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1301.7366
Marginalizing in Undirected Graph and Hypergraph Models
cs.AI
Given an undirected graph G or hypergraph X model for a given set of variables V, we introduce two marginalization operators for obtaining the undirected graph GA or hypergraph HA associated with a given subset A c V such that the marginal distribution of A factorizes according to GA or HA, respectively. Finally, we illustrate the method by its application to some practical examples. With them we show that hypergraph models allow defining a finer factorization or performing a more precise conditional independence analysis than undirected graph models.
1301.7367
Utility Elicitation as a Classification Problem
cs.AI
We investigate the application of classification techniques to utility elicitation. In a decision problem, two sets of parameters must generally be elicited: the probabilities and the utilities. While the prior and conditional probabilities in the model do not change from user to user, the utility models do. Thus it is necessary to elicit a utility model separately for each new user. Elicitation is long and tedious, particularly if the outcome space is large and not decomposable. There are two common approaches to utility function elicitation. The first is to base the determination of the users utility function solely ON elicitation OF qualitative preferences.The second makes assumptions about the form AND decomposability OF the utility function.Here we take a different approach: we attempt TO identify the new USERs utility function based on classification relative to a database of previously collected utility functions. We do this by identifying clusters of utility functions that minimize an appropriate distance measure. Having identified the clusters, we develop a classification scheme that requires many fewer and simpler assessments than full utility elicitation and is more robust than utility elicitation based solely on preferences. We have tested our algorithm on a small database of utility functions in a prenatal diagnosis domain and the results are quite promising.
1301.7368
Irrelevance and Independence Relations in Quasi-Bayesian Networks
cs.AI
This paper analyzes irrelevance and independence relations in graphical models associated with convex sets of probability distributions (called Quasi-Bayesian networks). The basic question in Quasi-Bayesian networks is, How can irrelevance/independence relations in Quasi-Bayesian networks be detected, enforced and exploited? This paper addresses these questions through Walley's definitions of irrelevance and independence. Novel algorithms and results are presented for inferences with the so-called natural extensions using fractional linear programming, and the properties of the so-called type-1 extensions are clarified through a new generalization of d-separation.
1301.7369
Dynamic Jointrees
cs.AI
It is well known that one can ignore parts of a belief network when computing answers to certain probabilistic queries. It is also well known that the ignorable parts (if any) depend on the specific query of interest and, therefore, may change as the query changes. Algorithms based on jointrees, however, do not seem to take computational advantage of these facts given that they typically construct jointrees for worst-case queries; that is, queries for which every part of the belief network is considered relevant. To address this limitation, we propose in this paper a method for reconfiguring jointrees dynamically as the query changes. The reconfiguration process aims at maintaining a jointree which corresponds to the underlying belief network after it has been pruned given the current query. Our reconfiguration method is marked by three characteristics: (a) it is based on a non-classical definition of jointrees; (b) it is relatively efficient; and (c) it can reuse some of the computations performed before a jointree is reconfigured. We present preliminary experimental results which demonstrate significant savings over using static jointrees when query changes are considerable.
1301.7370
On the Semi-Markov Equivalence of Causal Models
cs.AI
The variability of structure in a finite Markov equivalence class of causally sufficient models represented by directed acyclic graphs has been fully characterized. Without causal sufficiency, an infinite semi-Markov equivalence class of models has only been characterized by the fact that each model in the equivalence class entails the same marginal statistical dependencies. In this paper, we study the variability of structure of causal models within a semi-Markov equivalence class and propose a systematic approach to construct models entailing any specific marginal statistical dependencies.
1301.7371
Comparative Uncertainty, Belief Functions and Accepted Beliefs
cs.AI
This paper relates comparative belief structures and a general view of belief management in the setting of deductively closed logical representations of accepted beliefs. We show that the range of compatibility between the classical deductive closure and uncertain reasoning covers precisely the nonmonotonic 'preferential' inference system of Kraus, Lehmann and Magidor and nothing else. In terms of uncertain reasoning any possibility or necessity measure gives birth to a structure of accepted beliefs. The classes of probability functions and of Shafer's belief functions which yield belief sets prove to be very special ones.
1301.7372
Qualitative Decision Theory with Sugeno Integrals
cs.AI
This paper presents an axiomatic framework for qualitative decision under uncertainty in a finite setting. The corresponding utility is expressed by a sup-min expression, called Sugeno (or fuzzy) integral. Technically speaking, Sugeno integral is a median, which is indeed a qualitative counterpart to the averaging operation underlying expected utility. The axiomatic justification of Sugeno integral-based utility is expressed in terms of preference between acts as in Savage decision theory. Pessimistic and optimistic qualitative utilities, based on necessity and possibility measures, previously introduced by two of the authors, can be retrieved in this setting by adding appropriate axioms.
1301.7373
The Bayesian Structural EM Algorithm
cs.LG cs.AI stat.ML
In recent years there has been a flurry of works on learning Bayesian networks from data. One of the hard problems in this area is how to effectively learn the structure of a belief network from incomplete data- that is, in the presence of missing values or hidden variables. In a recent paper, I introduced an algorithm called Structural EM that combines the standard Expectation Maximization (EM) algorithm, which optimizes parameters, with structure search for model selection. That algorithm learns networks based on penalized likelihood scores, which include the BIC/MDL score and various approximations to the Bayesian score. In this paper, I extend Structural EM to deal directly with Bayesian model selection. I prove the convergence of the resulting algorithm and show how to apply it for learning a large class of probabilistic models, including Bayesian networks and some variants thereof.
1301.7374
Learning the Structure of Dynamic Probabilistic Networks
cs.AI cs.LG
Dynamic probabilistic networks are a compact representation of complex stochastic processes. In this paper we examine how to learn the structure of a DPN from data. We extend structure scoring rules for standard probabilistic networks to the dynamic case, and show how to search for structure when some of the variables are hidden. Finally, we examine two applications where such a technology might be useful: predicting and classifying dynamic behaviors, and learning causal orderings in biological processes. We provide empirical results that demonstrate the applicability of our methods in both domains.
1301.7375
Learning by Transduction
cs.LG stat.ML
We describe a method for predicting a classification of an object given classifications of the objects in the training set, assuming that the pairs object/classification are generated by an i.i.d. process from a continuous probability distribution. Our method is a modification of Vapnik's support-vector machine; its main novelty is that it gives not only the prediction itself but also a practicable measure of the evidence found in support of that prediction. We also describe a procedure for assigning degrees of confidence to predictions made by the support vector machine. Some experimental results are presented, and possible extensions of the algorithms are discussed.
1301.7376
Graphical Models and Exponential Families
cs.LG stat.ML
We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks with several families of local distributions, are curved exponential families (CEFs) and graphical models with hidden variables are stratified exponential families (SEFs). An SEF is a finite union of CEFs satisfying a frontier condition. In addition, we illustrate how one can automatically generate independence and non-independence constraints on the distributions over the observable variables implied by a Bayesian network with hidden variables. The relevance of these results for model selection is examined.
1301.7377
Psychological and Normative Theories of Causal Power and the Probabilities of Causes
cs.AI stat.ME
This paper (1)shows that the best supported current psychological theory (Cheng, 1997) of how human subjects judge the causal power or influence of variations in presence or absence of one feature on another, given data on their covariation, tacitly uses a Bayes network which is either a noisy or gate (for causes that promote the effect) or a noisy and gate (for causes that inhibit the effect); (2)generalizes Chengs theory to arbitrary acyclic networks of noisy or and noisy and gates; (3)gives various sufficient conditions for the estimation of the parameters in such networks when there are independent, unobserved causes; (4)distinguishes direct causal influence of one feature on another (influence along a path with one edge) from total influence (influence along all paths from one variable to another) and gives sufficient conditions for estimating each when there are unobserved causes of the outcome variable; (5)describes the relation between Cheng models and a simplified version of the Rubin framework for representing causal relations.
1301.7378
Minimum Encoding Approaches for Predictive Modeling
cs.LG stat.ML
We analyze differences between two information-theoretically motivated approaches to statistical inference and model selection: the Minimum Description Length (MDL) principle, and the Minimum Message Length (MML) principle. Based on this analysis, we present two revised versions of MML: a pointwise estimator which gives the MML-optimal single parameter model, and a volumewise estimator which gives the MML-optimal region in the parameter space. Our empirical results suggest that with small data sets, the MDL approach yields more accurate predictions than the MML estimators. The empirical results also demonstrate that the revised MML estimators introduced here perform better than the original MML estimator suggested by Wallace and Freeman.
1301.7379
Towards Case-Based Preference Elicitation: Similarity Measures on Preference Structures
cs.AI
While decision theory provides an appealing normative framework for representing rich preference structures, eliciting utility or value functions typically incurs a large cost. For many applications involving interactive systems this overhead precludes the use of formal decision-theoretic models of preference. Instead of performing elicitation in a vacuum, it would be useful if we could augment directly elicited preferences with some appropriate default information. In this paper we propose a case-based approach to alleviating the preference elicitation bottleneck. Assuming the existence of a population of users from whom we have elicited complete or incomplete preference structures, we propose eliciting the preferences of a new user interactively and incrementally, using the closest existing preference structures as potential defaults. Since a notion of closeness demands a measure of distance among preference structures, this paper takes the first step of studying various distance measures over fully and partially specified preference structures. We explore the use of Euclidean distance, Spearmans footrule, and define a new measure, the probabilistic distance. We provide computational techniques for all three measures.
1301.7380
Solving POMDPs by Searching in Policy Space
cs.AI
Most algorithms for solving POMDPs iteratively improve a value function that implicitly represents a policy and are said to search in value function space. This paper presents an approach to solving POMDPs that represents a policy explicitly as a finite-state controller and iteratively improves the controller by search in policy space. Two related algorithms illustrate this approach. The first is a policy iteration algorithm that can outperform value iteration in solving infinitehorizon POMDPs. It provides the foundation for a new heuristic search algorithm that promises further speedup by focusing computational effort on regions of the problem space that are reachable, or likely to be reached, from a start state.
1301.7381
Hierarchical Solution of Markov Decision Processes using Macro-actions
cs.AI
We investigate the use of temporally abstract actions, or macro-actions, in the solution of Markov decision processes. Unlike current models that combine both primitive actions and macro-actions and leave the state space unchanged, we propose a hierarchical model (using an abstract MDP) that works with macro-actions only, and that significantly reduces the size of the state space. This is achieved by treating macroactions as local policies that act in certain regions of state space, and by restricting states in the abstract MDP to those at the boundaries of regions. The abstract MDP approximates the original and can be solved more efficiently. We discuss several ways in which macro-actions can be generated to ensure good solution quality. Finally, we consider ways in which macro-actions can be reused to solve multiple, related MDPs; and we show that this can justify the computational overhead of macro-action generation.
1301.7382
Inferring Informational Goals from Free-Text Queries: A Bayesian Approach
cs.IR cs.AI cs.CL
People using consumer software applications typically do not use technical jargon when querying an online database of help topics. Rather, they attempt to communicate their goals with common words and phrases that describe software functionality in terms of structure and objects they understand. We describe a Bayesian approach to modeling the relationship between words in a user's query for assistance and the informational goals of the user. After reviewing the general method, we describe several extensions that center on integrating additional distinctions and structure about language usage and user goals into the Bayesian models.
1301.7383
Evaluating Las Vegas Algorithms - Pitfalls and Remedies
cs.AI
Stochastic search algorithms are among the most sucessful approaches for solving hard combinatorial problems. A large class of stochastic search approaches can be cast into the framework of Las Vegas Algorithms (LVAs). As the run-time behavior of LVAs is characterized by random variables, the detailed knowledge of run-time distributions provides important information for the analysis of these algorithms. In this paper we propose a novel methodology for evaluating the performance of LVAs, based on the identification of empirical run-time distributions. We exemplify our approach by applying it to Stochastic Local Search (SLS) algorithms for the satisfiability problem (SAT) in propositional logic. We point out pitfalls arising from the use of improper empirical methods and discuss the benefits of the proposed methodology for evaluating and comparing LVAs.
1301.7384
An Anytime Algorithm for Decision Making under Uncertainty
cs.AI
We present an anytime algorithm which computes policies for decision problems represented as multi-stage influence diagrams. Our algorithm constructs policies incrementally, starting from a policy which makes no use of the available information. The incremental process constructs policies which includes more of the information available to the decision maker at each step. While the process converges to the optimal policy, our approach is designed for situations in which computing the optimal policy is infeasible. We provide examples of the process on several large decision problems, showing that, for these examples, the process constructs valuable (but sub-optimal) policies before the optimal policy would be available by traditional methods.
1301.7385
The Lumiere Project: Bayesian User Modeling for Inferring the Goals and Needs of Software Users
cs.AI cs.HC
The Lumiere Project centers on harnessing probability and utility to provide assistance to computer software users. We review work on Bayesian user models that can be employed to infer a users needs by considering a user's background, actions, and queries. Several problems were tackled in Lumiere research, including (1) the construction of Bayesian models for reasoning about the time-varying goals of computer users from their observed actions and queries, (2) gaining access to a stream of events from software applications, (3) developing a language for transforming system events into observational variables represented in Bayesian user models, (4) developing persistent profiles to capture changes in a user expertise, and (5) the development of an overall architecture for an intelligent user interface. Lumiere prototypes served as the basis for the Office Assistant in the Microsoft Office '97 suite of productivity applications.
1301.7386
Any Time Probabilistic Reasoning for Sensor Validation
cs.AI
For many real time applications, it is important to validate the information received from the sensors before entering higher levels of reasoning. This paper presents an any time probabilistic algorithm for validating the information provided by sensors. The system consists of two Bayesian network models. The first one is a model of the dependencies between sensors and it is used to validate each sensor. It provides a list of potentially faulty sensors. To isolate the real faults, a second Bayesian network is used, which relates the potential faults with the real faults. This second model is also used to make the validation algorithm any time, by validating first the sensors that provide more information. To select the next sensor to validate, and measure the quality of the results at each stage, an entropy function is used. This function captures in a single quantity both the certainty and specificity measures of any time algorithms. Together, both models constitute a mechanism for validating sensors in an any time fashion, providing at each step the probability of correct/faulty for each sensor, and the total quality of the results. The algorithm has been tested in the validation of temperature sensors of a power plant.
1301.7387
Measure Selection: Notions of Rationality and Representation Independence
cs.AI
We take another look at the general problem of selecting a preferred probability measure among those that comply with some given constraints. The dominant role that entropy maximization has obtained in this context is questioned by arguing that the minimum information principle on which it is based could be supplanted by an at least as plausible "likelihood of evidence" principle. We then review a method for turning given selection functions into representation independent variants, and discuss the tradeoffs involved in this transformation.
1301.7388
Implementing Resolute Choice Under Uncertainty
cs.GT cs.AI
The adaptation to situations of sequential choice under uncertainty of decision criteria which deviate from (subjective) expected utility raises the problem of ensuring the selection of a nondominated strategy. In particular, when following the suggestion of Machina and McClennen of giving up separability (also known as consequentialism), which requires the choice of a substrategy in a subtree to depend only on data relevant to that subtree, one must renounce to the use of dynamic programming, since Bellman's principle is no longer valid. An interpretation of McClennen's resolute choice, based on cooperation between the successive Selves of the decision maker, is proposed. Implementations of resolute choice which prevent Money Pumps negative prices of information or, more generally, choices of dominated strategies, while remaining computationally tractable, are proposed.
1301.7389
Dealing with Uncertainty on the Initial State of a Petri Net
cs.AI cs.SY
This paper proposes a method to find the actual state of a complex dynamic system from information coming from the sensors on the system himself, or on its environment. The nominal evolution of the system is a priori known and can be modeled (by an expert, for example), by different methods. In this paper, the Petri nets have been chosen. Contrary to the usual use of the Petri nets, the initial state of the system is unknown. So a degree of belief is bound to each places, or set of places. The theory used to model this uncertainty is the Dempster-Shafer's one which is well adapted to this type of problems. From the given Petri net characterizing the nominal evolution of the dynamic system, and from the observation inputs, the proposed method allows to determine according to the reliability of the model and the inputs, the state of the system at any time.
1301.7390
Hierarchical Mixtures-of-Experts for Exponential Family Regression Models with Generalized Linear Mean Functions: A Survey of Approximation and Consistency Results
cs.LG stat.ML
We investigate a class of hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form psi(ga+fx^Tfgb) are mixed. Here psi(...) is the inverse link function. Suppose the true response y follows an exponential family regression model with mean function belonging to a class of smooth functions of the form psi(h(fx)) where h(...)in W_2^infty (a Sobolev class over [0,1]^{s}). It is shown that the HME probability density functions can approximate the true density, at a rate of O(m^{-2/s}) in L_p norm, and at a rate of O(m^{-4/s}) in Kullback-Leibler divergence. These rates can be achieved within the family of HME structures with no more than s-layers, where s is the dimension of the predictor fx. It is also shown that likelihood-based inference based on HME is consistent in recovering the truth, in the sense that as the sample size n and the number of experts m both increase, the mean square error of the predicted mean response goes to zero. Conditions for such results to hold are stated and discussed.
1301.7391
Exact Inference of Hidden Structure from Sample Data in Noisy-OR Networks
cs.AI
In the literature on graphical models, there has been increased attention paid to the problems of learning hidden structure (see Heckerman [H96] for survey) and causal mechanisms from sample data [H96, P88, S93, P95, F98]. In most settings we should expect the former to be difficult, and the latter potentially impossible without experimental intervention. In this work, we examine some restricted settings in which perfectly reconstruct the hidden structure solely on the basis of observed sample data.
1301.7392
Large Deviation Methods for Approximate Probabilistic Inference
cs.LG stat.ML
We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is intractable, we show how to compute upper and lower bounds on many probabilities of interest. In particular, using methods from large deviation theory, we derive rigorous bounds on marginal probabilities such as Pr[children] and prove rates of convergence for the accuracy of our bounds as a function of network size. Our results apply to networks with generic transfer function parameterizations of the conditional probability tables, such as sigmoid and noisy-OR. They also explicitly illustrate the types of averaging behavior that can simplify the problem of inference in large networks.
1301.7393
Mixture Representations for Inference and Learning in Boltzmann Machines
cs.LG stat.ML
Boltzmann machines are undirected graphical models with two-state stochastic variables, in which the logarithms of the clique potentials are quadratic functions of the node states. They have been widely studied in the neural computing literature, although their practical applicability has been limited by the difficulty of finding an effective learning algorithm. One well-established approach, known as mean field theory, represents the stochastic distribution using a factorized approximation. However, the corresponding learning algorithm often fails to find a good solution. We conjecture that this is due to the implicit uni-modality of the mean field approximation which is therefore unable to capture multi-modality in the true distribution. In this paper we use variational methods to approximate the stochastic distribution using multi-modal mixtures of factorized distributions. We present results for both inference and learning to demonstrate the effectiveness of this approach.
1301.7394
A Comparison of Lauritzen-Spiegelhalter, Hugin, and Shenoy-Shafer Architectures for Computing Marginals of Probability Distributions
cs.AI
In the last decade, several architectures have been proposed for exact computation of marginals using local computation. In this paper, we compare three architectures - Lauritzen-Spiegelhalter, Hugin, and Shenoy-Shafer - from the perspective of graphical structure for message propagation, message-passing scheme, computational efficiency, and storage efficiency.
1301.7395
Incremental Tradeoff Resolution in Qualitative Probabilistic Networks
cs.AI
Qualitative probabilistic reasoning in a Bayesian network often reveals tradeoffs: relationships that are ambiguous due to competing qualitative influences. We present two techniques that combine qualitative and numeric probabilistic reasoning to resolve such tradeoffs, inferring the qualitative relationship between nodes in a Bayesian network. The first approach incrementally marginalizes nodes that contribute to the ambiguous qualitative relationships. The second approach evaluates approximate Bayesian networks for bounds of probability distributions, and uses these bounds to determinate qualitative relationships in question. This approach is also incremental in that the algorithm refines the state spaces of random variables for tighter bounds until the qualitative relationships are resolved. Both approaches provide systematic methods for tradeoff resolution at potentially lower computational cost than application of purely numeric methods.
1301.7396
Using Qualitative Relationships for Bounding Probability Distributions
cs.AI
We exploit qualitative probabilistic relationships among variables for computing bounds of conditional probability distributions of interest in Bayesian networks. Using the signs of qualitative relationships, we can implement abstraction operations that are guaranteed to bound the distributions of interest in the desired direction. By evaluating incrementally improved approximate networks, our algorithm obtains monotonically tightening bounds that converge to exact distributions. For supermodular utility functions, the tightening bounds monotonically reduce the set of admissible decision alternatives as well.
1301.7397
Magic Inference Rules for Probabilistic Deduction under Taxonomic Knowledge
cs.AI
We present locally complete inference rules for probabilistic deduction from taxonomic and probabilistic knowledge-bases over conjunctive events. Crucially, in contrast to similar inference rules in the literature, our inference rules are locally complete for conjunctive events and under additional taxonomic knowledge. We discover that our inference rules are extremely complex and that it is at first glance not clear at all where the deduced tightest bounds come from. Moreover, analyzing the global completeness of our inference rules, we find examples of globally very incomplete probabilistic deductions. More generally, we even show that all systems of inference rules for taxonomic and probabilistic knowledge-bases over conjunctive events are globally incomplete. We conclude that probabilistic deduction by the iterative application of inference rules on interval restrictions for conditional probabilities, even though considered very promising in the literature so far, seems very limited in its field of application.
1301.7398
Lazy Propagation in Junction Trees
cs.AI
The efficiency of algorithms using secondary structures for probabilistic inference in Bayesian networks can be improved by exploiting independence relations induced by evidence and the direction of the links in the original network. In this paper we present an algorithm that on-line exploits independence relations induced by evidence and the direction of the links in the original network to reduce both time and space costs. Instead of multiplying the conditional probability distributions for the various cliques, we determine on-line which potentials to multiply when a message is to be produced. The performance improvement of the algorithm is emphasized through empirical evaluations involving large real world Bayesian networks, and we compare the method with the HUGIN and Shafer-Shenoy inference algorithms.
1301.7399
Constructing Situation Specific Belief Networks
cs.AI
This paper describes a process for constructing situation-specific belief networks from a knowledge base of network fragments. A situation-specific network is a minimal query complete network constructed from a knowledge base in response to a query for the probability distribution on a set of target variables given evidence and context variables. We present definitions of query completeness and situation-specific networks. We describe conditions on the knowledge base that guarantee query completeness. The relationship of our work to earlier work on KBMC is also discussed.
1301.7401
An Experimental Comparison of Several Clustering and Initialization Methods
cs.LG stat.ML
We examine methods for clustering in high dimensions. In the first part of the paper, we perform an experimental comparison between three batch clustering algorithms: the Expectation-Maximization (EM) algorithm, a winner take all version of the EM algorithm reminiscent of the K-means algorithm, and model-based hierarchical agglomerative clustering. We learn naive-Bayes models with a hidden root node, using high-dimensional discrete-variable data sets (both real and synthetic). We find that the EM algorithm significantly outperforms the other methods, and proceed to investigate the effect of various initialization schemes on the final solution produced by the EM algorithm. The initializations that we consider are (1) parameters sampled from an uninformative prior, (2) random perturbations of the marginal distribution of the data, and (3) the output of hierarchical agglomerative clustering. Although the methods are substantially different, they lead to learned models that are strikingly similar in quality.
1301.7402
From Likelihood to Plausibility
cs.AI
Several authors have explained that the likelihood ratio measures the strength of the evidence represented by observations in statistical problems. This idea works fine when the goal is to evaluate the strength of the available evidence for a simple hypothesis versus another simple hypothesis. However, the applicability of this idea is limited to simple hypotheses because the likelihood function is primarily defined on points (simple hypotheses) of the parameter space. In this paper we define a general weight of evidence that is applicable to both simple and composite hypotheses. It is based on the Dempster-Shafer concept of plausibility and is shown to be a generalization of the likelihood ratio. Functional models are of a fundamental importance for the general weight of evidence proposed in this paper. The relevant concepts and ideas are explained by means of a familiar urn problem and the general analysis of a real-world medical problem is presented.
1301.7403
A Multivariate Discretization Method for Learning Bayesian Networks from Mixed Data
cs.AI cs.LG
In this paper we address the problem of discretization in the context of learning Bayesian networks (BNs) from data containing both continuous and discrete variables. We describe a new technique for <EM>multivariate</EM> discretization, whereby each continuous variable is discretized while taking into account its interaction with the other variables. The technique is based on the use of a Bayesian scoring metric that scores the discretization policy for a continuous variable given a BN structure and the observed data. Since the metric is relative to the BN structure currently being evaluated, the discretization of a variable needs to be dynamically adjusted as the BN structure changes.
1301.7404
Resolving Conflicting Arguments under Uncertainties
cs.AI
Distributed knowledge based applications in open domain rely on common sense information which is bound to be uncertain and incomplete. To draw the useful conclusions from ambiguous data, one must address uncertainties and conflicts incurred in a holistic view. No integrated frameworks are viable without an in-depth analysis of conflicts incurred by uncertainties. In this paper, we give such an analysis and based on the result, propose an integrated framework. Our framework extends definite argumentation theory to model uncertainty. It supports three views over conflicting and uncertain knowledge. Thus, knowledge engineers can draw different conclusions depending on the application context (i.e. view). We also give an illustrative example on strategical decision support to show the practical usefulness of our framework.
1301.7405
Flexible Decomposition Algorithms for Weakly Coupled Markov Decision Problems
cs.AI
This paper presents two new approaches to decomposing and solving large Markov decision problems (MDPs), a partial decoupling method and a complete decoupling method. In these approaches, a large, stochastic decision problem is divided into smaller pieces. The first approach builds a cache of policies for each part of the problem independently, and then combines the pieces in a separate, light-weight step. A second approach also divides the problem into smaller pieces, but information is communicated between the different problem pieces, allowing intelligent decisions to be made about which piece requires the most attention. Both approaches can be used to find optimal policies or approximately optimal policies with provable bounds. These algorithms also provide a framework for the efficient transfer of knowledge across problems that share similar structure.
1301.7406
Logarithmic Time Parallel Bayesian Inference
cs.AI
I present a parallel algorithm for exact probabilistic inference in Bayesian networks. For polytree networks with n variables, the worst-case time complexity is O(log n) on a CREW PRAM (concurrent-read, exclusive-write parallel random-access machine) with n processors, for any constant number of evidence variables. For arbitrary networks, the time complexity is O(r^{3w}*log n) for n processors, or O(w*log n) for r^{3w}*n processors, where r is the maximum range of any variable, and w is the induced width (the maximum clique size), after moralizing and triangulating the network.
1301.7407
Learning From What You Don't Observe
cs.AI
The process of diagnosis involves learning about the state of a system from various observations of symptoms or findings about the system. Sophisticated Bayesian (and other) algorithms have been developed to revise and maintain beliefs about the system as observations are made. Nonetheless, diagnostic models have tended to ignore some common sense reasoning exploited by human diagnosticians; In particular, one can learn from which observations have not been made, in the spirit of conversational implicature. There are two concepts that we describe to extract information from the observations not made. First, some symptoms, if present, are more likely to be reported before others. Second, most human diagnosticians and expert systems are economical in their data-gathering, searching first where they are more likely to find symptoms present. Thus, there is a desirable bias toward reporting symptoms that are present. We develop a simple model for these concepts that can significantly improve diagnostic inference.
1301.7408
Context-Specific Approximation in Probabilistic Inference
cs.AI
There is evidence that the numbers in probabilistic inference don't really matter. This paper considers the idea that we can make a probabilistic model simpler by making fewer distinctions. Unfortunately, the level of a Bayesian network seems too coarse; it is unlikely that a parent will make little difference for all values of the other parents. In this paper we consider an approximation scheme where distinctions can be ignored in some contexts, but not in other contexts. We elaborate on a notion of a parent context that allows a structured context-specific decomposition of a probability distribution and the associated probabilistic inference scheme called probabilistic partial evaluation (Poole 1997). This paper shows a way to simplify a probabilistic model by ignoring distinctions which have similar probabilities, a method to exploit the simpler model, a bound on the resulting errors, and some preliminary empirical results on simple networks.
1301.7409
Empirical Evaluation of Approximation Algorithms for Probabilistic Decoding
cs.AI
It was recently shown that the problem of decoding messages transmitted through a noisy channel can be formulated as a belief updating task over a probabilistic network [McEliece]. Moreover, it was observed that iterative application of the (linear time) Pearl's belief propagation algorithm designed for polytrees outperformed state of the art decoding algorithms, even though the corresponding networks may have many cycles. This paper demonstrates empirically that an approximation algorithm approx-mpe for solving the most probable explanation (MPE) problem, developed within the recently proposed mini-bucket elimination framework [Dechter96], outperforms iterative belief propagation on classes of coding networks that have bounded induced width. Our experiments suggest that approximate MPE decoders can be good competitors to the approximate belief updating decoders.
1301.7410
Decision Theoretic Foundations of Graphical Model Selection
cs.AI
This paper describes a decision theoretic formulation of learning the graphical structure of a Bayesian Belief Network from data. This framework subsumes the standard Bayesian approach of choosing the model with the largest posterior probability as the solution of a decision problem with a 0-1 loss function and allows the use of more general loss functions able to trade-off the complexity of the selected model and the error of choosing an oversimplified model. A new class of loss functions, called disintegrable, is introduced, to allow the decision problem to match the decomposability of the graphical model. With this class of loss functions, the optimal solution to the decision problem can be found using an efficient bottom-up search strategy.
1301.7411
On the Geometry of Bayesian Graphical Models with Hidden Variables
cs.LG stat.ML
In this paper we investigate the geometry of the likelihood of the unknown parameters in a simple class of Bayesian directed graphs with hidden variables. This enables us, before any numerical algorithms are employed, to obtain certain insights in the nature of the unidentifiability inherent in such models, the way posterior densities will be sensitive to prior densities and the typical geometrical form these posterior densities might take. Many of these insights carry over into more complicated Bayesian networks with systematic missing data.
1301.7412
Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)
cs.AI
One of the benefits of belief networks and influence diagrams is that so much knowledge is captured in the graphical structure. In particular, statements of conditional irrelevance (or independence) can be verified in time linear in the size of the graph. To resolve a particular inference query or decision problem, only some of the possible states and probability distributions must be specified, the "requisite information." This paper presents a new, simple, and efficient "Bayes-ball" algorithm which is well-suited to both new students of belief networks and state of the art implementations. The Bayes-ball algorithm determines irrelevant sets and requisite information more efficiently than existing methods, and is linear in the size of the graph for belief networks and influence diagrams.
1301.7413
Switching Portfolios
q-fin.PM cs.AI
A constant rebalanced portfolio is an asset allocation algorithm which keeps the same distribution of wealth among a set of assets along a period of time. Recently, there has been work on on-line portfolio selection algorithms which are competitive with the best constant rebalanced portfolio determined in hindsight. By their nature, these algorithms employ the assumption that high returns can be achieved using a fixed asset allocation strategy. However, stock markets are far from being stationary and in many cases the wealth achieved by a constant rebalanced portfolio is much smaller than the wealth achieved by an ad-hoc investment strategy that adapts to changes in the market. In this paper we present an efficient Bayesian portfolio selection algorithm that is able to track a changing market. We also describe a simple extension of the algorithm for the case of a general transaction cost, including the transactions cost models recently investigated by Blum and kalai. We provide a simple analysis of the competitiveness of the algorithm and check its performance on real stock data from the New York Stock Exchange accumulated during a 22-year period.
1301.7414
Bayesian Networks from the Point of View of Chain Graphs
cs.AI
AThe paper gives a few arguments in favour of the use of chain graphs for description of probabilistic conditional independence structures. Every Bayesian network model can be equivalently introduced by means of a factorization formula with respect to a chain graph which is Markov equivalent to the Bayesian network. A graphical characterization of such graphs is given. The class of equivalent graphs can be represented by a distinguished graph which is called the largest chain graph. The factorization formula with respect to the largest chain graph is a basis of a proposal of how to represent the corresponding (discrete) probability distribution in a computer (i.e. parametrize it). This way does not depend on the choice of a particular Bayesian network from the class of equivalent networks and seems to be the most efficient way from the point of view of memory demands. A separation criterion for reading independency statements from a chain graph is formulated in a simpler way. It resembles the well-known d-separation criterion for Bayesian networks and can be implemented locally.
1301.7415
Learning Mixtures of DAG Models
cs.LG cs.AI stat.ML
We describe computationally efficient methods for learning mixtures in which each component is a directed acyclic graphical model (mixtures of DAGs or MDAGs). We argue that simple search-and-score algorithms are infeasible for a variety of problems, and introduce a feasible approach in which parameter and structure search is interleaved and expected data is treated as real data. Our approach can be viewed as a combination of (1) the Cheeseman--Stutz asymptotic approximation for model posterior probability and (2) the Expectation--Maximization algorithm. We evaluate our procedure for selecting among MDAGs on synthetic and real examples.
1301.7416
Probabilistic Inference in Influence Diagrams
cs.AI
This paper is about reducing influence diagram (ID) evaluation into Bayesian network (BN) inference problems. Such reduction is interesting because it enables one to readily use one's favorite BN inference algorithm to efficiently evaluate IDs. Two such reduction methods have been proposed previously (Cooper 1988, Shachter and Peot 1992). This paper proposes a new method. The BN inference problems induced by the mew method are much easier to solve than those induced by the two previous methods.
1301.7417
Planning with Partially Observable Markov Decision Processes: Advances in Exact Solution Method
cs.AI
There is much interest in using partially observable Markov decision processes (POMDPs) as a formal model for planning in stochastic domains. This paper is concerned with finding optimal policies for POMDPs. We propose several improvements to incremental pruning, presently the most efficient exact algorithm for solving POMDPs.
1301.7418
Flexible and Approximate Computation through State-Space Reduction
cs.AI
In the real world, insufficient information, limited computation resources, and complex problem structures often force an autonomous agent to make a decision in time less than that required to solve the problem at hand completely. Flexible and approximate computations are two approaches to decision making under limited computation resources. Flexible computation helps an agent to flexibly allocate limited computation resources so that the overall system utility is maximized. Approximate computation enables an agent to find the best satisfactory solution within a deadline. In this paper, we present two state-space reduction methods for flexible and approximate computation: quantitative reduction to deal with inaccurate heuristic information, and structural reduction to handle complex problem structures. These two methods can be applied successively to continuously improve solution quality if more computation is available. Our results show that these reduction methods are effective and efficient, finding better solutions with less computation than some existing well-known methods.
1301.7455
Opinion Maximization in Social Networks
cs.SI physics.soc-ph
The process of opinion formation through synthesis and contrast of different viewpoints has been the subject of many studies in economics and social sciences. Today, this process manifests itself also in online social networks and social media. The key characteristic of successful promotion campaigns is that they take into consideration such opinion-formation dynamics in order to create a overall favorable opinion about a specific information item, such as a person, a product, or an idea. In this paper, we adopt a well-established model for social-opinion dynamics and formalize the campaign-design problem as the problem of identifying a set of target individuals whose positive opinion about an information item will maximize the overall positive opinion for the item in the social network. We call this problem CAMPAIGN. We study the complexity of the CAMPAIGN problem, and design algorithms for solving it. Our experiments on real data demonstrate the efficiency and practical utility of our algorithms.
1301.7464
Variable-Length Coding with Feedback: Finite-Length Codewords and Periodic Decoding
cs.IT math.IT
Theoretical analysis has long indicated that feedback improves the error exponent but not the capacity of single-user memoryless channels. Recently Polyanskiy et al. studied the benefit of variable-length feedback with termination (VLFT) codes in the non-asymptotic regime. In that work, achievability is based on an infinite length random code and decoding is attempted at every symbol. The coding rate backoff from capacity due to channel dispersion is greatly reduced with feedback, allowing capacity to be approached with surprisingly small expected latency. This paper is mainly concerned with VLFT codes based on finite-length codes and decoding attempts only at certain specified decoding times. The penalties of using a finite block-length $N$ and a sequence of specified decoding times are studied. This paper shows that properly scaling $N$ with the expected latency can achieve the same performance up to constant terms as with $N = \infty$. The penalty introduced by periodic decoding times is a linear term of the interval between decoding times and hence the performance approaches capacity as the expected latency grows if the interval between decoding times grows sub-linearly with the expected latency.
1301.7473
Information driven self-organization of complex robotic behaviors
cs.RO cs.IT cs.LG math.IT
Information theory is a powerful tool to express principles to drive autonomous systems because it is domain invariant and allows for an intuitive interpretation. This paper studies the use of the predictive information (PI), also called excess entropy or effective measure complexity, of the sensorimotor process as a driving force to generate behavior. We study nonlinear and nonstationary systems and introduce the time-local predicting information (TiPI) which allows us to derive exact results together with explicit update rules for the parameters of the controller in the dynamical systems framework. In this way the information principle, formulated at the level of behavior, is translated to the dynamics of the synapses. We underpin our results with a number of case studies with high-dimensional robotic systems. We show the spontaneous cooperativity in a complex physical system with decentralized control. Moreover, a jointly controlled humanoid robot develops a high behavioral variety depending on its physics and the environment it is dynamically embedded into. The behavior can be decomposed into a succession of low-dimensional modes that increasingly explore the behavior space. This is a promising way to avoid the curse of dimensionality which hinders learning systems to scale well.
1301.7482
Technical Report: A Receding Horizon Algorithm for Informative Path Planning with Temporal Logic Constraints
cs.RO
This technical report is an extended version of the paper 'A Receding Horizon Algorithm for Informative Path Planning with Temporal Logic Constraints' accepted to the 2013 IEEE International Conference on Robotics and Automation (ICRA). This paper considers the problem of finding the most informative path for a sensing robot under temporal logic constraints, a richer set of constraints than have previously been considered in information gathering. An algorithm for informative path planning is presented that leverages tools from information theory and formal control synthesis, and is proven to give a path that satisfies the given temporal logic constraints. The algorithm uses a receding horizon approach in order to provide a reactive, on-line solution while mitigating computational complexity. Statistics compiled from multiple simulation studies indicate that this algorithm performs better than a baseline exhaustive search approach.
1301.7491
On the Construction and Decoding of Concatenated Polar Codes
cs.IT math.IT
A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes, while having a significantly better error-decay rate. We show that for any $\epsilon > 0$, and total frame length $N$, the parameters of the scheme can be set such that the frame error probability is less than $2^{-N^{1-\epsilon}}$, while the scheme is still capacity achieving. This improves upon $2^{-N^{0.5-\eps}}$, the frame error probability of Arikan's polar codes. We also propose decoding algorithms for concatenated polar codes, which significantly improve the error-rate performance at finite block lengths while preserving the low decoding complexity.
1301.7503
Finite Length Analysis on Listing Failure Probability of Invertible Bloom Lookup Tables
cs.IT math.IT
The Invertible Bloom Lookup Tables (IBLT) is a data structure which supports insertion, deletion, retrieval and listing operations of the key-value pair. The IBLT can be used to realize efficient set reconciliation for database synchronization. The most notable feature of the IBLT is the complete listing operation of the key-value pairs based on the algorithm similar to the peeling algorithm for low-density generator-matrix (LDGM) codes. In this paper, we will present a stopping set (SS) analysis for the IBLT which reveals finite length behaviors of the listing failure probability. The key of the analysis is enumeration of the number of stopping matrices of given size. We derived a novel recursive formula useful for computationally efficient enumeration. An upper bound on the listing failure probability based on the union bound accurately captures the error floor behaviors. It will be shown that, in the error floor region, the dominant SS have size 2. We propose a simple modification on hash functions, which are called SS avoiding hash functions, for preventing occurrences of the SS of size 2.
1301.7504
Improved Lower Bounds on the Total Variation Distance for the Poisson Approximation
cs.IT math.IT
New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is addressed.
1301.7506
A Fully Distributed Opportunistic Network Coding Scheme for Cellular Relay Networks
cs.IT math.IT
In this paper, we propose an opportunistic network coding (ONC) scheme in cellular relay networks, which operates depending on whether the relay decodes source messages successfully or not. A fully distributed method is presented to implement the proposed opportunistic network coding scheme without the need of any feedback between two network nodes. We consider the use of proposed ONC for cellular downlink transmissions and derive its closed-form outage probability expression considering cochannel interference in a Rayleigh fading environment. Numerical results show that the proposed ONC scheme outperforms the traditional non-cooperation in terms of outage probability. We also develop the diversity-multiplexing tradeoff (DMT) of proposed ONC and show that the ONC scheme obtains the full diversity and an increased multiplexing gain as compared with the conventional cooperation protocols.
1301.7515
Energy Efficiency of Network Cooperation for Cellular Uplink Transmissions
cs.IT math.IT
There is a growing interest in energy efficient or so-called "green" wireless communication to reduce the energy consumption in cellular networks. Since today's wireless terminals are typically equipped with multiple network access interfaces such as Bluetooth, Wi-Fi, and cellular networks, this paper investigates user terminals cooperating with each other in transmitting their data packets to a base station (BS) by exploiting the multiple network access interfaces, referred to as inter-network cooperation, to improve the energy efficiency in cellular uplink transmission. Given target outage probability and data rate requirements, we develop a closed-form expression of energy efficiency in Bits-per-Joule for the inter-network cooperation by taking into account the path loss, fading, and thermal noise effects. Numerical results show that when the cooperating users move towards to each other, the proposed inter-network cooperation significantly improves the energy efficiency as compared with the traditional non-cooperation and intra-network cooperation. This implies that given a certain amount of bits to be transmitted, the inter-network cooperation requires less energy than the traditional non-cooperation and intra-network cooperation, showing the energy saving benefit of inter-network cooperation.
1301.7519
Non-Adaptive Group Testing based on Sparse Pooling Graphs
cs.IT math.IT
In this paper, an information theoretic analysis on non-adaptive group testing schemes based on sparse pooling graphs is presented. The binary status of the objects to be tested are modeled by i.i.d. Bernoulli random variables with probability p. An (l, r, n)-regular pooling graph is a bipartite graph with left node degree l and right node degree r, where n is the number of left nodes. Two scenarios are considered: a noiseless setting and a noisy one. The main contributions of this paper are direct part theorems that give conditions for the existence of an estimator achieving arbitrary small estimation error probability. The direct part theorems are proved by averaging an upper bound on estimation error probability of the typical set estimator over an (l,r, n)-regular pooling graph ensemble. Numerical results indicate sharp threshold behaviors in the asymptotic regime.
1301.7542
An Analysis on Minimum s-t Cut Capacity of Random Graphs with Specified Degree Distribution
cs.IT math.IT
The capacity (or maximum flow) of an unicast network is known to be equal to the minimum s-t cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or unknown, it is not so trivial to predict statistical properties on the maximum flow of the network. In this paper, we present a probabilistic analysis for evaluating the accumulate distribution of the minimum s-t cut capacity on random graphs. The graph ensemble treated in this paper consists of weighted graphs with arbitrary specified degree distribution. The main contribution of our work is a lower bound for the accumulate distribution of the minimum s-t cut capacity. From some computer experiments, it is observed that the lower bound derived here reflects the actual statistical behavior of the minimum s-t cut capacity of random graphs with specified degrees.
1301.7564
Multiset Codes for Permutation Channels
cs.IT math.IT
This paper introduces the notion of multiset codes as relevant to the problem of reliable information transmission over permutation channels. The motivation for studying permutation channels comes from the effect of out of order delivery of packets in some types of packet networks. The proposed codes are a generalization of the so-called subset codes, recently proposed by the authors. Some of the basic properties of multiset codes are established, among which their equivalence to integer codes under the Manhattan metric. The presented coding-theoretic framework follows closely the one proposed by Koetter and Kschischang for the operator channels. The two mathematical models are similar in many respects, and the basic idea is presented in a way which admits a unified view on coding for these types of channels.
1301.7566
On the Capacity of Special Classes of Gaussian Relay Networks with Orthogonal Components and Noncausal State Information at Source
cs.IT math.IT
In this paper, we study relay networks with orthogonal components in presence of noncausal channel state information (CSI) available at the source. We propose an upper bound on the capacity of the discrete memoryless model (DM)for the case in which just the source component intended for the destination is encoded against the CSI known non-causally at the source. Also, we derive capacity for two special classes of the Gaussian structure of the model. The first class is the one for which we have obtained the upper bound and the second class is the one in which all of the source components intended for the relays and destination are encoded against the noncausal CSI, however, no interference at the relays and destination exists in this case.
1301.7592
Paradoxes in Social Networks with Multiple Products
cs.GT cs.SI
Recently, we introduced in arXiv:1105.2434 a model for product adoption in social networks with multiple products, where the agents, influenced by their neighbours, can adopt one out of several alternatives. We identify and analyze here four types of paradoxes that can arise in these networks. To this end, we use social network games that we recently introduced in arxiv:1202.2209. These paradoxes shed light on possible inefficiencies arising when one modifies the sets of products available to the agents forming a social network. One of the paradoxes corresponds to the well-known Braess paradox in congestion games and shows that by adding more choices to a node, the network may end up in a situation that is worse for everybody. We exhibit a dual version of this, where removing available choices from someone can eventually make everybody better off. The other paradoxes that we identify show that by adding or removing a product from the choice set of some node may lead to permanent instability. Finally, we also identify conditions under which some of these paradoxes cannot arise.
1301.7619
Rank regularization and Bayesian inference for tensor completion and extrapolation
cs.IT cs.LG math.IT stat.ML
A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and prediction capabilities. This probabilistic approach can naturally accommodate general models for the data distribution, lending itself to various fitting criteria that yield optimum estimates in the maximum-a-posteriori sense. In particular, two algorithms are devised for Gaussian- and Poisson-distributed data, that minimize the rank-regularized least-squares error and Kullback-Leibler divergence, respectively. The proposed technique is able to recover the "ground-truth'' tensor rank when tested on synthetic data, and to complete brain imaging and yeast gene expression datasets with 50% and 15% of missing entries respectively, resulting in recovery errors at -10dB and -15dB.
1301.7627
Load curve data cleansing and imputation via sparsity and low rank
math.OC cs.IT cs.SY math.IT
The smart grid vision is to build an intelligent power network with an unprecedented level of situational awareness and controllability over its services and infrastructure. This paper advocates statistical inference methods to robustify power monitoring tasks against the outlier effects owing to faulty readings and malicious attacks, as well as against missing data due to privacy concerns and communication errors. In this context, a novel load cleansing and imputation scheme is developed leveraging the low intrinsic-dimensionality of spatiotemporal load profiles and the sparse nature of "bad data.'' A robust estimator based on principal components pursuit (PCP) is adopted, which effects a twofold sparsity-promoting regularization through an $\ell_1$-norm of the outliers, and the nuclear norm of the nominal load profiles. Upon recasting the non-separable nuclear norm into a form amenable to decentralized optimization, a distributed (D-) PCP algorithm is developed to carry out the imputation and cleansing tasks using networked devices comprising the so-termed advanced metering infrastructure. If D-PCP converges and a qualification inequality is satisfied, the novel distributed estimator provably attains the performance of its centralized PCP counterpart, which has access to all networkwide data. Computer simulations and tests with real load curve data corroborate the convergence and effectiveness of the novel D-PCP algorithm.
1301.7630
An Extended Fano's Inequality for the Finite Blocklength Coding
cs.IT math.IT
Fano's inequality reveals the relation between the conditional entropy and the probability of error . It has been the key tool in proving the converse of coding theorems in the past sixty years. In this paper, an extended Fano's inequality is proposed, which is tighter and more applicable for codings in the finite blocklength regime. Lower bounds on the mutual information and an upper bound on the codebook size are also given, which are shown to be tighter than the original Fano's inequality. Especially, the extended Fano's inequality is tight for some symmetric channels such as the $q$-ary symmetric channels (QSC).
1301.7641
Multi-scale Discriminant Saliency with Wavelet-based Hidden Markov Tree Modelling
cs.CV
The bottom-up saliency, an early stage of humans' visual attention, can be considered as a binary classification problem between centre and surround classes. Discriminant power of features for the classification is measured as mutual information between distributions of image features and corresponding classes . As the estimated discrepancy very much depends on considered scale level, multi-scale structure and discriminant power are integrated by employing discrete wavelet features and Hidden Markov Tree (HMT). With wavelet coefficients and Hidden Markov Tree parameters, quad-tree like label structures are constructed and utilized in maximum a posterior probability (MAP) of hidden class variables at corresponding dyadic sub-squares. Then, a saliency value for each square block at each scale level is computed with discriminant power principle. Finally, across multiple scales is integrated the final saliency map by an information maximization rule. Both standard quantitative tools such as NSS, LCC, AUC and qualitative assessments are used for evaluating the proposed multi-scale discriminant saliency (MDIS) method against the well-know information based approach AIM on its released image collection with eye-tracking data. Simulation results are presented and analysed to verify the validity of MDIS as well as point out its limitation for further research direction.
1301.7657
Energy-Efficient Power Allocation in OFDM Systems with Wireless Information and Power Transfer
cs.IT math.IT
This paper considers an orthogonal frequency division multiplexing (OFDM) downlink point-to-point system with simultaneous wireless information and power transfer. It is assumed that the receiver is able to harvest energy from noise, interference, and the desired signals. We study the design of power allocation algorithms maximizing the energy efficiency of data transmission (bit/Joule delivered to the receiver). In particular, the algorithm design is formulated as a high-dimensional non-convex optimization problem which takes into account the circuit power consumption, the minimum required data rate, and a constraint on the minimum power delivered to the receiver. Subsequently, by exploiting the properties of nonlinear fractional programming, the considered non-convex optimization problem, whose objective function is in fractional form, is transformed into an equivalent optimization problem having an objective function in subtractive form, which enables the derivation of an efficient iterative power allocation algorithm. In each iteration, the optimal power allocation solution is derived based on dual decomposition and a one-dimensional search. Simulation results illustrate that the proposed iterative power allocation algorithm converges to the optimal solution, and unveil the trade-off between energy efficiency, system capacity, and wireless power transfer: (1) In the low transmit power regime, maximizing the system capacity may maximize the energy efficiency. (2) Wireless power transfer can enhance the energy efficiency, especially in the interference limited regime.
1301.7661
Fast non parametric entropy estimation for spatial-temporal saliency method
cs.CV
This paper formulates bottom-up visual saliency as center surround conditional entropy and presents a fast and efficient technique for the computation of such a saliency map. It is shown that the new saliency formulation is consistent with self-information based saliency, decision-theoretic saliency and Bayesian definition of surprises but also faces the same significant computational challenge of estimating probability density in very high dimensional spaces with limited samples. We have developed a fast and efficient nonparametric method to make the practical implementation of these types of saliency maps possible. By aligning pixels from the center and surround regions and treating their location coordinates as random variables, we use a k-d partitioning method to efficiently estimating the center surround conditional entropy. We present experimental results on two publicly available eye tracking still image databases and show that the new technique is competitive with state of the art bottom-up saliency computational methods. We have also extended the technique to compute spatiotemporal visual saliency of video and evaluate the bottom-up spatiotemporal saliency against eye tracking data on a video taken onboard a moving vehicle with the driver's eye being tracked by a head mounted eye-tracker.
1301.7664
Approximate Optimal Trajectory Tracking for Continuous Time Nonlinear Systems
cs.SY math.OC
Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has remained a non-trivial open problem. The control development in this paper guarantees ultimately bounded tracking of a desired trajectory, while also ensuring that the controller converges to an approximate optimal policy.
1301.7669
Extending the logical update view with transaction support
cs.PL cs.DB
Since the database update view was standardised in the Prolog ISO standard, the so called logical update view is available in all actively maintained Prolog systems. While this update view provided a well defined update semantics and allows for efficient handling of dynamic code, it does not help in maintaining consistency of the dynamic database. With the introduction of multiple threads and deployment of Prolog in continuously running server applications, consistency of the dynamic database becomes important. In this article, we propose an extension to the generation-based implementation of the logical update view that supports transactions. Generation-based transactions have been implemented according to this description in the SWI-Prolog RDF store. The aim of this paper is to motivate transactions, outline an implementation and generate discussion on the desirable semantics and interface prior to implementation.
1301.7673
Toward a Dynamic Programming Solution for the 4-peg Tower of Hanoi Problem with Configurations
cs.PL cs.AI
The Frame-Stewart algorithm for the 4-peg variant of the Tower of Hanoi, introduced in 1941, partitions disks into intermediate towers before moving the remaining disks to their destination. Algorithms that partition the disks have not been proven to be optimal, although they have been verified for up to 30 disks. This paper presents a dynamic programming approach to this algorithm, using tabling in B-Prolog. This study uses a variation of the problem, involving configurations of disks, in order to contrast the tabling approach with the approaches utilized by other solvers. A comparison of different partitioning locations for the Frame-Stewart algorithm indicates that, although certain partitions are optimal for the classic problem, they need to be modified for certain configurations, and that random configurations might require an entirely new algorithm.
1301.7676
Efficient Partial Order CDCL Using Assertion Level Choice Heuristics
cs.AI cs.LO
We previously designed Partial Order Conflict Driven Clause Learning (PO-CDCL), a variation of the satisfiability solving CDCL algorithm with a partial order on decision levels, and showed that it can speed up the solving on problems with a high independence between decision levels. In this paper, we more thoroughly analyze the reasons of the efficiency of PO-CDCL. Of particular importance is that the partial order introduces several candidates for the assertion level. By evaluating different heuristics for this choice, we show that the assertion level selection has an important impact on solving and that a carefully designed heuristic can significantly improve performances on relevant benchmarks.
1301.7693
Optimal Locally Repairable Codes and Connections to Matroid Theory
cs.IT math.IT
Petabyte-scale distributed storage systems are currently transitioning to erasure codes to achieve higher storage efficiency. Classical codes like Reed-Solomon are highly sub-optimal for distributed environments due to their high overhead in single-failure events. Locally Repairable Codes (LRCs) form a new family of codes that are repair efficient. In particular, LRCs minimize the number of nodes participating in single node repairs during which they generate small network traffic. Two large-scale distributed storage systems have already implemented different types of LRCs: Windows Azure Storage and the Hadoop Distributed File System RAID used by Facebook. The fundamental bounds for LRCs, namely the best possible distance for a given code locality, were recently discovered, but few explicit constructions exist. In this work, we present an explicit and optimal LRCs that are simple to construct. Our construction is based on grouping Reed-Solomon (RS) coded symbols to obtain RS coded symbols over a larger finite field. We then partition these RS symbols in small groups, and re-encode them using a simple local code that offers low repair locality. For the analysis of the optimality of the code, we derive a new result on the matroid represented by the code generator matrix.
1301.7724
Axiomatic Construction of Hierarchical Clustering in Asymmetric Networks
cs.LG cs.SI stat.ML
This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a connectivity parameter, induced by the given dissimilarity structures. Our construction of hierarchical clustering methods is based on defining admissible methods to be those methods that abide by the axioms of value - nodes in a network with two nodes are clustered together at the maximum of the two dissimilarities between them - and transformation - when dissimilarities are reduced, the network may become more clustered but not less. Several admissible methods are constructed and two particular methods, termed reciprocal and nonreciprocal clustering, are shown to provide upper and lower bounds in the space of admissible methods. Alternative clustering methodologies and axioms are further considered. Allowing the outcome of hierarchical clustering to be asymmetric, so that it matches the asymmetry of the original data, leads to the inception of quasi-clustering methods. The existence of a unique quasi-clustering method is shown. Allowing clustering in a two-node network to proceed at the minimum of the two dissimilarities generates an alternative axiomatic construction. There is a unique clustering method in this case too. The paper also develops algorithms for the computation of hierarchical clusters using matrix powers on a min-max dioid algebra and studies the stability of the methods proposed. We proved that most of the methods introduced in this paper are such that similar networks yield similar hierarchical clustering results. Algorithms are exemplified through their application to networks describing internal migration within states of the United States (U.S.) and the interrelation between sectors of the U.S. economy.
1301.7738
PyPLN: a Distributed Platform for Natural Language Processing
cs.CL cs.IR
This paper presents a distributed platform for Natural Language Processing called PyPLN. PyPLN leverages a vast array of NLP and text processing open source tools, managing the distribution of the workload on a variety of configurations: from a single server to a cluster of linux servers. PyPLN is developed using Python 2.7.3 but makes it very easy to incorporate other softwares for specific tasks as long as a linux version is available. PyPLN facilitates analyses both at document and corpus level, simplifying management and publication of corpora and analytical results through an easy to use web interface. In the current (beta) release, it supports English and Portuguese languages with support to other languages planned for future releases. To support the Portuguese language PyPLN uses the PALAVRAS parser\citep{Bick2000}. Currently PyPLN offers the following features: Text extraction with encoding normalization (to UTF-8), part-of-speech tagging, token frequency, semantic annotation, n-gram extraction, word and sentence repertoire, and full-text search across corpora. The platform is licensed as GPL-v3.
1302.0017
Adaptive Control of Scalar Plants in the Presence of Unmodeled Dynamics
cs.SY math.OC
Robust adaptive control of scalar plants in the presence of unmodeled dynamics is established in this paper. It is shown that implementation of a projection algorithm with standard adaptive control of a scalar plant ensures global boundedness of the overall adaptive system for a class of unmodeled dynamics.
1302.0019
Fixed-to-Variable Length Distribution Matching
cs.IT math.IT
Fixed-to-variable length (f2v) matchers are used to reversibly transform an input sequence of independent and uniformly distributed bits into an output sequence of bits that are (approximately) independent and distributed according to a target distribution. The degree of approximation is measured by the informational divergence between the output distribution and the target distribution. An algorithm is developed that efficiently finds optimal f2v codes. It is shown that by encoding the input bits blockwise, the informational divergence per bit approaches zero as the block length approaches infinity. A relation to data compression by Tunstall coding is established.
1302.0033
On extremal self-dual codes of length 120
cs.IT math.IT
We prove that the only primes which may divide the order of the automorphism group of a putative binary self-dual doubly-even [120, 60, 24] code are 2, 3, 5, 7, 19, 23 and 29. Furthermore we prove that automorphisms of prime order $p \geq 5$ have a unique cycle structure.
1302.0050
Universal Wyner-Ziv Coding for Distortion Constrained General Side-Information
cs.IT math.IT
We investigate the Wyner-Ziv coding in which the statistics of the principal source is known but the statistics of the channel generating the side-information is unknown except that it is in a certain class. The class consists of channels such that the distortion between the principal source and the side-information is smaller than a threshold, but channels may be neither stationary nor ergodic. In this situation, we define a new rate-distortion function as the minimum rate such that there exists a Wyner-Ziv code that is universal for every channel in the class. Then, we show an upper bound and a lower bound on the rate-distortion function, and derive a matching condition such that the upper and lower bounds coincide. The relation between the new rate-distortion function and the rate-distortion function of the Heegard-Berger problem is also discussed.
1302.0059
A coding approach to guarantee information integrity against a Byzantine relay
cs.IT math.IT
This paper presents a random coding scheme with which two nodes can exchange information with guaranteed integrity over a two-way Byzantine relay. This coding scheme is employed to obtain an inner bound on the capacity region with guaranteed information integrity. No pre-shared secret or secret transmission is needed for the proposed scheme. Hence the inner bound obtained is generally larger than those achieved based on secret transmission schemes. This approach advocates the separation of supporting information integrity and secrecy.
1302.0070
Towards the full information chain theory: solution methods for optimal information acquisition problem
physics.data-an cs.IT math.IT
When additional information sources are available in decision making problems that allow stochastic optimization formulations, an important question is how to optimally use the information the sources are capable of providing. A framework that relates information accuracy determined by the source's knowledge structure to its relevance determined by the problem being solved was proposed in a companion paper. There, the problem of optimal information acquisition was formulated as that of minimization of the expected loss of the solution subject to constraints dictated by the information source knowledge structure and depth. Approximate solution methods for this problem are developed making use of probability metrics method and its application for scenario reduction in stochastic optimization.
1302.0077
Sparse MRI for motion correction
cs.CV physics.bio-ph physics.med-ph
MR image sparsity/compressibility has been widely exploited for imaging acceleration with the development of compressed sensing. A sparsity-based approach to rigid-body motion correction is presented for the first time in this paper. A motion is sought after such that the compensated MR image is maximally sparse/compressible among the infinite candidates. Iterative algorithms are proposed that jointly estimate the motion and the image content. The proposed method has a lot of merits, such as no need of additional data and loose requirement for the sampling sequence. Promising results are presented to demonstrate its performance.
1302.0081
Robust Compressive Phase Retrieval via L1 Minimization With Application to Image Reconstruction
physics.comp-ph cs.IT math.IT math.OC
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to reduce the required number of measurements, known as compressive phase retrieval (CPR). In this paper, l1 minimization problems are formulated for CPR to exploit the signal sparsity and alternating direction algorithms are presented for problem solving. For real-valued, nonnegative image reconstruction, the image of interest is shown to be an optimal solution of the formulated l1 minimization in the noise free case. Numerical simulations demonstrate that the proposed approach is fast, accurate and robust to measurements noises.
1302.0082
Distribution-Free Distribution Regression
stat.ML cs.LG math.ST stat.TH
`Distribution regression' refers to the situation where a response Y depends on a covariate P where P is a probability distribution. The model is Y=f(P) + mu where f is an unknown regression function and mu is a random error. Typically, we do not observe P directly, but rather, we observe a sample from P. In this paper we develop theory and methods for distribution-free versions of distribution regression. This means that we do not make distributional assumptions about the error term mu and covariate P. We prove that when the effective dimension is small enough (as measured by the doubling dimension), then the excess prediction risk converges to zero with a polynomial rate.
1302.0084
Peak-to-average power ratio of good codes for Gaussian channel
cs.IT math.IT
Consider a problem of forward error-correction for the additive white Gaussian noise (AWGN) channel. For finite blocklength codes the backoff from the channel capacity is inversely proportional to the square root of the blocklength. In this paper it is shown that codes achieving this tradeoff must necessarily have peak-to-average power ratio (PAPR) proportional to logarithm of the blocklength. This is extended to codes approaching capacity slower, and to PAPR measured at the output of an OFDM modulator. As a by-product the convergence of (Smith's) amplitude-constrained AWGN capacity to Shannon's classical formula is characterized in the regime of large amplitudes. This converse-type result builds upon recent contributions in the study of empirical output distributions of good channel codes.
1302.0103
A Survey on Array Storage, Query Languages, and Systems
cs.DB
Since scientific investigation is one of the most important providers of massive amounts of ordered data, there is a renewed interest in array data processing in the context of Big Data. To the best of our knowledge, a unified resource that summarizes and analyzes array processing research over its long existence is currently missing. In this survey, we provide a guide for past, present, and future research in array processing. The survey is organized along three main topics. Array storage discusses all the aspects related to array partitioning into chunks. The identification of a reduced set of array operators to form the foundation for an array query language is analyzed across multiple such proposals. Lastly, we survey real systems for array processing. The result is a thorough survey on array data storage and processing that should be consulted by anyone interested in this research topic, independent of experience level. The survey is not complete though. We greatly appreciate pointers towards any work we might have forgotten to mention.
1302.0126
Proceedings of the 12th International Colloquium on Implementation of Constraint and LOgic Programming Systems
cs.PL cs.AI
This volume contains the papers presented at CICLOPS'12: 12th International Colloquium on Implementation of Constraint and LOgic Programming Systems held on Tueseday September 4th, 2012 in Budapest. The program included 1 invited talk, 9 technical presentations and a panel discussion on Prolog open standards (open.pl). Each programme paper was reviewed by 3 reviewers. CICLOPS'12 continues a tradition of successful workshops on Implementations of Logic Programming Systems, previously held in Budapest (1993) and Ithaca (1994), the Compulog Net workshops on Parallelism and Implementation Technologies held in Madrid (1993 and 1994), Utrecht (1995) and Bonn (1996), the Workshop on Parallelism and Implementation Technology for (Constraint) Logic Programming Languages held in Port Jefferson (1997), Manchester (1998), Las Cruces (1999), and London (2000), and more recently the Colloquium on Implementation of Constraint and LOgic Programming Systems in Paphos (2001), Copenhagen (2002), Mumbai (2003), Saint Malo (2004), Sitges (2005), Seattle (2006), Porto (2007), Udine (2008), Pasadena (2009), Edinburgh (2010) - together with WLPE, Lexington (2011). We would like to thank all the authors, Tom Schrijvers for his invited talk, the programme committee members, and the ICLP 2012 organisers. We would like to also thank arXiv.org for providing permanent hosting.
1302.0164
Aperiodic dynamics in a deterministic model of attitude formation in social groups
physics.soc-ph cs.SI nlin.AO
Homophily and social influence are the fundamental mechanisms that drive the evolution of attitudes, beliefs and behaviour within social groups. Homophily relates the similarity between pairs of individuals' attitudinal states to their frequency of interaction, and hence structural tie strength, while social influence causes the convergence of individuals' states during interaction. Building on these basic elements, we propose a new mathematical modelling framework to describe the evolution of attitudes within a group of interacting agents. Specifically, our model describes sub-conscious attitudes that have an activator-inhibitor relationship. We consider a homogeneous population using a deterministic, continuous-time dynamical system. Surprisingly, the combined effects of homophily and social influence do not necessarily lead to group consensus or global monoculture. We observe that sub-group formation and polarisation-like effects may be transient, the long-time dynamics being quasi-periodic with sensitive dependence to initial conditions. This is due to the interplay between the evolving interaction network and Turing instability associated with the attitudinal state dynamics.
1302.0189
Non-adaptive pooling strategies for detection of rare faulty items
cs.IT cond-mat.stat-mech math.IT q-bio.GN q-bio.QM
We study non-adaptive pooling strategies for detection of rare faulty items. Given a binary sparse N-dimensional signal x, how to construct a sparse binary MxN pooling matrix F such that the signal can be reconstructed from the smallest possible number M of measurements y=Fx? We show that a very low number of measurements is possible for random spatially coupled design of pools F. Our design might find application in genetic screening or compressed genotyping. We show that our results are robust with respect to the uncertainty in the matrix F when some elements are mistaken.
1302.0212
PREMIER - PRobabilistic Error-correction using Markov Inference in Errored Reads
cs.IT math.IT
In this work we present a flexible, probabilistic and reference-free method of error correction for high throughput DNA sequencing data. The key is to exploit the high coverage of sequencing data and model short sequence outputs as independent realizations of a Hidden Markov Model (HMM). We pose the problem of error correction of reads as one of maximum likelihood sequence detection over this HMM. While time and memory considerations rule out an implementation of the optimal Baum-Welch algorithm (for parameter estimation) and the optimal Viterbi algorithm (for error correction), we propose low-complexity approximate versions of both. Specifically, we propose an approximate Viterbi and a sequential decoding based algorithm for the error correction. Our results show that when compared with Reptile, a state-of-the-art error correction method, our methods consistently achieve superior performances on both simulated and real data sets.
1302.0215
Informational Divergence Approximations to Product Distributions
cs.IT math.IT
The minimum rate needed to accurately approximate a product distribution based on an unnormalized informational divergence is shown to be a mutual information. This result subsumes results of Wyner on common information and Han-Verd\'{u} on resolvability. The result also extends to cases where the source distribution is unknown but the entropy is known.
1302.0216
Comparison between the two definitions of AI
cs.AI
Two different definitions of the Artificial Intelligence concept have been proposed in papers [1] and [2]. The first definition is informal. It says that any program that is cleverer than a human being, is acknowledged as Artificial Intelligence. The second definition is formal because it avoids reference to the concept of human being. The readers of papers [1] and [2] might be left with the impression that both definitions are equivalent and the definition in [2] is simply a formal version of that in [1]. This paper will compare both definitions of Artificial Intelligence and, hopefully, will bring a better understanding of the concept.
1302.0226
Plug-and-Play Decentralized Model Predictive Control
cs.SY
In this paper we consider a linear system structured into physically coupled subsystems and propose a decentralized control scheme capable to guarantee asymptotic stability and satisfaction of constraints on system inputs and states. The design procedure is totally decentralized, since the synthesis of a local controller uses only information on a subsystem and its neighbors, i.e. subsystems coupled to it. We first derive tests for checking if a subsystem can be plugged into (or unplugged from) an existing plant without spoiling overall stability and constraint satisfaction. When this is possible, we show how to automatize the design of local controllers so that it can be carried out in parallel by smart actuators equipped with computational resources and capable to exchange information with neighboring subsystems. In particular, local controllers exploit tube-based Model Predictive Control (MPC) in order to guarantee robustness with respect to physical coupling among subsystems. Finally, an application of the proposed control design procedure to frequency control in power networks is presented.
1302.0249
Bayesian Quadratic Network Game Filters
cs.SY cs.IT cs.SI math.IT
A repeated network game where agents have quadratic utilities that depend on information externalities -- an unknown underlying state -- as well as payoff externalities -- the actions of all other agents in the network -- is considered. Agents play Bayesian Nash Equilibrium strategies with respect to their beliefs on the state of the world and the actions of all other nodes in the network. These beliefs are refined over subsequent stages based on the observed actions of neighboring peers. This paper introduces the Quadratic Network Game (QNG) filter that agents can run locally to update their beliefs, select corresponding optimal actions, and eventually learn a sufficient statistic of the network's state. The QNG filter is demonstrated on a Cournot market competition game and a coordination game to implement navigation of an autonomous team.
1302.0250
Elections, Protest, and Alternation of Power
physics.soc-ph cs.GT cs.SI math.PR
Despite many examples to the contrary, most models of elections assume that rules determining the winner will be followed. We present a model where elections are solely a public signal of the incumbent popularity, and citizens can protests against leaders that do not step down from power. In this minimal setup, rule-based alternation of power as well as "semi-democratic" alternation of power independent of electoral rules can both arise in equilibrium. Compliance with electoral rules requires there to be multiple equilibria in the protest game, where the electoral rule serves as a focal point spurring protest against losers that do not step down voluntarily. Such multiplicity is possible when elections are informative and citizens not too polarized. Extensions to the model are consistent with the facts that protests often center around accusations of electoral fraud and that in the democratic case turnover is peaceful while semi-democratic turnover often requires citizens to actually take to the streets.
1302.0265
Compound Polar Codes
cs.IT math.IT
A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar codes and then discuss our proposed scheme. Instead of encoding separately across the individual underlying channels, which requires multiple encoders and decoders, we take advantage of the recursive structure of polar codes to construct a unified scheme with a single encoder and decoder that can be used over the multi-channels. We prove that the scheme achieves the capacity over this multi-channel. Numerical analysis and simulation results for BICM channels at finite block lengths shows a considerable improvement in the probability of error comparing to a conventional separated scheme.