Property testing and its connection to learning and approximation

  title={Property testing and its connection to learning and approximation},
  author={Oded Goldreich and Shafi Goldwasser and Dana Ron},
  journal={Proceedings of 37th Conference on Foundations of Computer Science},
The authors study the question of determining whether an unknown function has a particular property or is /spl epsiv/-far from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the function on instances of its choice. First, they establish some connections between property testing and problems in learning theory. Next, they focus on testing graph properties, and… 

Property Testing: A Learning Theory Perspective

Property testing [15,9] is the study of the following class of problems: Given the ability to perform local queries concerning a particular object, the problem is to determine whether the object has a predetermined global property, or differs significantly from any object that has the property.

Property Testing

  • D. Ron
  • Computer Science
    Algorithms for Big Data
  • 2020
Property Testing: A Learning Theory Perspective takes the learning-theory point of view of property testing and focuses on results for testing properties of functions that are of interest to the learning theory community, including algebraic properties, which include testing whether a function is (multi-)linear and more generally whether it is a polynomial of bounded degree.

Testing versus estimation of graph properties

It is shown here that in the setting of the dense graph model, all testable properties are not only tolerantly testable, but also admit a constant query size algorithm that estimates the distance from the property up to any fixed additive constant.

Combinatorial property testing (a survey)

  • Oded Goldreich
  • Mathematics
    Randomization Methods in Algorithm Design
  • 1997
This work considers the question of determining whether a given object has a predetermined property or is \far" from any object having the property, and focuses on combinatorial properties, and speciically on graph properties.

Three theorems regarding testing graph properties

  • Oded GoldreichL. Trevisan
  • Mathematics, Computer Science
    Proceedings 2001 IEEE International Conference on Cluster Computing
  • 2001
Three theorems regarding testing graph properties in the adjacency matrix representation are presented and every graph property that can be tested making a number of queries that is independent of the size of the graph, can be so tested by uniformly selecting a set of vertices.

Algorithmic and Analysis Techniques in Property Testing

  • D. Ron
  • Computer Science, Mathematics
    Found. Trends Theor. Comput. Sci.
  • 2009
This monograph surveys results in property testing, where the emphasis is on common analysis and algorithmic techniques.

Active Property Testing

A general notion of the testing dimension of a given property with respect to a given distribution is developed, that characterizes (up to constant factors) the intrinsic number of label requests needed to test that property.

The Classi cation Problem in Relational Property Testing

This thesis introduces a generalization of property testing which is inspired by the classical problem for decidability and considers the testability of various syntactic fragments of rst-order logic.

Testing Eulerianity and connectivity in directed sparse graphs

On the Testability of Graph Partition Properties

This work studies the testability of a family of graph partition properties that generalizes a family previously studied by Goldreich, Goldwasser, and Ron and shows that every property in GPP is testable by a one-sided error algorithm that has query complexity poly(1/ ) and that if P ∈ GPP\GPP0,1 then it cannot have aOne- sided error testing algorithm whose query complexity is independent of the input graph's size.



Property Testing in Bounded Degree Graphs

This work develops the study of testing graph properties as initiated by Goldreich, Goldwasser and Ron and presents randomized algorithms for testing whether an unknown bounded-degree graph is connected, k -connected (for k>1 ), cycle-free and Eulerian.

On the learnability of discrete distributions

A new model of learning probability distributions from independent draws is introduced, inspired by the popular Probably Approximately Correct (PAC) model for learning boolean functions from labeled examples, in the sense that it emphasizes efficient and approximate learning, and it studies the learnability of restricted classes of target distributions.

An Ω(n5/4) lower bound on the randomized complexity of graph properties

Yao's lower bound on the randomized complexity of any nontrivial monotone graph property from Ω (n log1/12n) to Ω(n5/4) is improved.

A Sublinear Bipartiteness Tester for Bounded Degree Graphs

The contrapositive statement by which slow convergence implies small cuts in the graph is applied, and this implication is applied in showing that for any graph, the graph vertices can be divided into disjoint subsets such that each subset itself exhibits a certain mixing property that is useful in the analysis.

On the time required to recognize properties of graphs: a problem

In a recent paper [i], Holt and Reingold have proved the following results: any algorithm which, given an n-node graph, detects whether or not the graph enjoys property P must in the worst case probe 0(n 2) entries of the incidence matrix.

Can Finite Samples Detect Singularities of Real-Valued Functions?

The class of DIL problems is analyzed and an algorithm is offered for any DIL problem and a necessary and sufficient condition for the membership of a decision problem in this class is provided.

The algorithmic aspects of the regularity lemma

The authors first demonstrate the computational difficulty of finding a regular partition; they show that deciding if a given partition of an input graph satisfies the properties guaranteed by the lemma is co-NP-complete, and prove that despite this difficulty theLemma can be made constructive.

Probably Almost Discriminative Learning

This paper demonstrates that the sample complexity bound for the MDL-based discrimination algorithm is essentially related to Barron and Cover's index of resolvability, and gives a new view at the relationship between the index of RESOLvability and theMDL principle from the PAD-learning viewpoint.