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

A "sequential processing" algorithm using bicolor interchange that five-colors an n vertex planar graph in $O(n^2)$ time was given by Matula, Marble, and Isaacson [1972]. Lipton and Miller used a "batch processing" algorithm with bicolor interchange for the same problem and achieved an improved O(n log n) time bound [1978]. In this paper we use graph contraction arguments instead of bicolor interchange and improve both the sequential processing and batch processing methods to obtain five-coloring algorithms that operate in O(n) time.

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Two linear-time algorithms for five-coloring a planar graph

We introduce the rank-pairing heap, an implementation of heaps that combines the asymptotic efficiency of Fibonacci heaps with much of the simplicity of pairing heaps. Other heap implementations that match the bounds of Fibonacci heaps do so by maintaining a balance condition on the trees representing the heap. In contrast to these structures but like pairing heaps, our trees can evolve to have arbitrary (unbalanced) structure. Also like pairing heaps, our structure requires at most one cut and no other restructuring per key decrease, in the worst case: the only changes that can cascade during a key decrease are changes in node ranks. Although our data structure is simple, its analysis is not.

Rank-Pairing Heaps

This paper derives asymptotically tight bounds on the time-space tradeoffs for pebbling three different classes of directed acyclic graphs. Let N be the size of the graph, S the number of available pebbles, and T the time necessary for pebbling the graph. (a) A time space tradeoff of the form ST = t(N2) is proved for a special class of permutation graphs which implement the bit reversal permutation. (b) A time-space tradeoff of the form T = S t(N/S)t(N/S) is proved for a class of graphs constructed by stacking superconcentrators in series. (c) A time-space tradeoff of the form T = S.22t(N/S)is proved for pebbling general directed acyclic graphs.

Upper and lower bounds on time-space tradeoffs

In this paper we study the amortized complexity of two well-known algorithms used in system software, These are the "move-to-front" rule for maintaining an unsorted linear list representing a set, and the "least-recently-used" replacement rule for reducing page faults in a two-level paged memory. These algorithms have been subjected to much analysis, most of it average case. By studying the amortized complexity of these algorithms we are able to gain additional insight into their behavior.

Amortized efficiency of list update rules

Let $F_1$, $F_2$,..., $F_m$ be a set of Boolean functions of the form $F_i$ = $\wedge$ {x$\in X_i$}, where $\wedge$ denotes conjunction and each $X_i$ is a subset of a set X of n Boolean variables. We study the size of monotone Boolean networks for computing such sets of functions. We exhibit anomalous sets of conujunctions whose smallest monotone networks contain disjunctions. We show that if |$F_i$| is sufficiently small for all i, such anomalies cannot happen. We exhibit sets of m conjunctions in n unknowns which require $c_2$m$\alpha$(m,n) binary conjunctions, where $\alpha$(m,n) is a very slowly growing function related to a functional inverse of Ackermann''s function. This class of examples shows that an algorithm given in [STAN-CS-75-512] for computing functions defined on paths in trees is optimum to within a constant factor.

Robert E. Tarjan

Papers

Two linear-time algorithms for five-coloring a planar graph

Rank-Pairing Heaps

Upper and lower bounds on time-space tradeoffs

Amortized efficiency of list update rules

Complexity of monotone networks for computing conjunctions