Related papers: Some properties are not even partially testable
The primary problem in property testing is to decide whether a given function satisfies a certain property, or is far from any function satisfying it. This crucially requires a notion of distance between functions. The most prevalent notion…
We consider the problem of learning a non-deterministic probabilistic system consistent with a given finite set of positive and negative tree samples. Consistency is defined with respect to strong simulation conformance. We propose learning…
We study the query complexity of testing for properties defined by read once formulas, as instances of {\em massively parametrized properties}, and prove several testability and non-testability results. First we prove the testability of any…
We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…
Decision trees are popular classification models, providing high accuracy and intuitive explanations. However, as the tree size grows the model interpretability deteriorates. Traditional tree-induction algorithms, such as C4.5 and CART,…
Researchers have long observed that the ``small-world" property, which combines the concepts of high transitivity or clustering with a low average path length, is ubiquitous for networks obtained from a variety of disciplines, including…
Let $\mathcal{P}$ be a property of function $\mathbb{F}_p^n \to \{0,1\}$ for a fixed prime $p$. An algorithm is called a tester for $\mathcal{P}$ if, given a query access to the input function $f$, with high probability, it accepts when $f$…
A Partial Conjunction Hypothesis (PCH) test combines information across a set of base hypotheses to determine whether some subset is non-null. PCH tests arise in a diverse array of fields, but standard PCH testing methods can be highly…
We introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…
Let F = F_p for any fixed prime p >= 2. An affine-invariant property is a property of functions on F^n that is closed under taking affine transformations of the domain. We prove that all affine-invariant property having local…
Property-based testing (PBT) is a popular technique for establishing confidence in software, where users write properties -- i.e., executable specifications -- that can be checked many times in a loop by a testing framework. In modern PBT…
Genetic algorithms are a widely used method in chemometrics for extracting variable subsets with high prediction power. Most fitness measures used by these genetic algorithms are based on the ordinary least-squares fit of the resulting…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to…
In this set of three companion manuscripts/articles, we unveil our new results on primality testing and reveal new primality testing algorithms enabled by those results. The results have been classified (and referred to) as…
We present a technique of proving lower bounds for noisy computations. This is achieved by a theorem connecting computations on a kind of randomized decision trees and sampling based algorithms. This approach is surprisingly powerful, and…
We propose to extend property-based testing to substructural logics to overcome the current lack of reasoning tools in the field. We take the first step by implementing a property-based testing system for specifications written in the…
The assumption of separability is a simplifying and very popular assumption in the analysis of spatio-temporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…
The null space condition for $\ell_1$ minimization in compressed sensing is a necessary and sufficient condition on the sensing matrices under which a sparse signal can be uniquely recovered from the observation data via $\ell_1$…