Related papers: The Power of Many Samples in Query Complexity
The classical Yao principle states that the complexity R_epsilon(f) of an optimal randomized algorithm for a function f with success probability 1-epsilon equals the complexity max_mu D_epsilon^mu(f) of an optimal deterministic algorithm…
Given a small random sample of $n$-bit strings labeled by an unknown Boolean function, which properties of this function can be tested computationally efficiently? We show an equivalence between properties that are efficiently testable from…
Social and real-world considerations such as robustness, fairness, social welfare and multi-agent tradeoffs have given rise to multi-distribution learning paradigms, such as collaborative learning, group distributionally robust…
In the claw detection problem we are given two functions $f:D\rightarrow R$ and $g:D\rightarrow R$ ($|D|=n$, $|R|=k$), and we have to determine if there is exist $x,y\in D$ such that $f(x)=g(y)$. We show that the quantum query complexity of…
We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends…
We give a strong direct sum theorem for computing $xor \circ g$. Specifically, we show that for every function g and every $k\geq 2$, the randomized query complexity of computing the xor of k instances of g satisfies…
We consider query-based data acquisition and the corresponding information recovery problem, where the goal is to recover $k$ binary variables (information bits) from parity measurements of those variables. The queries and the corresponding…
Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…
We prove a query complexity variant of the weak polynomial Freiman-Ruzsa conjecture in the following form. For any $\epsilon > 0$, a set $A \subset \mathbb{Z}^d$ with doubling $K$ has a subset of size at least $K^{-\frac{4}{\epsilon}}|A|$…
The main reason for query model's prominence in complexity theory and quantum computing is the presence of concrete lower bounding techniques: polynomial and adversary method. There have been considerable efforts to give lower bounds using…
A large set of signals can sometimes be described sparsely using a dictionary, that is, every element can be represented as a linear combination of few elements from the dictionary. Algorithms for various signal processing applications,…
A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
Most work on adaptive data analysis assumes that samples in the dataset are independent. When correlations are allowed, even the non-adaptive setting can become intractable, unless some structural constraints are imposed. To address this,…
We study the query complexity of computing a function f:{0,1}^n-->R_+ in expectation. This requires the algorithm on input x to output a nonnegative random variable whose expectation equals f(x), using as few queries to the input x as…
There has been significant study on the sample complexity of testing properties of distributions over large domains. For many properties, it is known that the sample complexity can be substantially smaller than the domain size. For example,…
We characterize the symmetric distributions that can be (approximately) generated by shallow Boolean circuits. More precisely, let $f\colon \{0,1\}^m \to \{0,1\}^n$ be a Boolean function where each output bit depends on at most $d$ input…
We study the problem of sampling from a distribution $\mu$ with density $\propto e^{-V}$ for some potential function $V:\mathbb R^d\to \mathbb R$ with query access to $V$ and $\nabla V$. We start with the following standard assumptions: (1)…
Adaptivity is an important feature of data analysis---typically the choice of questions asked about a dataset depends on previous interactions with the same dataset. However, generalization error is typically bounded in a non-adaptive…
We study an extension of the standard two-party communication model in which Alice and Bob hold probability distributions $p$ and $q$ over domains $X$ and $Y$, respectively. Their goal is to estimate \[ \mathbb{E}_{x \sim p,\, y \sim…
In a sampling problem, we are given an input x, and asked to sample approximately from a probability distribution D_x. In a search problem, we are given an input x, and asked to find a member of a nonempty set A_x with high probability. (An…