Related papers: Testing Piecewise Functions
Given two testable properties $\mathcal{P}_{1}$ and $\mathcal{P}_{2}$, under what conditions are the union, intersection or set-difference of these two properties also testable? We initiate a systematic study of these basic set-theoretic…
Property testers are fast, randomized "election polling"-type algorithms that determine if an input (e.g., graph or hypergraph) has a certain property or is $\varepsilon$-far from the property. In the dense graph model of property testing,…
This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or…
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
We propose a Bayesian approach to detect multiple change-points in a piecewise-constant signal corrupted by a functional part corresponding to environmental or experimental disturbances. The piecewise constant part (also called segmentation…
For covariance test in functional data analysis, existing methods are developed only for fully observed curves, whereas in practice, trajectories are typically observed discretely and with noise. To bridge this gap, we employ a…
The goal of experiment design is to select the inputs of a dynamical system in such a way that the resulting data contain sufficient information for system identification and data-driven control. This paper investigates the problem of…
One of the motivations for property testing of boolean functions is the idea that testing can serve as a preprocessing step before learning. However, in most machine learning applications, it is not possible to request for labels of…
We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…
We derive several tests for the presence of a periodic component in a time series of functions. We consider both the traditional setting in which the periodic functional signal is contaminated by functional white noise, and a more general…
Property Testing is a formal framework to study the computational power and complexity of sampling from combinatorial objects. A central goal in standard graph property testing is to understand which graph properties are testable with…
We discuss technical results on learning function approximations using piecewise-linear basis functions, and analyze their stability and convergence using nonlinear contraction theory.
The field of property testing of probability distributions, or distribution testing, aims to provide fast and (most likely) correct answers to questions pertaining to specific aspects of very large datasets. In this work, we consider a…
We develop a test of normality for spatially indexed functions. The assumption of normality is common in spatial statistics, yet no significance tests, or other means of assessment, have been available for functional data. This paper aims…
In software testing, the large size of the input domain makes exhaustively testing the inputs a daunting and often impossible task. Pair-wise testing is a popular approach to combinatorial testing problems. This paper reviews Pair-wise…
Certified defenses against small-norm adversarial examples have received growing attention in recent years; though certified accuracies of state-of-the-art methods remain far below their non-robust counterparts, despite the fact that…
Aiming for accurate estimation of system reliability of load-sharing systems, a flexible model for such systems is constructed by approximating the cumulative hazard functions of component lifetimes using piecewise linear functions. The…
Modern multiscale type segmentation methods are known to detect multiple change-points with high statistical accuracy, while allowing for fast computation. Underpinning theory has been developed mainly for models that assume the signal as a…
Piecewise constant functions describe a variety of real-world phenomena in domains ranging from chemistry to manufacturing. In practice, it is often required to confidently identify the locations of the abrupt changes in these functions as…
In this paper we study the problem of tracking the mean of a piecewise stationary sequence of independent random variables. First we consider the case where the transition times are known and show that a direct running average performs the…