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.

/pdf/nonlinear-dimensionality-reduction-by-locally-linear-vmiazg4oee.pdf

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.

/pdf/community-detection-in-graphs-34rogm3r6p.pdf

Community detection in graphs

We develop a new approach to solving minimum-cost circulation problems. Our approach combines methods for solving the maximum flow problem with successive approximation techniques based on cost scaling. We measure the accuracy of a solution by the amount that the complementary slackness conditions are violated.

We propose a simple minimum-cost circulation algorithm, one version of which runs in On3lognC time on an n-vertex network with integer arc costs of absolute value at most C. By incorporating sophisticated data structures into the algorithm, we obtain a time bound of Onm logn2/mlognC on a network with m arcs. A slightly different use of our approach shows that a minimum-cost circulation can be computed by solving a sequence of On lognC blocking flow problems. A corollary of this result is an On2log nlognC-time, m-processor parallel minimum-cost circulation algorithm. Our approach also yields strongly polynomial minimum-cost circulation algorithms.

Our results provide evidence that the minimum-cost circulation problem is not much harder than the maximum flow problem. We believe that a suitable implementation of our method will perform extremely well in practice.

https://www.jstor.org/stable/info/3689990

Finding Minimum-Cost Circulations by Successive Approximation

An algorithm for minimum-cost matching on a general graph with integral edge costs is presented. The algorithm runs in time close to the fastest known bound for maximum-cardinality matching. Specifically, let n, m, and N denote the number of vertices, number of edges, and largest magnitude of a cost, respectively. The best known time bound for maximum-cardinal ity matching M 0( Am). The new algorithm for minimum-cost matching has time bound 0( in a ( m, n )Iog n m log ( nN)). A slight modification of the new algorithm finds a maximum-cardinality matching in 0( fire) time. Other applications of the new algorlthm are given, mchrding an efficient implementa- tion of Christofides' traveling salesman approximation algorithm and efficient solutions to update problems that require the linear programming duals for matching.

/pdf/faster-scaling-algorithms-for-general-graph-matching-7ew9i03qx7.pdf

Faster scaling algorithms for general graph matching problems

We devise a method for computing functions defined on paths in trees. The method is based on tree manipulation techniques first used for efficiently representing equivalence relations. It has an almost-linear running time. We apply the method to give O(m $\alpha$(m,n)) algorithms for two problems. A. Verifying a minimum spanning tree in an undirected graph (best previous bound: O(m log log n) ). B. Finding dominators in a directed graph (best previous bound: O(n log n + m) ). Here n is the number of vertices and m the number of edges in the problem graph, and $\alpha$(m,n) is a very slowly growing function which is related to a functional inverse of Ackermann''s function. The method is also useful for solving, in O(m $\alpha$(m,n)) time, certain kinds of pathfinding problems on reducible graphs. Such problems occur in global flow analysis of computer programs and in other contexts. A companion paper will discuss this application.

Robert E. Tarjan

Papers

Finding Minimum-Cost Circulations by Successive Approximation

Faster scaling algorithms for general graph matching problems

Applications of Path Compression on Balanced Trees

Triangulating a simple polygon

A class of algorithms which require nonlinear time to maintain disjoint sets