Extended Tree Augmented Naive Classifier

This work proposes an extended version of the well-known tree-augmented naive Bayes (TAN) classifier where the structure learning step is performed without requiring features to be connected to the class. Based on a modification of Edmonds’ algorithm, our structure learning procedure explores a superset of the structures that are considered by TAN, yet achieves global optimality of the learning score function in a very efficient way (quadratic in the number of features, the same complexity as learning TANs). A range of experiments show that we obtain models with better accuracy than TAN and comparable to the accuracy of the state-of-the-art classifier averaged one-dependence estimator.

A tree augmented classifier based on Extreme Imprecise Dirichlet Model

We present TANC, a TAN classifier (tree-augmented naive) based on imprecise probabilities. TANC models prior near-ignorance via the Extreme Imprecise Dirichlet Model (EDM). A first contribution of this paper is the experimental comparison between EDM and the global Imprecise Dirichlet Model using the naive credal classifier (NCC), with the aim of showing that EDM is a sensible approximation of the global IDM. TANC is able to deal with missing data in a conservative manner by considering all possible completions (without assuming them to be missing-at-random), but avoiding an exponential increase of the computational time. By experiments on real data sets, we show that TANC is more reliable than the Bayesian TAN and that it provides better performance compared to previous TANs based on imprecise probabilities. Yet, TANC is sometimes outperformed by NCC because the learned TAN structures are too complex; this calls for novel algorithms for learning the TAN structures, better suited for an imprecise probability classifier.

Bayesian network data imputation with application to survival tree analysis

Retrospective clinical datasets are often characterized by a relatively small sample size and many missing data. In this case, a common way for handling the missingness consists in discarding from the analysis patients with missing covariates, further reducing the sample size. Alternatively, if the mechanism that generated the missing allows, incomplete data can be imputed on the basis of the observed data, avoiding the reduction of the sample size and allowing methods to deal with complete data later on. Moreover, methodologies for data imputation might depend on the particular purpose and might achieve better results by considering specific characteristics of the domain. The problem of missing data treatment is studied in the context of survival tree analysis for the estimation of a prognostic patient stratification. Survival tree methods usually address this problem by using surrogate splits, that is, splitting rules that use other variables yielding similar results to the original ones. Instead, our methodology consists in modeling the dependencies among the clinical variables with a Bayesian network, which is then used to perform data imputation, thus allowing the survival tree to be applied on the completed dataset. The Bayesian network is directly learned from the incomplete data using a structural expectation–maximization (EM) procedure in which the maximization step is performed with an exact anytime method, so that the only source of approximation is due to the EM formulation itself. On both simulated and real data, our proposed methodology usually outperformed several existing methods for data imputation and the imputation so obtained improved the stratification estimated by the survival tree (especially with respect to using surrogate splits).

A Tree Augmented Classifier Based on Extreme Imprecise Dirichlet Model

In this paper we present TANC, i.e., a tree-augmented naive credal classifier based on imprecise probabilities; it models prior near-ignorance via the Extreme Imprecise Dirichlet Model (EDM) (Cano et al., 2007) and deals conservatively with missing data in the training set, without assuming them to be missing-at-random. The EDM is an approximation of the global Imprecise Dirichlet Model (IDM), which considerably simplifies the computation of upper and lower probabilities; yet, having been only recently introduced, the quality of the provided approximation needs still to be verified. As first contribution, we extensively compare the output of the naive credal classifier (one of the few cases in which the global IDM can be exactly implemented) when learned with the EDM and the global IDM; the output of the classifier appears to be identical in the vast majority of cases, thus supporting the adoption of the EDM in real classification problems. Then, by experiments we show that TANC is more reliable than the precise TAN (learned with uniform prior), and also that it provides better performance compared to a previous (Zaffalon, 2003) TAN model based on imprecise probabilities. TANC treats missing data by considering all possible completions of the training set, but avoiding an exponential increase of the computational times; eventually, we present some preliminary results with missing data.

NP-hardness of MAP in Ternary Tree Bayesian Networks

This paper strengthens the NP-hardness result for the (partial) maximum a posteriori (MAP) problem in Bayesian networks with topology of trees (every variable has at most one parent) and variable cardinality at most three. MAP is the problem of querying the most probable state configuration of some (not necessarily all) of the network variables given evidence. It is demonstrated that the problem remains hard even in such simplistic networks.

Design of an automated solar concentrator for the pyrolysis of scrap rubber

An automated solar reactor system was designed and built to carry out catalytic pyrolysis of scrap rubber tires at 550°C. To maximize solar energy concentration, a two degrees-of-freedom automated sun tracking system was developed and implemented. Both the azimuth and zenith angles were controlled via feedback from six photo-resistors positioned on a Fresnel lens. The pyrolysis of rubber tires was tested with the presence of two types of acidic catalysts, H-beta and H-USY. Additionally, a photoactive TiO<inf>2</inf> catalyst was used and the products were compared in terms of gas yields and composition. The catalysts were characterized by BET analysis and the pyrolysis gases and liquids were analyzed using GC-MS. The oil and gas yields were relatively high with the highest gas yield reaching 32.8% with H-beta catalyst while TiO<inf>2</inf> gave the same results as thermal pyrolysis without any catalyst. In the presence of zeolites, the dominant gasoline-like components in the gas were propene and cyclobutene. The TiO<inf>2</inf> and non-catalytic experiments produced a gas containing gasoline-like products of mainly isoprene (76.4% and 88.4% respectively). As for the liquids they were composed of numerous components spread over a wide distribution of C<inf>10</inf> to C<inf>29</inf> hydrocarbons of naphthalene and cyclohexane/ene derivatives.

Control of wild rubber extraction in the forests of northeast India, 1850-1880

This paper uses the history of rubber extraction to explore competing attempts to control the forest environments of Assam and beyond in the second half of the nineteenth century. Forest communities faced rival efforts at environmental control from both European and Indian traders, as well as from various centres of authority within the Raj. Government attempts to regulate rubber collection were undermined by the weak authority of the Raj in these regions, leading to widespread smuggling. Partly in response to the disruptive influence of rubber traders on the frontier, the Raj began to restrict the presence of outsiders in tribal regions, which came to be understood as distinct areas outside British control. When rubber yields from the forests nearest the Brahmaputra fell in the wake of intensive exploitation, India's scientific foresters demanded and from 1870 obtained the ability to regulate the Assamese forests, blaming indigenous rubber tapping strategies for the declining yields and arguing that Indian rubber could be ‘equal [to] if not better' than Amazonian rubber if only tappers would change their practices. The knowledge of the scientific foresters was fundamentally flawed, however, and their efforts to establish a new type of tapping practice failed. By 1880, the government had largely abandoned attempts to regulate wild Indian rubber, though wild sources continued to dominate the supply of global rubber until after 1910.

Averaged Extended Tree Augmented Naive Classifier

This work presents a new general purpose classifier named Averaged Extended Tree Augmented Naive Bayes (AETAN), which is based on combining the advantageous characteristics of Extended Tree Augmented Naive Bayes (ETAN) and Averaged One-Dependence Estimator (AODE) classifiers. We describe the main properties of the approach and algorithms for learning it, along with an analysis of its computational time complexity. Empirical results with numerous data sets indicate that the new approach is superior to ETAN and AODE in terms of both zero-one classification accuracy and log loss. It also compares favourably against weighted AODE and hidden Naive Bayes. The learning phase of the new approach is slower than that of its competitors, while the time complexity for the testing phase is similar. Such characteristics suggest that the new classifier is ideal in scenarios where online learning is not required.

Learning Extended Tree Augmented Naive Structures

This work proposes an extended version of the well-known tree-augmented naive Bayes (TAN) classifier where the structure learning step is performed without requiring features to be connected to the class. Based on a modification of Edmonds' algorithm, our structure learning procedure explores a superset of the structures that are considered by TAN, yet achieves global optimality of the learning score function in a very efficient way (quadratic in the number of features, the same complexity as learning TANs). We enhance our procedure with a new score function that only takes into account arcs that are relevant to predict the class, as well as an optimization over the equivalent sample size during learning. These ideas may be useful for structure learning of Bayesian networks in general. A range of experiments shows that we obtain models with better prediction accuracy than naive Bayes and TAN, and comparable to the accuracy of the state-of-the-art classifier averaged one-dependence estimator (AODE). We release our implementation of ETAN so that it can be easily installed and run within Weka.

Learning Bounded Tree-Width Bayesian Networks via Sampling

Learning Bayesian networks with bounded tree-width has attracted much attention recently, because low tree-width allows exact inference to be performed efficiently. Some existing methods [12, 14] tackle the problem by using k-trees to learn the optimal Bayesian network with tree-width up to k. In this paper, we propose a sampling method to efficiently find representative k-trees by introducing an Informative score function to characterize the quality of a k-tree. The proposed algorithm can efficiently learn a Bayesian network with tree-width at most k. Experiment results indicate that our approach is comparable with exact methods, but is much more computationally efficient.

Learning Bayesian Networks with Bounded Tree-Width via Guided Search

Bounding the tree-width of a Bayesian network can reduce the chance of overfitting, and allows exact inference to be performed efficiently. Several existing algorithms tackle the problem of learning bounded tree-width Bayesian networks by learning from k-trees as super-structures, but they do not scale to large domains and/or large tree-width. We propose a guided search algorithm to find k-trees with maximum Informative scores, which is a measure of quality for the k-tree in yielding good Bayesian networks. The algorithm achieves close to optimal performance compared to exact solutions in small domains, and can discover better networks than existing approximate methods can in large domains. It also provides an optimal elimination order of variables that guarantees small complexity for later runs of exact inference. Comparisons with well-known approaches in terms of learning and inference accuracy illustrate its capabilities.