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

The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected componen...

Depth-First Search and Linear Graph Algorithms

In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated F-heaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. F-heaps support arbitrary deletion from an n-item heap in O(log n) amortized time and all other standard heap operations in O(1) amortized time. Using F-heaps we are able to obtain improved running times for several network optimization algorithms. In particular, we obtain the following worst-case bounds, where n is the number of vertices and m the number of edges in the problem graph: O(n log n + m) for the single-source shortest path problem with nonnegative edge lengths, improved from O(mlog(m/n+2)n);O(n2log n + nm) for the all-pairs shortest path problem, improved from O(nm log(m/n+2)n);O(n2log n + nm) for the assignment problem (weighted bipartite matching), improved from O(nmlog(m/n+2)n);O(mβ(m, n)) for the minimum spanning tree problem, improved from O(mlog log(m/n+2)n); where β(m, n) = min {i | log(i)n ≤ m/n}. Note that β(m, n) ≤ log*n if m ≥ n.Of these results, the improved bound for minimum spanning trees is the most striking, although all the results give asymptotic improvements for graphs of appropriate densities.

/pdf/fibonacci-heaps-and-their-uses-in-improved-network-3s6u3e39gv.pdf

Fibonacci heaps and their uses in improved network optimization algorithms

In this article we study the amortized efficiency of the “move-to-front” and similar rules for dynamically maintaining a linear list. Under the assumption that accessing the ith element from the front of the list takes t(i) time, we show that move-to-front is within a constant factor of optimum among a wide class of list maintenance rules. Other natural heuristics, such as the transpose and frequency count rules, do not share this property. We generalize our results to show that move-to-front is within a constant factor of optimum as long as the access cost is a convex function. We also study paging, a setting in which the access cost is not convex. The paging rule corresponding to move-to-front is the “least recently used” (LRU) replacement rule. We analyze the amortized complexity of LRU, showing that its efficiency differs from that of the off-line paging rule (Belady's MIN algorithm) by a factor that depends on the size of fast memory. No on-line paging algorithm has better amortized performance.

Amortized efficiency of list update and paging rules

Foundations Disjoint Sets Heaps Search Trees Linking and Cutting Trees Minimum Spanning Trees Shortest Paths Network Flows Matchings

Data Structures and Network Algorithms

In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated F-heaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. F-heaps support arbitrary deletion from an n-item heap in 0(log n) amortized time and all other standard heap operations in 0(1) amortized time. Using F-heaps we are able to obtain improved running times for several network optimization algorithms.

Robert E. Tarjan

Papers

Depth-First Search and Linear Graph Algorithms

Fibonacci heaps and their uses in improved network optimization algorithms

Amortized efficiency of list update and paging rules

Data Structures and Network Algorithms

Fibonacci Heaps And Their Uses In Improved Network Optimization Algorithms