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.

Business Intelligence and Multi-market Competition

We consider a multi-market framework where a set of firms compete on two oligopolistic markets. The cost of production of each firm allows for spillovers across markets, ensuring that output decisions for both markets have to be made jointly. Prior to competing in these markets, firms can establish links gathering business intelligence about other firms. A link formed by a firm generates two types of externalities for competitors and consumers. We characterize the business intelligence equilibrium networks and networks that maximize social welfare. By contrast with single market competition, we show that in multi-market competition there exist situations where intelligence gathering activities are underdeveloped with regard to social welfare and should be tolerated, if not encouraged, by public authorities.

Platform Competition as Network Contestability

Recent research in industrial organisation has investigated the essential place that middlemen have in the networks that make up our global economy. In this paper we attempt to understand how such middlemen compete with each other through a game theoretic analysis using novel techniques from decision-making under ambiguity.
We model a purposely abstract and reduced model of one middleman who provides a two-sided platform, mediating surplus-creating interactions between two users. The middleman evaluates uncertain outcomes under positional ambiguity, taking into account the possibility of the emergence of an alternative middleman offering intermediary services to the two users.
Surprisingly, we find many situations in which the middleman will purposely extract maximal gains from her position. Only if there is relatively low probability of devastating loss of business under competition, the middleman will adopt a more competitive attitude and extract less from her position.

Phosphorus nutrition of arsenate-tolerant and nontolerant phenotypes of velvetgrass

Velvetgrass (Holcus lanatus L.), also known as Yorkshire fog grass, has evolved tolerance to high levels of arsenate, and this adaptation involves reduced accumulation of arsenate through the suppression of the high affinity phosphate-arsenate uptake system. To determine the role of P nutrition in arsenate tolerance, inhibition kinetics of arsenate influx by phosphate were determined. The concentration of inhibitor required to reduce maximum influx (V(max)) by 50%, K₁, of phosphate inhibition of arsenate influx was 0.02 mol m^-3 in both tolerant and nontolerant clones. This was compared with the concentration where influx is 50% of maximum, a K(m), for arsenate influx of 0.6 mol m^-3 for tolerants and 0.025 mol m^-3 for nontolerants and, therefore, phosphate was much more effective at inhibiting arsenate influx in tolerant genotypes. The high affinity phosphate uptake system is inducible under low plant phosphate status, this increasing plant phosphate status should increase tolerance by decreasing arsenate influx. Root extension in arsenate solutions of tolerant and nontolerant tillers grown under differing phosphate nutritional regimes showed that indeed, increased plant P status increased the tolerance to arsenate of both tolerant and nontolerant clones. That plant P status increased tolerance again argues that P nutrition has a critical role in arsenate tolerance. To determine if short term flux and solution culture studies were relevant to As and P accumulation in soils, soil and plant material from a range of As contaminated sites were analyzed. As predicted from the short-term competition studies, P was accumulated preferentially to As in arsenate tolerant clones growing on mine spoil soils even when acid extractable arsenate in the soils was much greater than acid extractable phosphate. Though phosphate was much more efficient at competing with arsenate for uptake, plants growing on arsenate contaminated land still accumulated considerable amounts of As. Plants from the differing habitats showed large variation in plant phosphate status, pasture plants having much higher P levels than plants growing on the most contaminated mine spoil soils. The selectivity of the phosphate-arsenate uptake system for phosphate compared with arsenate, coupled with the suppression of this uptake system enabled tolerant clones of the grass velvetgrass to grow on soils that were highly contaminated with arsenate and deficient in phosphate.

Home-range size in juveniles of the temperate reef fish, the common triplefin (Forsterygion lapillum)

An organism’s home range dictates the spatial scale on which important processes occur (e.g. competition and predation) and directly affects the relationship between individual fitness and local habitat quality. Many reef fish species have very restricted home ranges after settlement and, here, we quantify home-range size in juveniles of a widespread and abundant reef fish in New Zealand, the common triplefin (Forsterygion lapillum). We conducted visual observations on 49 juveniles (mean size = 35-mm total length) within the Wellington harbour, New Zealand. Home ranges were extremely small, 0.053 m2 ± 0.029 (mean ± s.d.) and were unaffected by adult density, body size or substrate composition. A regression tree indicated that home-range size sharply decreased ~4.5 juveniles m–2 and a linear mixed model confirmed that home-range sizes in high-density areas (>4.5 juveniles m–2) were significantly smaller (34%) than those in low-density areas (after accounting for a significant effect of fish movement on our home-range estimates). Our results suggest that conspecific density may have negative and non-linear effects on home-range size, which could shape the spatial distribution of juveniles within a population, as well as influence individual fitness across local density gradients.