RL), an agent first collects samples from an unknown environment without the supervision of reward signals, then is revealed with a reward and is asked to compute a corresponding…

We study {\em online} active learning of homogeneous halfspaces in $\mathbb{R}^d$ with adversarial noise where the overall probability of a noisy label is constrained to be at most $\nu$. Our main contribution is a Perceptron-like online…

Boosting is a powerful method that turns weak learners, which perform only slightly better than random guessing, into strong learners with high accuracy. While boosting is well understood in the classic setting, it is less so in the…