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An agnostic PAC learning algorithm finds a predictor that is competitive with the best predictor in a benchmark hypothesis class, where competitiveness is measured with respect to a given loss function. However, its predictions might be…
We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…
We give a polynomial-time algorithm for learning neural networks with one layer of sigmoids feeding into any Lipschitz, monotone activation function (e.g., sigmoid or ReLU). We make no assumptions on the structure of the network, and the…
The apparent difficulty of efficient distribution-free PAC learning has led to a large body of work on distribution-specific learning. Distributional assumptions facilitate the design of efficient algorithms but also limit their reach and…
We consider the Domain Adaptation problem, also known as the covariate shift problem, where the distributions that generate the training and test data differ while retaining the same labeling function. This problem occurs across a large…
PAC-Bayesian bounds are known to be tight and informative when studying the generalization ability of randomized classifiers. However, they require a loose and costly derandomization step when applied to some families of deterministic…
Carmosino et al. (2016) demonstrated that natural proofs of circuit lower bounds for $\Lambda$ imply efficient algorithms for learning $\Lambda$-circuits, but only over \textit{the uniform distribution}, with \textit{membership queries},…
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…
We prove that it is NP-hard to properly PAC learn decision trees with queries, resolving a longstanding open problem in learning theory (Bshouty 1993; Guijarro-Lavin-Raghavan 1999; Mehta-Raghavan 2002; Feldman 2016). While there has been a…
The approximate degree of a Boolean function f is the least degree of a real polynomial that approximates f pointwise to error at most 1/3. Approximate degree is known to be a lower bound on quantum query complexity. We resolve or nearly…
We study the power of query access for the task of agnostic learning under the Gaussian distribution. In the agnostic model, no assumptions are made on the labels and the goal is to compute a hypothesis that is competitive with the {\em…
We study the efficient learnability of low-degree polynomial threshold functions (PTFs) in the presence of a constant fraction of adversarial corruptions. Our main algorithmic result is a polynomial-time PAC learning algorithm for this…
We continue the study of doubly-efficient proof systems for verifying agnostic PAC learning, for which we obtain the following results. - We construct an interactive protocol for learning the $t$ largest Fourier characters of a given…
Transfer learning has received a lot of attention in the machine learning community over the last years, and several effective algorithms have been developed. However, relatively little is known about their theoretical properties,…
Despite its empirical success, deep learning still lacks a comprehensive theoretical understanding of model fitting and generalization. This paper proposes the probability distribution (PD) learning framework to analyze the optimization and…
We consider learning under the constraint of local differential privacy (LDP). For many learning problems known efficient algorithms in this model require many rounds of communication between the server and the clients holding the data…
Learning curves plot the expected error of a learning algorithm as a function of the number of labeled samples it receives from a target distribution. They are widely used as a measure of an algorithm's performance, but classic PAC learning…
It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these…
We generalize the PAC (probably approximately correct) learning model to the quantum world by generalizing the concepts from classical functions to quantum processes, defining the problem of \emph{PAC learning quantum process}, and study…
As learning solutions reach critical applications in social, industrial, and medical domains, the need to curtail their behavior has become paramount. There is now ample evidence that without explicit tailoring, learning can lead to biased,…