From the Publisher:
Probabilistic Reasoning in Intelligent Systems is a complete andaccessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertaintyand offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognitionin short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information.
Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference

Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text.

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Nonlinear dimensionality reduction by locally linear embedding.

From the Publisher:
With this text, you gain an understanding of the fundamental concepts of algorithms, the very heart of computer science. It introduces the basic data structures and programming techniques often used in efficient algorithms. Covers use of lists, push-down stacks, queues, trees, and graphs. Later chapters go into sorting, searching and graphing algorithms, the string-matching algorithms, and the Schonhage-Strassen integer-multiplication algorithm. Provides numerous graded exercises at the end of each chapter.


0201000296B04062001

The Design and Analysis of Computer Algorithms

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

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Community detection in graphs

: Mannila and Ukkonen have studied a variant of the classical disjoint set union (equivalence) problem in which an extra operation, called deunion, can undo the most recently performed union operation not yet undone They proposed a way to modify standard set union algorithms to handle deunion operations This document analyzes several algorithms based on their approach The most efficient such algorithms have an amortized running time of O(log n/log log n) per operation, where n is the total number of elements in all the sets These algorithms use O(n log n) space, but the space usage can be reduced to O(n) by a simple change It is proven that any separable pointer-based algorithm for the problem required omega(log n/log log n) time per operation, thus showing that our upper bound an amortized time is tight (KR)

Amortized Analysis of Algorithms for Set Union with Backtracking. Revision

: An algorithm for finding a maximum clique in an arbitrary graph is described. The algorithm has a worst-case time bound of k(1.286) sup N for some constant k, where n is the number of vertices in the graph. Within a fixed time, the algorithm can analyze a graph with 2 3/4 as many vertices as the largest graph which the obvious algorithm (examining all subsets of vertices) can analyze. (Author)

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Finding a Maximum Clique.

An efficient planarity algorithm

We describe an efficient, purely functional implementation of deques with catenation. In addition to being an intriguing problem in its own right, finding a purely functional implementation of catenable deques is required to add certain sophisticated programming constructs to functional programming languages. Our solution has a worst-case running time of O(1) for each push, pop, inject, eject and catenation. The best previously known solution has an O(log*k) time bound for the kth deque operation. Our solution is not only faster but simpler. A key idea used in our result is an algorithmic technique related to the redundant digital representations used to avoid carry propagation in binary counting.

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Purely functional, real-time deques with catenation

This paper considers path problems on directed graphs which are solvable by a method similar to Gaussian elimination. The paper gives an axiom system for such problems which is a weakening of Salomaa''s axioms for a regular algebra. The paper presents a general solution method which requires O($n^3$) time for dense graphs with n vertices and considerably less time for sparse graphs. The paper also presents a decomposition method which solves a path problem by breaking it into subproblems, solving each subproblem by elimination, and combining the solutions. This method is a generalization of the "reducibility" notion of data flow analysis, and is a kind of single-element "tearing". Efficiently implemented, the method requires O(m $\alpha$(m,n)) time plus time to solve the subproblems, for problem graphs with n vertices and m edges. Here $\alpha$(m,n) is a very slowly growing function which is a functional inverse of Ackermann''s function. The paper considers variants of the axiom system for which the solution methods still work, and presents several applications including solving simultaneous linear equations and analyzing control flow in computer programs.

Robert E. Tarjan

Papers

Amortized Analysis of Algorithms for Set Union with Backtracking. Revision

Finding a Maximum Clique.

An efficient planarity algorithm

Purely functional, real-time deques with catenation

Solving path problems on directed graphs.