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The efficiency of inference in both the Hugin and, most notably, the Shafer-Shenoy architectures can be improved by exploiting the independence relations induced by the incoming messages of a clique. That is, the message to be sent from a…
The efficiency of algorithms using secondary structures for probabilistic inference in Bayesian networks can be improved by exploiting independence relations induced by evidence and the direction of the links in the original network. In…
Efficient index structures for fast approximate nearest neighbor queries are required in many applications such as recommendation systems. In high-dimensional spaces, many conventional methods suffer from excessive usage of memory and slow…
The main goal of this paper is to describe a data structure called binary join trees that are useful in computing multiple marginals efficiently using the Shenoy-Shafer architecture. We define binary join trees, describe their utility, and…
Contemporary accelerator designs exhibit a high degree of spatial localization, wherein two-dimensional physical distance determines communication costs between processing elements. This situation presents considerable algorithmic…
The local computation technique (Shafer et al. 1987, Shafer and Shenoy 1988, Shenoy and Shafer 1986) is used for propagating belief functions in so called a Markov Tree. In this paper, we describe an efficient implementation of belief…
In the last decade, several architectures have been proposed for exact computation of marginals using local computation. In this paper, we compare three architectures - Lauritzen-Spiegelhalter, Hugin, and Shenoy-Shafer - from the…
Consider the situation where some evidence e has been entered to a Bayesian network. When performing conflict analysis, sensitivity analysis, or when answering questions like "What if the finding on X had been y instead of x?" you need…
Across a wide range of hardware scenarios, the computational efficiency and physical size of the arithmetic units significantly influence the speed and footprint of the overall hardware system. Nevertheless, the effectiveness of prior…
In this paper, we describe a scheme for propagating belief functions in certain kinds of trees using only local computations. This scheme generalizes the computational scheme proposed by Shafer and Logan1 for diagnostic trees of the type…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
We introduce a data distribution scheme for $\mathcal{H}$-matrices and a distributed-memory algorithm for $\mathcal{H}$-matrix-vector multiplication. Our data distribution scheme avoids an expensive $\Omega(P^2)$ scheduling procedure used…
Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…
We review some existing methods for the computation of first order moments on junction trees using Shafer-Shenoy algorithm. First, we consider the problem of first order moments computation as vertices problem in junction trees. In this…
In an earlier paper we introduced a special kind of k-width junction tree, called k-th order t-cherry junction tree in order to approximate a joint probability distribution. The approximation is the best if the Kullback-Leibler divergence…
The paper presents an iterative version of join-tree clustering that applies the message passing of join-tree clustering algorithm to join-graphs rather than to join-trees, iteratively. It is inspired by the success of Pearl's belief…
Random forest (RF) stands out as a highly favored machine learning approach for classification problems. The effectiveness of RF hinges on two key factors: the accuracy of individual trees and the diversity among them. In this study, we…
The construction of cut trees (also known as Gomory-Hu trees) for a given graph enables the minimum-cut size of the original graph to be obtained for any pair of vertices. Cut trees are a powerful back-end for graph management and mining,…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
This paper is devoted to expressiveness of hypergraphs for which uncertainty propagation by local computations via Shenoy/Shafer method applies. It is demonstrated that for this propagation method for a given joint belief distribution no…