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We prove a new structural lemma for partial Boolean functions $f$, which we call the seed lemma for DNF. Using the lemma, we give the first subexponential algorithm for proper learning of DNF in Angluin's Equivalence Query (EQ) model. The…

Machine Learning · Computer Science 2011-11-07 Lisa Hellerstein , Devorah Kletenik , Linda Sellie , Rocco Servedio

We present two new results about exact learning by quantum computers. First, we show how to exactly learn a $k$-Fourier-sparse $n$-bit Boolean function from $O(k^{1.5}(\log k)^2)$ uniform quantum examples for that function. This improves…

We make progress on two important problems regarding attribute efficient learnability. First, we give an algorithm for learning decision lists of length $k$ over $n$ variables using $2^{\tilde{O}(k^{1/3})} \log n$ examples and time…

Machine Learning · Computer Science 2007-05-23 Adam R. Klivans , Rocco A. Servedio

We present an efficient algorithm for learning mixed membership models when the number of variables $p$ is much larger than the number of hidden components $k$. This algorithm reduces the computational complexity of state-of-the-art tensor…

Machine Learning · Computer Science 2017-07-04 Zilong Tan , Sayan Mukherjee

In the polytope membership problem, a convex polytope $K$ in $\mathbb{R}^d$ is given, and the objective is to preprocess $K$ into a data structure so that, given any query point $q \in \mathbb{R}^d$, it is possible to determine efficiently…

Computational Geometry · Computer Science 2018-01-11 Sunil Arya , Guilherme D. da Fonseca , David M. Mount

We consider the following problem: Given a set S of at most n elements from a universe of size m, represent it in memory as a bit string so that membership queries of the form "Is x in S?" can be answered by making at most t probes into the…

Data Structures and Algorithms · Computer Science 2022-01-03 Shyam Dhamapurkar , Shubham Vivek Pawar , Jaikumar Radhakrishnan

We consider the natural problem of learning a ReLU network from queries, which was recently remotivated by model extraction attacks. In this work, we present a polynomial-time algorithm that can learn a depth-two ReLU network from queries…

Machine Learning · Computer Science 2023-03-07 Amit Daniely , Elad Granot

The model of learning with \emph{local membership queries} interpolates between the PAC model and the membership queries model by allowing the learner to query the label of any example that is similar to an example in the training set. This…

Machine Learning · Computer Science 2016-03-14 Galit Bary-Weisberg , Amit Daniely , Shai Shalev-Shwartz

We consider the Stochastic Boolean Function Evaluation (SBFE) problem where the task is to efficiently evaluate a known Boolean function $f$ on an unknown bit string $x$ of length $n$. We determine $f(x)$ by sequentially testing the…

Data Structures and Algorithms · Computer Science 2022-08-09 Lisa Hellerstein , Devorah Kletenik , Naifeng Liu , R. Teal Witter

Given a partition of a graph into connected components, the membership oracle asserts whether any two vertices of the graph lie in the same component or not. We prove that for $n\ge k\ge 2$, learning the components of an $n$-vertex hidden…

Machine Learning · Computer Science 2022-06-20 Xizhi Liu , Sayan Mukherjee

Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. However, BO is practically limited to…

Machine Learning · Statistics 2020-09-28 Riccardo Moriconi , Marc P. Deisenroth , K. S. Sesh Kumar

We present an algorithm for solving binary classification problems when the dataset is not fully representative of the problem being solved, and obtaining more data is not possible. It relies on a trained model with loose accuracy…

Machine Learning · Computer Science 2025-07-11 Adrian de Wynter

We give the first polynomial-time algorithm for the testable learning of halfspaces in the presence of adversarial label noise under the Gaussian distribution. In the recently introduced testable learning model, one is required to produce a…

Machine Learning · Computer Science 2023-03-10 Ilias Diakonikolas , Daniel M. Kane , Vasilis Kontonis , Sihan Liu , Nikos Zarifis

Scaling Bayesian optimisation (BO) to high-dimensional search spaces is a active and open research problems particularly when no assumptions are made on function structure. The main reason is that at each iteration, BO requires to find…

Machine Learning · Statistics 2026-04-28 Hung Tran-The , Sunil Gupta , Santu Rana , Svetha Venkatesh

We describe and analyze a new algorithm for agnostically learning kernel-based halfspaces with respect to the \emph{zero-one} loss function. Unlike most previous formulations which rely on surrogate convex loss functions (e.g. hinge-loss in…

Machine Learning · Computer Science 2010-08-03 Shai Shalev-Shwartz , Ohad Shamir , Karthik Sridharan

Given a finite set $X \subset \mathbb{R}^d$ and a binary linear classifier $c: \mathbb{R}^d \to \{0,1\}$, how many queries of the form $c(x)$ are required to learn the label of every point in $X$? Known as \textit{point location}, this…

Computational Geometry · Computer Science 2020-04-27 Max Hopkins , Daniel M. Kane , Shachar Lovett , Gaurav Mahajan

We study the fundamental problem of polytope membership aiming at large convex polytopes, i.e. in high dimension and with many facets, given as an intersection of halfspaces. Standard data-structures as well as brute force methods cannot…

Computational Geometry · Computer Science 2018-05-01 Evangelos Anagnostopoulos , Ioannis Z. Emiris , Vissarion Fisikopoulos

The problem "Given a Boolean function $f$ of $n$ variables by its truth table vector. Find (if exists) a vector $\alpha \in \{0,1\}^n$ of maximal (or minimal) weight, such that $f(\alpha)= 1$." is considered here. It is closely related to…

Discrete Mathematics · Computer Science 2020-02-17 Valentin Bakoev

Several recent works [DHLNSY25, CPPS25a, CPPS25b] have studied a model of property testing of Boolean functions under a \emph{relative-error} criterion. In this model, the distance from a target function $f: \{0,1\}^n \to \{0,1\}$ that is…

Computational Complexity · Computer Science 2026-03-24 Xi Chen , Anindya De , Yizhi Huang , Shivam Nadimpalli , Rocco A. Servedio , Tianqi Yang

Recent work of Klivans, Stavropoulos, and Vasilyan initiated the study of testable learning with distribution shift (TDS learning), where a learner is given labeled samples from training distribution $\mathcal{D}$, unlabeled samples from…

Data Structures and Algorithms · Computer Science 2024-05-22 Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan