Related papers: Active Learning Polynomial Threshold Functions

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…

Intelligent systems have the ability to improve their behaviour over time taking observations, experiences or explicit feedback into account. Traditional approaches separate the learning problem and make isolated use of techniques from…

Motivated by the recent empirical successes of deep generative models, we study the computational complexity of the following unsupervised learning problem. For an unknown neural network $F:\mathbb{R}^d\to\mathbb{R}^{d'}$, let $D$ be the…

Active Learning (AL) is an active domain of research, but is seldom used in the industry despite the pressing needs. This is in part due to a misalignment of objectives, while research strives at getting the best results on selected…

Power-law scaling indicates that large-scale training with uniform sampling is prohibitively slow. Active learning methods aim to increase data efficiency by prioritizing learning on the most relevant examples. Despite their appeal, these…

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…

Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting…

While learning in an unknown Markov Decision Process (MDP), an agent should trade off exploration to discover new information about the MDP, and exploitation of the current knowledge to maximize the reward. Although the agent will…

Active learning aims to reduce annotation cost by predicting which samples are useful for a human expert to label. Although this field is quite old, several important challenges to using active learning in real-world settings still remain…

We count algebraic points of bounded height and degree on the graphs of certain functions analytic on the unit disk, obtaining a bound which is polynomial in the degree and in the logarithm of the multiplicative height. We combine this work…

We investigate the problem of active learning on a given tree whose nodes are assigned binary labels in an adversarial way. Inspired by recent results by Guillory and Bilmes, we characterize (up to constant factors) the optimal placement of…

We consider the problem of actively learning an unknown binary decision tree using only membership queries, a setting in which the learner must reason about a large hypothesis space while maintaining formal guarantees. Rather than…

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…

We consider the problem of active feature acquisition, where we sequentially select the subset of features in order to achieve the maximum prediction performance in the most cost-effective way. In this work, we formulate this active feature…

The existence of string functions, which are not polynomial time computable, but whose graph is checkable in polynomial time, is a basic assumption in cryptography. We prove that in the framework of algebraic complexity, there are no such…

Data-efficient learning algorithms are essential in many practical applications where data collection is expensive, e.g., in robotics due to the wear and tear. To address this problem, meta-learning algorithms use prior experience about…

Many cases exist in which a black-box function $f$ with high evaluation cost depends on two types of variables $\bm x$ and $\bm w$, where $\bm x$ is a controllable \emph{design} variable and $\bm w$ are uncontrollable \emph{environmental}…

Datasets often incorporate various functional patterns related to different aspects or regimes, which are typically not equally present throughout the dataset. We propose a novel, general-purpose partitioning algorithm that utilizes…

Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…

Safety filters, particularly those based on control barrier functions, have gained increased interest as effective tools for safe control of dynamical systems. Existing correct-by-construction synthesis algorithms for such filters, however,…