Related papers: Number Field Sieve with Provable Complexity

We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative…

Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…

The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true…

Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes the use of VB in many…

We describe a very general abstract form of sieve based on a large sieve inequality which generalizes both the classical sieve inequality of Montgomery (and its higher-dimensional variants), and our recent sieve for Frobenius over function…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

In this note, we recall main properties of generalized random fields and present a proof of the continuity theorem of Paul L\'evy for generalized random fields in the space of tempered distributions. This theorem was first proved by…

In this paper the authors study set expansion in finite fields. Fourier analytic proofs are given for several results recently obtained by Solymosi, Vinh and Vu using spectral graph theory. In addition, several generalizations of these…

We introduce a notion of algorithmic randomness for algebraic fields. We prove the existence of a continuum of algebraic extensions of $\mathbb{Q}$ that are random according to our definition. We show that there are noncomputable algebraic…

The Posterior distribution of the Likelihood Ratio (PLR) is proposed by Dempster in 1974 for significance testing in the simple vs composite hypotheses case. In this hypotheses test case, classical frequentist and Bayesian hypotheses tests…

Priors are important for achieving proper posteriors with physically meaningful covariance structures for Gaussian random fields (GRFs) since the likelihood typically only provides limited information about the covariance structure under…

In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. In this paper, we slightly modify this notion to obtain the so-called irreducible-expansion complexity which is more suitable for…

An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…

The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion…

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al.…

We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the…

In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…

Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at…

In this paper we give a survey of recent methods for the asymptotic and exact enumeration of number fields with given Galois group of the Galois closure. In particular, the case of fields of degree up to 4 is now almost completely solved,…

We would like to congratulate the authors of "A Bayesian Conjugate Gradient Method" on their insightful paper, and welcome this publication which we firmly believe will become a fundamental contribution to the growing field of probabilistic…