The complexity of estimating min-entropy

Watson, Thomas

doi:10.1007/s00037-014-0091-2

Cited by 8 publications

(4 citation statements)

References 33 publications

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“…Testing various properties of polynomial-time samplable distributions such as uniformity, entropy, and closeness is a fundamental problem that characterizes several zero-knowledge complexity classes [20,14,11]. We show our hardness result employing a connection between testing polynomial-time samplable distributions and testing Bayesian networks.…”

Section: Related Workmentioning

confidence: 95%

Efficient inference of interventional distributions

Bhattacharyya

Gayen²,

Kandasamy

et al. 2021

Preprint

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We consider the problem of efficiently inferring interventional distributions in a causal Bayesian network from a finite number of observations. Let P be a causal model on a set V of observable variables on a given causal graph G. For sets X, Y ⊆ V, and setting x to X, let P x (Y) denote the interventional distribution on Y with respect to an intervention x to variables X. Shpitser and Pearl (AAAI 2006), building on the work of Tian and Pearl (AAAI 2001), gave an exact characterization of the class of causal graphs for which the interventional distribution P x (Y) can be uniquely determined.We give the first efficient version of the Shpitser-Pearl algorithm. In particular, under natural assumptions, we give a polynomial-time algorithm that on input a causal graph G on observable variables V, a setting x of a set X ⊆ V of bounded size, outputs succinct descriptions of both an evaluator and a generator for a distribution P that is ε-close (in total variation distance) toWe also show that when Y is an arbitrary set, there is no efficient algorithm that outputs an evaluator of a distribution that is ε-close to P x (Y) unless all problems that have statistical zero-knowledge proofs, including the Graph Isomorphism problem, have efficient randomized algorithms.

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Section: Related Workmentioning

confidence: 95%

Efficient inference of interventional distributions

Bhattacharyya

Gayen²,

Kandasamy

et al. 2021

Preprint

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“…For a general unknown source, estimating the minentropy is far from trivial. The problem is intractable for any reasonable sampling circuit with limited size (Lyngsø and Pedersen, 2002;Watson, 2016). We can only determine min-entropy from measurement inefficiently.…”

Section: Entropy Estimationmentioning

confidence: 99%

Quantum random number generators

2017

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Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation is one of the most mature quantum technologies with many alternative generation methods. We discuss the different technologies in quantum random number generation from the early devices based on radioactive decay to the multiple ways to use the quantum states of light to gather entropy from a quantum origin. We also discuss randomness extraction and amplification and the notable possibility of generating trusted random numbers even with untrusted hardware using device independent generation protocols.

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“…The reduction uses the "blow-up" idea used to prove hardness of approximate counting for MONOTONE-2-CNF-SAT in [JVV86]. We will closely follow the instantiation of this technique in [Wat12].…”

Section: Theorem 68 If Assumption 1 Holds True Then There Exists An A...mentioning

confidence: 99%

Inverse problems in approximate uniform generation

De,

Diakonikolas,

Servedio

2012

Preprint

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We initiate the study of inverse problems in approximate uniform generation, focusing on uniform generation of satisfying assignments of various types of Boolean functions. In such an inverse problem, the algorithm is given uniform random satisfying assignments of an unknown function f belonging to a class C of Boolean functions (such as linear threshold functions or polynomial-size DNF formulas), and the goal is to output a probability distribution D which is ǫ-close, in total variation distance, to the uniform distribution over f −1 (1). Problems of this sort comprise a natural type of unsupervised learning problem in which the unknown distribution to be learned is the uniform distribution over satisfying assignments of an unknown function f ∈ C.

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The complexity of estimating min-entropy

Cited by 8 publications

References 33 publications

Efficient inference of interventional distributions

Efficient inference of interventional distributions

Quantum random number generators

Inverse problems in approximate uniform generation

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