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We define, in a consistent way, non-local pseudo-differential operators acting on a space of analytic functionals. These operators include the fractional derivative case. In this context we show how to solve homogeneous and inhomogeneous…
Distributed inference/estimation in Bayesian framework in the context of sensor networks has recently received much attention due to its broad applicability. The variational Bayesian (VB) algorithm is a technique for approximating…
A new symbolic algorithmic implementation of the general scheme of the exponentially convergent functional-discrete (FD-) method is developed and justified for the Sturm-Liouville problem on a finite interval for the Schr\"odinger equation…
We present a method for improving a Non Local Means operator by computing its low-rank approximation. The low-rank operator is constructed by applying a filter to the spectrum of the original Non Local Means operator. This results in an…
This paper studies stochastic minimization of a finite-sum loss $ F (\mathbf{x}) = \frac{1}{N} \sum_{\xi=1}^N f(\mathbf{x};\xi) $. In many real-world scenarios, the Hessian matrix of such objectives exhibits a low-rank structure on a batch…
A stochastic incremental subgradient algorithm for the minimization of a sum of convex functions is introduced. The method sequentially uses partial subgradient information and the sequence of partial subgradients is determined by a general…
Normals with unknown parameters (NUP) can be used to convert nontrivial model-based estimation problems into iterations of linear least-squares or Gaussian estimation problems. In this paper, we extend this approach by augmenting factor…
We introduce a new algorithm for the simulation of Euclidean dynamical triangulations that mimics the Metropolis-Hastings algorithm, but where all proposed moves are accepted. This rejection-free algorithm allows for the factorization of…
A new deterministic algorithm for finding square divisors, and finding $r$-power divisors in general, is presented. This algorithm is based on Lehman's method for integer factorization and is straightforward to implement. While the…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic algorithms. However, polynomial approximation is occasionally…
In this paper, we introduce, for the first time, the fractional--logarithmic Laplacian \( (-\Delta)^{s+\log} \), defined as the derivative of the fractional Laplacian \( (-\Delta)^t \) at \( t=s \). It is a singular integral operator with…
We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…
We present two improvements to arithmetic in the Jacobian of global function fields based on the approach of Hess. The first reduces the number of expensive reduction steps by optimizing for typical inputs rather than worst-case behavior,…
This paper studies the problem of globally optimizing a variable of interest that is part of a causal model in which a sequence of interventions can be performed. This problem arises in biology, operational research, communications and,…
In this paper we penetrate and extend the notion of local constancy in graphical models that has been introduced by Honorio et al. (2009). We propose Neighborhood-Fused Lasso, a method for model selection in high-dimensional graphical…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…
In this paper, we consider solving a class of convex optimization problem which minimizes the sum of three convex functions $f(x)+g(x)+h(Bx)$, where $f(x)$ is differentiable with a Lipschitz continuous gradient, $g(x)$ and $h(x)$ have a…
Dynamic programming algorithms have been successfully applied to propositional stochastic planning problems by using compact representations, in particular algebraic decision diagrams, to capture domain dynamics and value functions. Work on…
In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and…