Related papers: Recurrence relations and fast algorithms
We introduce a class of algorithms for constructing Fourier representations of Gaussian processes in $1$ dimension that are valid over ranges of hyperparameter values. The scaling and frequencies of the Fourier basis functions are evaluated…
We present a new algorithm for the computation of the inverse Abel transform, a problem which emerges in many areas of physics and engineering. We prove that the Legendre coefficients of a given function coincide with the Fourier…
This paper provides an introduction to the design of augmented data structures that offer an efficient representation of a mathematical sequence and fast sequential summation algorithms, which guarantee both logarithmic running time and…
We derive formulas which connect cumulants of particle numbers observed with efficiency losses with the original ones based on the binomial model. These formulas can describe the case with multiple efficiencies in a compact form. Compared…
A matrix algorithm is said to be superfast (that is, runs at sublinear cost) if it involves much fewer scalars and flops than the input matrix has entries. Such algorithms have been extensively studied and widely applied in modern…
In this paper we firstly review how to \textit{explicitly} solve a system of $3$ \textit{first-order linear recursions }and outline the main properties of these solutions. Next, via a change of variables, we identify a class of systems of…
A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
We present efficient algorithms for computing the $N$-point correlation functions (NPCFs) of random fields in arbitrary $D$-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences, and provide a…
With the ansatz that a data set's correlation matrix has a certain parametrized form (one general enough, however, to allow the arbitrary specification of a slowly-varying decorrelation distance and population variance) the general…
Linear mixed models with large imbalanced crossed random effects structures pose severe computational problems for maximum likelihood estimation and for Bayesian analysis. The costs can grow as fast as $N^{3/2}$ when there are N…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
A modified dynamic programming algorithm rapidly and accurately solves large 0/1 knapsack problems. It has computational O(nlogn), space O(nlogn) and predictable maximum error. Experimentally it's accuracy increases faster than linearly…
Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational…
A key functionality of emerging connected autonomous systems such as smart cities, smart transportation systems, and the industrial Internet-of-Things, is the ability to process and learn from data collected at different physical locations.…
Recurrent neural networks are often used for learning time-series data. Based on a few assumptions we model this learning task as a minimization problem of a nonlinear least-squares cost function. The special structure of the cost function…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
In this paper we show how specific families of positive definite kernels serve as powerful tools in analyses of iteration algorithms for multiple layer feedforward Neural Network models. Our focus is on particular kernels that adapt well to…
We show that a simple single-pass semi-streaming variant of the Pivot algorithm for Correlation Clustering gives a (3 + {\epsilon})-approximation using O(n/{\epsilon}) words of memory. This is a slight improvement over the recent results of…