Related papers: Multiple Random Oracles Are Better Than One

An interesting classical result due to Jackson allows polynomial-time learning of the function class DNF using membership queries. Since in most practical learning situations access to a membership oracle is unrealistic, this paper explores…

We develop an extension of recently developed methods for obtaining time-space tradeoff lower bounds for problems of learning from random test samples to handle the situation where the space of tests is signficantly smaller than the space…

We consider the problem of learning unions of rectangles over the domain $[b]^n$, in the uniform distribution membership query learning setting, where both b and n are "large". We obtain poly$(n, \log b)$-time algorithms for the following…

This paper presents a new algorithm for online linear regression whose efficiency guarantees satisfy the requirements of the KWIK (Knows What It Knows) framework. The algorithm improves on the complexity bounds of the current…

We study the problem of estimating a manifold from random samples. In particular, we consider piecewise constant and piecewise linear estimators induced by k-means and k-flats, and analyze their performance. We extend previous results for…

Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…

Let $\Phi = (V, \mathcal{C})$ be a constraint satisfaction problem on variables $v_1,\dots, v_n$ such that each constraint depends on at most $k$ variables and such that each variable assumes values in an alphabet of size at most $[q]$.…

If K/k is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in K. The algorithm is flexible enough to find factors subject to additional…

We consider the problem of identifying, from statistics, a distribution of discrete random variables $X_1,\ldots,X_n$ that is a mixture of $k$ product distributions. The best previous sample complexity for $n \in O(k)$ was $(1/\zeta)^{O(k^2…

For a function $f \colon \{0,1\}^n \to \{0,1\}$, the junta testing problem asks whether $f$ depends on only $k$ variables. If $f$ depends on only $k$ variables, the feature selection problem asks to find those variables. We prove that these…

Sharing information between multiple tasks enables algorithms to achieve good generalization performance even from small amounts of training data. However, in a realistic scenario of multi-task learning not all tasks are equally related to…

We study the structure and learnability of sums of independent integer random variables (SIIRVs). For $k \in \mathbb{Z}_{+}$, a $k$-SIIRV of order $n \in \mathbb{Z}_{+}$ is the probability distribution of the sum of $n$ independent random…

We pursue a systematic study of the following problem. Let f:{0,1}^n -> {0,1} be a (usually monotone) Boolean function whose behaviour is well understood when the input bits are identically independently distributed. What can be said about…

We study the problem of learning mixtures of $k$ Gaussians in $d$ dimensions. We make no separation assumptions on the underlying mixture components: we only require that the covariance matrices have bounded condition number and that the…

We offer a new understanding of some aspects of practical SAT-solvers that are based on DPLL with unit-clause propagation, clause-learning, and restarts. We do so by analyzing a concrete algorithm which we claim is faithful to what…

We consider the problem of learning a latent $k$-vertex simplex $K\subset\mathbb{R}^d$, given access to $A\in\mathbb{R}^{d\times n}$, which can be viewed as a data matrix with $n$ points that are obtained by randomly perturbing latent…

We prove that every distributional problem solvable in polynomial time on the average with respect to the uniform distribution has a frequently self-knowingly correct polynomial-time algorithm. We also study some features of probability…

We give a non-adaptive algorithm that makes $2^{\tilde{O}(\sqrt{k\log(1/\varepsilon_2 - \varepsilon_1)})}$ queries to a Boolean function $f:\{\pm 1\}^n \rightarrow \{\pm 1\}$ and distinguishes between $f$ being $\varepsilon_1$-close to some…

We give highly efficient algorithms, and almost matching lower bounds, for a range of basic statistical problems that involve testing and estimating the L_1 distance between two k-modal distributions $p$ and $q$ over the discrete domain…

We study the problem of computationally efficient proper agnostic learning of multidimensional concept classes under the Gaussian distribution. In this setting, given i.i.d. labeled samples from an unknown distribution over $\mathbb{R}^d…