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The Bayesian Learning Rule provides a framework for generic algorithm design but can be difficult to use for three reasons. First, it requires a specific parameterization of exponential family. Second, it uses gradients which can be…
We introduce a new framework for solving an important class of computational problems involving finite permutation groups, which includes calculating set stabilisers, intersections of subgroups, and isomorphisms of combinatorial structures.…
Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic…
Polynomial-time algorithms are given to find a central decomposition of maximum size for a finite p-group of class 2 and for a nilpotent Lie ring of class 2. The algorithms use Las Vegas probabilistic routines to compute the structure of…
We propose a computationally efficient and high-performance classification algorithm by incorporating class structural information in analysis dictionary learning. To achieve more consistent classification, we associate a class…
Methods are described for the solution of linear inference problems subject to deterministic constraints. The approach builds on work by Backus (1970a,b,c) and Parker (1977), but a range useful advances are suggested to address both…
We present an improved Bayesian framework for performing inference of affine transformations of constrained functions. We focus on quadrature with nonnegative functions, a common task in Bayesian inference. We consider constraints on the…
We introduce a novel aggregation method to efficiently perform image denoising. Preliminary filters are aggregated in a non-linear fashion, using a new metric of pixel proximity based on how the pool of filters reaches a consensus. We…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
Let K be a complete discretely valued field of mixed characteristic (0, p) with possibly imperfect residue field. We prove a Hasse-Arf theorem for the arithmetic ramification filtrations on G_K, except possibly in the absolutely unramified…
In this paper, we enhance a recent algorithm for approximate spectral factorization of matrix functions, extending its capabilities to precisely factorize rational matrices when an exact lower-upper triangular factorization is available.…
We show that, under fairly general conditions, many elements of a p-adic group can be well approximated by a product whose factors have properties that are helpful in performing explicit character computations.
Computer algebra systems are really good at factoring polynomials, i.e. writing f as a product of irreducible factors. It is relatively easy to verify that we have a factorisation, but verifying that these factors are irreducible is a much…
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
In this paper, we describe an algorithm that efficiently collect relations in class groups of number fields defined by a small defining polynomial. This conditional improvement consists in testing directly the smoothness of principal ideals…
Reduction of combinatorial filters involves compressing state representations that robots use. Such optimization arises in automating the construction of minimalist robots. But exact combinatorial filter reduction is an NP-complete problem…
Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…
We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in reactive verification; coalgebraic generality implies in particular that we cover not only classical…
In today's data driven world, storing, processing, and gleaning insights from large-scale data are major challenges. Data compression is often required in order to store large amounts of high-dimensional data, and thus, efficient inference…
We present an algorithm for factoring linear differential operators with coefficients in a finite separable extension of F p (x). Our methods rely on specific tools arising in positive characteristic: p-curvature, structure of simple…