In this paper, two new classes of lower bounds on the probability of error for m-ary hypothesis testing are proposed. Computation of the minimum probability of error which is attained by the maximum a-posteriori probability (MAP) criterion, is usually not tractable. The new classes are derived using Hölder’s inequality and reverse Hölder’s inequality. The bounds in these classes provide good pr...

We first give a brief introduction to the field of property testing. Section 3 gives upper bounds for the canonical property of “monotonicity testing,” and Section 4 shows how to derive property testing lower bounds from communication complexity lower bounds. We won’t need to develop any new communication complexity; our existing toolbox (specifically, Disjointness) is already rich enough to de...

We present quantum query and time complexity bounds for group testing problems. For a set S and a binary operation on S, we consider the decision problem whether a groupoid, semigroup or quasigroup is a group. Our quantum algorithms for these problems improve the best known classical complexity bounds. We also present upper and lower bounds for testing associativity, distributivity and commutat...

We study the fundamental problems of identity testing (goodness of fit), and closeness testing (two sample test) of distributions over k elements, under differential privacy. While the problems have a long history in statistics, finite sample bounds for these problems have only been established recently. In this work, we derive upper and lower bounds on the sample complexity of both the problem...

Symmetric Division Deg index is one of the 148 discrete Adriatic indices that showed good predictive properties on the testing sets provided by International Academy of Mathematical Chemistry. Symmetric Division Deg index is defined by $$ SDD(G) = sumE left( frac{min{d_u,d_v}}{max{d_u,d_v}} + frac{max{d_u,d_v}}{min{d_u,d_v}} right), $$ where $d_i$ is the degree of vertex $i$ in graph $G$. In th...

We begin in this section with a brief introduction to the field of property testing. Section 2 explains the famous example of “linearity testing.” Section 3 gives upper bounds for the canonical problem of “monotonicity testing,” and Section 4 shows how to derive property testing lower bounds from communication complexity lower bounds. These lower bounds will follow from our existing communicati...