differences of weighted composition operators from bloch space to h on the unit ball abstract in this paper we study the boundness and compactness of differences of weighted composition operators from the bloch space b to the space h of bounded analytic functions on the open unit ball of c n moreover we estimate the norm and the essential norm of differences of composition operators from b to h

a probabilistic plan recognition algorithm based on plan tree grammars we present the phatt algorithm for plan recognition unlike previous approaches to plan recognition phatt is based on a model of plan execution we show that this clarifies several difficult issues in plan recognition including the execution of multiple interleaved root goals partially ordered plans and failing to observe actions we present the phatt algorithm s theoretical basis and an implementation based on tree structures we also investigate the algorithm s complexity both analytically and empirically finally we present phatt s integrated constraint reasoning for parametrized actions and temporal constraints

controlled generation of hard and easy bayesian networks impact on maximal clique size in tree clustering this article presents and analyzes algorithms that systematically generate random bayesian networks of varying difficulty levels with respect to inference using tree clustering the results are relevant to research on efficient bayesian network inference such as computing a most probable explanation or belief updating since they allow controlled experimentation to determine the impact of improvements to inference algorithms the results are also relevant to research on machine learning of bayesian networks since they support controlled generation of a large number of data sets at a given difficulty level our generation algorithms called bpart and mpart support controlled but random construction of bipartite and multipartite bayesian networks the bayesian network parameters that we vary are the total number of nodes degree of connectivity the ratio of the number of non root nodes to the number of root nodes regularity of the underlying graph and characteristics of the conditional probability tables the main dependent parameter is the size of the maximal clique as generated by tree clustering this article presents extensive empirical analysis using the hugin tree clustering approach as well as theoretical analysis related to the random generation of bayesian networks using bpart and mpart

spectra of weighted algebras of holomorphic functions we consider weighted algebras of holomorphic functions on a banach space we determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial schauder decompositions we study the spectra of weighted algebras and endow them with an analytic structure we also deal with composition operators and algebra homomorphisms in particular to investigate how their induced mappings act on the analytic structure of the spectrum moreover a banach stone type question is addressed

an algorithm for finding maps for belief networks through cost based abduction abstract in cost based abduction the objective is to find the least cost set of hypotheses that are sufficient to explain the observed evidence in the maximuma posteriori map assignment problem on bayesian belief networks the objective is to find the network assignment a with highest conditional probability p a e where l represents the observed evidence in this paper we present a provablycorrect linear time transformation that allows algorithms and heuristic methods for cost based abduction such as charniak and shimony s best first search method or santos integer linear programming approach to be used for the map problem

mandatory leaf node prediction in hierarchical multilabel classification in hierarchical classification the output labels reside on a tree or directed acyclic graph dag structured hierarchy on testing the prediction paths of a given test example may be required to end at leaf nodes of the label hierarchy this is called mandatory leaf node prediction mlnp and is particularly useful when the leaf nodes have much stronger semantic meaning than the internal nodes however while there have been a lot of mlnp methods in hierarchical multiclass classification performing mlnp in hierarchical multilabel classification is difficult in this paper we propose novel mlnp algorithms that consider the global label hierarchy structure we show that the joint posterior probability over all the node labels can be efficiently maximized by dynamic programming for label trees or greedy algorithm for label dags in addition both algorithms can be further extended for the minimization of the expected symmetric loss experiments are performed on real world mlnp data sets with label trees and label dags the proposed method consistently outperforms other hierarchical and flat multilabel classification methods

approximating maps for belief networks is np hard and other theorems abstract finding maximum a posteriori map assignments also called most probable explanations is an important problem on bayesian belief networks shimony has shown that finding maps is np hard in this paper we show that approximating maps with a constant ratio bound is also np hard in addition we examine the complexity of two related problems which have been mentioned in the literature we show that given the map for a belief network and evidence set or the family of maps if the optimal is not unique it remains np hard to find or approximate alternative next best explanations furthermore we show that given the map or maps for a belief network and an initial evidence set it is also np hard to find or approximate the map assignment for the same belief network with a modified evidence set that differs from the initial set by the addition or removal of even a single node assignment finally we show that our main result applies to networks with constrained in degree and out degree applies to randomized approximation and even still applies if the ratio bound instead of being constant is allowed to be a polynomial function of various aspects of the network topology

compact differences of composition operators abstract a characterization of compact difference is given for composition operators acting on the standard weighted bergman spaces and necessary conditions are given on a larger scale of weighted dirichlet spaces conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts the additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component

norm product belief propagation primal dual message passing for approximate inference inference problems in graphical models can be represented as a constrained optimization of a free energy function in this paper we treat both forms of probabilistic inference estimating marginal probabilities of the joint distribution and finding the most probable assignment through a unified message passing algorithm architecture in particular we generalize the belief propagation bp algorithms of sum product and max product and tree reweighted trw sum and max product algorithms trbp and introduce a new set of convergent algorithms based on convex free energy and linear programming lp relaxation as a zero temperature of a convex free energy the main idea of this work arises from taking a general perspective on the existing bp and trbp algorithms while observing that they all are reductions from the basic optimization formula of f ihi where the function f is an extended valued strictly convex but nonsmooth and the functions hi are extended valued functions not necessarily convex we use tools from convex duality to present the primal dual ascent algorithm which is an extension of the bregman successive projection scheme and is designed to handle optimization of the general type f ihi we then map the fractional free energy variational principle for approximate inference onto the optimization formula above and introduce the norm product message passing algorithm special cases of the norm product include sum product and max product bp algorithms trbp and nmplp algorithms when the fractional free energy is set to be convex convex free energy the norm product is globally convergent for the estimation of marginal probabilities and for approximating the lp relaxation we also introduce another branch of the norm product which arises as the zero temperature of the convex free energy which we refer to as the convex max product the convex max product is convergent unlike max product and aims at solving the lp relaxation

an axiomatic treatment of three qualitative decision criteria the need for computationally efficient decision making techniques together with the desire to simplify the processes of knowledge acquisition and agent specification have led various researchers in artificial intelligence to examine qualitative decision tools however the adequacy of such tools is not clear this paper investigates the foundations of maximin minmax regret and competitive ratio three central qualitative decision criteria by characterizing those behaviors that could result from their use this characterizaton provides two important insights 1 under what conditions can we employ an agent model based on these basic qualitative decision criteria and 2 how rational are these decision procedures for the competitive ratio criterion in particular this latter issue is of central importance to our understanding of current work on on line algorithms our main result is a constructive representation theorem that uses two choice axioms to characterize maximin minmax regret and competitive ratio

approximating probabilistic inference in bayesian belief networks is np hard abstract it is known that exact computation of conditional probabilities in belief networks is np hard many investigators in the ai community have tacitly assumed that algorithms for performing approximate inference with belief networks are of polynomial complexity indeed special cases of approximate inference can be performed in time polynomial in the input size however we have discovered that the general problem of approximating conditional probabilities with belief networks like exact inference resides in the np hard complexity class we develop a complexity analysis to elucidate the difficulty of approximate probabilistic inference more specifically we show that the existence of a polynomial time relative approximation algorithm for major classes of problem instances implies that np p we present our proof and explore the implications of the result

compact differences of weighted composition operators from weighted bergman spaces to weighted type spaces abstract we characterize the compactness of differences of weighted composition operators from the weighted bergman space a p 0 1 to the weighted type space h v of analytic functions on the open unit disk d in terms of inducing symbols 1 2 d d and u 1 u 2 d c for the case 1

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

the computational complexity of probabilistic inference using bayesian belief networks research note abstract bayesian belief networks provide a natural efficient method for representing probabilistic dependencies among a set of variables for these reasons numerous researchers are exploring the use of belief networks as a knowledge representation in artificial intelligence algorithms have been developed previously for efficient probabilistic inference using special classes of belief networks more general classes of belief networks however have eluded efforts to develop efficient inference algorithms we show that probabilistic inference using belief networks is np hard therefore it seems unlikely that an exact algorithm can be developed to perform probabilistic inference efficiently over all classes of belief networks this result suggests that research should be directed away from the search for a general efficient probabilistic inference algorithm and toward the design of efficient special case average case and approximation algorithms

weighted composition operators from weighted bergman spaces to weighted type spaces on the unit ball we calculate the operator norm of the weighted composition operator from a weighted bergman space to a weighted type space on the unit ball of c n we also characterize the compactness of the operator

finding maps for belief networks is np hard given a probabilistic world model an important problem is to find the maximum a posteriori probability map instantiation of all the random variables given the evidence numerous researchers using such models employ some graph representation for the distributions such as a bayesian belief network this representation simplifies the complexity of specifying the distributions from exponential in n the number of variables in the model to linear in n in many interesting cases we show however that finding the map is np hard in the general case when these representations are used even if the size of the representation happens to be linear in n furthermore minor modifications to the proof show that the problem remains np hard for various restrictions of the topology of the graphs the same technique can be applied to the results of a related paper by cooper to further restrict belief network topology in the proof that probabilistic inference is np hard

projective modules over overrings of polynomial rings abstract let a be a commutative noetherian ring of dimension d and let p be a projective r a x 1 x l y 1 y m 1 f 1 f m module of rank r max 2 dim a 1 where f i a y i then i the natural map r gl r r el r 1 r k 1 r is surjective 3 8 ii assume f i is a monic polynomial then r 1 is an isomorphism 3 8 iii el 1 r p acts transitively on um r p in particular p is cancellative 3 12 iv if a is an affine algebra over a field then p has a unimodular element 3 13 in the case of laurent polynomial ring i e f i y i i ii are due to suslin 1977 12 iii is due to lindel 1995 4 and iv is due to bhatwadekar lindel and rao 1985 2

essential norm of differences of weighted composition operators between weighted type spaces on the unit ball abstract we find an asymptotically equivalent expression to the essential norm of differences of weighted composition operators between weighted type spaces of holomorphic functions on the unit ball in c n as a consequence we characterize the compactness of these operators the boundedness of these operators is also characterized

weighted composition operators from zygmund spaces into bloch spaces abstract let be an analytic self map and u be a fixed analytic function on the open unit disk d in the complex plane c the weighted composition operator is defined by uc f z u z f z z d f h d this paper studies the boundedness and compactness of weighted composition operators from zygmund spaces into bloch spaces

a linear constraint satisfaction approach to cost based abduction santos jr e a linear constraint satisfaction approach to cost based abduction artificial intelligence 65 1994 1 27 abduction is the problem of finding the best explanation for a given set of observations within ai this has been modeled as proving the observation by assuming some set of hypotheses cost based abduction associates a cost with each hypothesis the best proof is the one which assumes the least costly set previous approaches to finding the least cost set have formalized cost based abduction as a heuristic graph search problem however efficient admissible heuristics have proven difficult to find in this paper we present a new technique for finding least cost sets by using linear constraints to represent causal relationships in particular we are able to recast the problem as a 0 1 integer linear programming problem we can then use the highly efficient optimization tools of operations research yielding a computationally efficient method for solving cost based abduction problems experiments comparing our linear constraint satisfaction approach to standard graph searching methodologies suggest that our approach is superior to existing search techniques in that our approach exhibits an expected case polynomial run time growth rate

norm of weighted composition operators from α bloch spaces to weighted type spaces we calculate in an elegant way operator norm of the weighted composition operator from the a bloch space with a 0 1 to a weighted type space on the unit ball this result can be regarded as a complement to our recent result regarding the same problem for the case a 1

differences of composition operators between weighted type spaces of holomorphic functions on the unit ball of cn we consider differences of composition operators between weighted type or little weighted type spaces of analytic functions on the unit ball with weighted sup norms and give estimates for the distance of these differences to the space of compact operators we also study the boundedness and compactness of these operators

on the existence of unimodular elements and cancellation of projective modules over noetherian and non noetherian rings let r be a commutative ring of dimension d s r x or r x 1 x and p a finitely generated projective s module of rank r then p is cancellative if p has a unimodular element and r d 1 moreover if r dim s then p has a unimodular element and therefore p is cancellative as an application we prove that if r is a ring of dimension d of finite type over a prufer domain and p is a projective r x or r x 1 x module of rank at least d 1 then p has a unimodular element and is cancellative