DeepAI

# Adaptive Lower Bound for Testing Monotonicity on the Line

In the property testing model, the task is to distinguish objects possessing some property from the objects that are far from it. One of such properties is monotonicity, when the objects are functions from one poset to another. It is an active area of research. Recently, Pallavoor, Raskhodnikova and Varma (ITCS'17) proposed an ε-tester for monotonicity of a function f [n]→[r], whose complexity depends on the size of the range as O( r/ε). In this paper, we prove a nearly matching lower bound of Ω( r/ r) for adaptive two-sided testers. Additionally, we give an alternative proof of the Ω(ε^-1d n - ε^-1ε^-1) lower bound for testing monotonicity on the hypergrid [n]^d due to Chackrabarty and Seshadhri (RANDOM'13).

04/09/2020

### Lecture Note on LCSSX's Lower Bounds for Non-Adaptive Distribution-free Property Testing

In this lecture note we give Liu-Chen-Servedio-Sheng-Xie's (LCSSX) lower...
11/10/2022

### Directed Isoperimetric Theorems for Boolean Functions on the Hypergrid and an O(n√(d)) Monotonicity Tester

The problem of testing monotonicity for Boolean functions on the hypergr...
07/28/2019

### A Lower Bound on Cycle-Finding in Sparse Digraphs

We consider the problem of finding a cycle in a sparse directed graph G ...
12/09/2020

### Optimal distributed testing in high-dimensional Gaussian models

In this paper study the problem of signal detection in Gaussian noise in...
04/19/2019

### Uncertainty about Uncertainty: Near-Optimal Adaptive Algorithms for Estimating Binary Mixtures of Unknown Coins

Given a mixture between two populations of coins, "positive" coins that ...
02/16/2021

### Unifying Lower Bounds on Prediction Dimension of Consistent Convex Surrogates

Given a prediction task, understanding when one can and cannot design a ...
04/10/2019

### Testing Unateness Nearly Optimally

We present an Õ(n^2/3/ϵ^2)-query algorithm that tests whether an unknown...