Related papers: Faster Algorithms for Agnostically Learning Disjun…
We study the problem of agnostically learning halfspaces which is defined by a fixed but unknown distribution $\mathcal{D}$ on $\mathbb{Q}^n\times \{\pm 1\}$. We define $\mathrm{Err}_{\mathrm{HALF}}(\mathcal{D})$ as the least error of a…
We study the problem of {\em properly} learning large margin halfspaces in the agnostic PAC model. In more detail, we study the complexity of properly learning $d$-dimensional halfspaces on the unit ball within misclassification error…
We consider the problem of distributed learning, where a network of agents collectively aim to agree on a hypothesis that best explains a set of distributed observations of conditionally independent random processes. We propose a…
We describe a framework for designing efficient active learning algorithms that are tolerant to random classification noise and are differentially-private. The framework is based on active learning algorithms that are statistical in the…
The increased availability of data in recent years has led several authors to ask whether it is possible to use data as a {\em computational} resource. That is, if more data is available, beyond the sample complexity limit, is it possible…
Sample complexity bounds are a common performance metric in the Reinforcement Learning literature. In the discounted cost, infinite horizon setting, all of the known bounds have a factor that is a polynomial in $1/(1-\gamma)$, where $\gamma…
We study efficient PAC learning of homogeneous halfspaces in $\mathbb{R}^d$ in the presence of malicious noise of Valiant (1985). This is a challenging noise model and only until recently has near-optimal noise tolerance bound been…
The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…
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,…
It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example…
We give an algorithm for properly learning Poisson binomial distributions. A Poisson binomial distribution (PBD) of order $n$ is the discrete probability distribution of the sum of $n$ mutually independent Bernoulli random variables. Given…
How quickly can a given class of concepts be learned from examples? It is common to measure the performance of a supervised machine learning algorithm by plotting its "learning curve", that is, the decay of the error rate as a function of…
Multi-group agnostic learning is a formal learning criterion that is concerned with the conditional risks of predictors within subgroups of a population. The criterion addresses recent practical concerns such as subgroup fairness and hidden…
Algorithms for noiseless collaborative PAC learning have been analyzed and optimized in recent years with respect to sample complexity. In this paper, we study collaborative PAC learning with the goal of reducing communication cost at…
A single-index model (SIM) is a function of the form $\sigma(\mathbf{w}^{\ast} \cdot \mathbf{x})$, where $\sigma: \mathbb{R} \to \mathbb{R}$ is a known link function and $\mathbf{w}^{\ast}$ is a hidden unit vector. We study the task of…
We study the complexity of training neural network models with one hidden nonlinear activation layer and an output weighted sum layer. We analyze Gradient Descent applied to learning a bounded target function on $n$ real-valued inputs. We…
We initiate the study of tolerant adversarial PAC-learning with respect to metric perturbation sets. In adversarial PAC-learning, an adversary is allowed to replace a test point $x$ with an arbitrary point in a closed ball of radius $r$…
Previous research has explored the computational expressivity of Transformer models in simulating Boolean circuits or Turing machines. However, the learnability of these simulators from observational data has remained an open question. Our…
We study active learning where the labeler can not only return incorrect labels but also abstain from labeling. We consider different noise and abstention conditions of the labeler. We propose an algorithm which utilizes abstention…
We study the task of agnostic learning of multiclass linear classifiers under the Gaussian distribution. Given labeled examples $(x, y)$ from a distribution over $\mathbb{R}^d \times [k]$, with Gaussian $x$-marginal, the goal is to output a…