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Data Mining Practical Machine Learning Tools and Techniques

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Though research on the Semantic Web has progressed at a steady pace, its promise has yet to be realized. One major difficulty is that, by its very nature, the Semantic Web is a large, uncensored system to which anyone may contribute. This raises the question of how much credence to give each source. We cannot expect each user to know the trustworthiness of each source, nor would we want to assign top-down or global credibility values due to the subjective nature of trust. We tackle this problem by employing a web of trust, in which each user maintains trusts in a small number of other users. We then compose these trusts into trust values for all other users. The result of our computation is not an agglomerate "trustworthiness" of each user. Instead, each user receives a personalized set of trusts, which may vary widely from person to person. We define properties for combination functions which merge such trusts, and define a class of functions for which merging may be done locally while maintaining these properties. We give examples of specific functions and apply them to data from Epinions and our BibServ bibliography server. Experiments confirm that the methods are robust to noise, and do not put unreasonable expectations on users. We hope that these methods will help move the Semantic Web closer to fulfilling its promise.

Trust management for the Semantic Web

Buildings are among the largest consumers of electricity in the US. A significant portion of this energy use in buildings can be attributed to HVAC systems used to maintain comfort for occupants. In most cases these building HVAC systems run on fixed schedules and do not employ any fine grained control based on detailed occupancy information. In this paper we present the design and implementation of a presence sensor platform that can be used for accurate occupancy detection at the level of individual offices. Our presence sensor is low-cost, wireless, and incrementally deployable within existing buildings. Using a pilot deployment of our system across ten offices over a two week period we identify significant opportunities for energy savings due to periods of vacancy. Our energy measurements show that our presence node has an estimated battery lifetime of over five years, while detecting occupancy accurately. Furthermore, using a building simulation framework and the occupancy information from our testbed, we show potential energy savings from 10% to 15% using our system.

[ACM Press the 2nd ACM Workshop - Zurich, Switzerland (2010.11.02-2010.11.02)] Proceedings of the 2nd ACM Workshop on Embedded Sensing Systems for Energy-Efficiency in Building - BuildSys \'10 - Occupancy-driven energy management for smart building automation

Evaluating credal classifiers by utility-discounted predictive accuracy

We present a novel approach for multilabel classification based on an ensemble of Bayesian networks. The class variables are connected by a tree; each model of the ensemble uses a different class as root of the tree. We assume the features to be conditionally independent given the classes, thus generalizing the naive Bayes assumption to the multi-class case. This assumption allows us to optimally identify the correlations between classes and features; such correlations are moreover shared across all models of the ensemble. Inferences are drawn from the ensemble via logarithmic opinion pooling. To minimize Hamming loss, we compute the marginal probability of the classes by running standard inference on each Bayesian network in the ensemble, and then pooling the inferences. To instead minimize the subset 0/1 loss, we pool the joint distributions of each model and cast the problem as a MAP inference in the corresponding graphical model. Experiments show that the approach is competitive with state-of-the-art methods for multilabel classification.

An ensemble of Bayesian networks for multilabel classification

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove a similar result for inference in naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and naive Bayes structures are used in real applications of imprecise probability.

/pdf/probabilistic-inference-in-credal-networks-new-complexity-qa9m2fz4os.pdf

Probabilistic inference in credal networks: new complexity results

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables and 1064 solutions. We show that these problems are NP-hard even if the underlying graph structure of the problem has low treewidth and the variables take on a bounded number of states, and that they admit no provably good approximation if variables can take on an arbitrary number of states.

/pdf/solving-limited-memory-influence-diagrams-40byv7pry8.pdf

Solving limited memory influence diagrams

This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sampling $k$-trees (maximal graphs of treewidth $k$), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that $k$-tree. Some properties of these methods are discussed and proven. The approaches are empirically compared to each other and to a state-of-the-art method for learning bounded treewidth structures on a collection of public data sets with up to 100 variables. The experiments show that our exact algorithm outperforms the state of the art, and that the approximate approach is fairly accurate.

Denis Deratani Mauá

Papers

Evaluating credal classifiers by utility-discounted predictive accuracy

An ensemble of Bayesian networks for multilabel classification

Probabilistic inference in credal networks: new complexity results

Solving limited memory influence diagrams

Advances in Learning Bayesian Networks of Bounded Treewidth