New Complexity Results for MAP in Bayesian Networks

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. It is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure), which extends previous complexity results. Furthermore, a Fully Polynomial Time Approximation Scheme for MAP in networks with bounded treewidth and bounded number of states per variable is developed. Approximation schemes were thought to be impossible, but here it is shown otherwise under the assumptions just mentioned, which are adopted in most applications.

New Results for the MAP Problem in Bayesian Networks

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. First, it is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure). Such proofs extend previous complexity results for the problem. Inapproximability results are also derived in the case of trees if the number of states per variable is not bounded. Although the problem is shown to be hard and inapproximable even in very simple scenarios, a new exact algorithm is described that is empirically fast in networks of bounded treewidth and bounded number of states per variable. The same algorithm is used as basis of a Fully Polynomial Time Approximation Scheme for MAP under such assumptions. Approximation schemes were generally thought to be impossible for this problem, but we show otherwise for classes of networks that are important in practice. The algorithms are extensively tested using some well-known networks as well as random generated cases to show their effectiveness.

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.

Anytime Marginal MAP Inference

This paper presents a new anytime algorithm for the marginal MAP problem in graphical models of bounded treewidth. We show asymptotic convergence and theoretical error bounds for any fixed step. Experiments show that it compares well to a state-of-the-art systematic search algorithm.

Deriving meteorological variables across Africa for the study and control of vector-borne disease:a comparison of remote sensing and spatial interpolation of climate

This paper presents the results of an investigation into the utility of remote sensing (RS) using meteorological satellites sensors and spatial interpolation (SI) of data from meteorological stations, for the prediction of spatial variation in monthly climate across continental Africa in 1990. Information from the Advanced Very High Resolution Radiometer (AVHRR) of the National Oceanic and Atmospheric Administration's (NOAA) polar-orbiting meteorological satellites was used to estimate land surface temperature (LST) and atmospheric moisture. Cold cloud duration (CCD) data derived from the High Resolution Radiometer (HRR) onboard the European Meteorological Satellite programme's (EUMETSAT) Meteosat satellite series were also used as a RS proxy measurement of rainfall. Temperature, atmospheric moisture and rainfall surfaces were independently derived from SI of measurements from the World Meteorological Organization (WMO) member stations of Africa. These meteorological station data were then used to test the accuracy of each methodology, so that the appropriateness of the two techniques for epidemiological research could be compared. SI was a more accurate predictor of temperature, whereas RS provided a better surrogate for rainfall; both were equally accurate at predicting atmospheric moisture. The implications of these results for mapping short and long-term climate change and hence their potential for the study anti control of disease vectors are considered. Taking into account logistic and analytical problems, there were no clear conclusions regarding the optimality of either technique, but there was considerable potential for synergy.

Physical map and cosmid contig encompassing a new interstitial deletion of the X-linked lymphoproliferative syndrome region

The X-linked lymphoproliferative syndrome (XLP) is an inherited immuno-deficiency to Epstein-Barr virus infection that has been mapped to chromosome Xq25. Molecular analysis of XLP patients from ten different families identified a small interstitial constitutional deletion in 1 patient (XLP-D). This deletion, initially defined by a single marker, DF83, known to map to interval Xq24-q26.1, is nested within a previously reported and much larger deletion in another XLP patient (XLP-739). A cosmid minilibrary was constructed from a single mega-YAC and used to establish a contig encompassing the whole XLP-D deletion and a portion of the XLP-739 deletion. Based on this contig, the size of the XLP-D deletion can be estimated at 130 kb. The identification of this minimal deletion, within which at least a portion of the XLP gene is likely to reside, should greatly facilitate efforts in isolating the gene.

An Investigation of Compressor Map Width Enhancement and the Inducer Flow Field Using Various Configurations of Shroud Bleed Slot

This paper describes an investigation of various shroud bleed slot configurations of a centrifugal compressor using CFD with a manual multi-block structured grid generation method. The compressor under investigation is used in a turbocharger application for a heavy duty diesel engine of approximately 400hp. The baseline numerical model has been developed and validated against experimental performance measurements. The influence of the bleed slot flow field on a range of operating conditions between surge and choke has been analysed in detail. The impact of the returning bleed flow on the incidence at the impeller blade leading edge due to its mixing with the main through-flow has also been studied. From the baseline geometry, a number of modifications to the bleed slot width have been proposed, and a detailed comparison of the flow characteristics performed. The impact of slot variations on the inlet incidence angle has been investigated, highlighting the improvement in surge and choked flow capability. Along with this, the influence of the bleed slot on stabilizing the blade passage flow by the suction of the tip and over-tip vortex flow by the slot has been considered near surge.

A Case Study of OpenMP applied to Map/Reduce-style Computations

As data analytics are growing in importance they are also quickly becoming one of the dominant application domains that require parallel processing. This paper investigates the applicability of OpenMP, the dominant shared-memory parallel programming model in high-performance computing, to the domain of data analytics. We contrast the performance and programmability of key data analytics benchmarks against Phoenix++, a state-of-the-art shared memory map/reduce programming system. Our study shows that OpenMP outperforms the Phoenix++ system by a large margin for several benchmarks. In other cases, however, the programming model is lacking support for this application domain.

The single component geochemical map: Fact or fiction?

Single component geochemical maps are the most basic representation of spatial elemental distributions and commonly used in environmental and exploration geochemistry. However, the compositional nature of geochemical data imposes several limitations on how the data should be presented. The problems relate to the constant sum problem (closure), and the inherently multivariate relative information conveyed by compositional data. Well known is, for instance, the tendency of all heavy metals to show lower values in soils with significant contributions of diluting elements (e.g., the quartz dilution effect); or the contrary effect, apparent enrichment in many elements due to removal of potassium during weathering. The validity of classical single component maps is thus investigated, and reasonable alternatives that honour the compositional character of geochemical concentrations are presented. The first recommended such method relies on knowledge-driven log-ratios, chosen to highlight certain geochemical relations or to filter known artefacts (e.g. dilution with SiO2 or volatiles). This is similar to the classical normalisation approach to a single element. The second approach uses the (so called) log-contrasts, that employ suitable statistical methods (such as classification techniques, regression analysis, principal component analysis, clustering of variables, etc.) to extract potentially interesting geochemical summaries. The caution from this work is that if a compositional approach is not used, it becomes difficult to guarantee that any identified pattern, trend or anomaly is not an artefact of the constant sum constraint. In summary the authors recommend a chain of enquiry that involves searching for the appropriate statistical method that can answer the required geological or geochemical question whilst maintaining the integrity of the compositional nature of the data. The required log-ratio transformations should be applied followed by the chosen statistical method. Interpreting the results may require a closer working relationship between statisticians, data analysts and geochemists.

What defines a geochemical map? Implications for environmental assessment.

The environmental quality of land is often assessed by the calculation of threshold values which aim to differentiate between concentrations of elements based on whether the soils are in residential or industrial sites. In Europe, for example, soil guideline values exist for agricultural and grazing land. A threshold is often set to differentiate between concentrations of the element that naturally occur in the soil and concentrations that result from diffuse anthropogenic sources. Regional geochemistry and, in particular, single component geochemical maps are increasingly being used to determine these baseline environmental assessments. The key question raised in this paper is whether the geochemical map can provide an accurate interpretation on its own. Implicit is the thought that single component geochemical maps represent absolute abundances. However,because of the compositional (closed) nature of the data univariate geochemical maps cannot be compared directly with one another.. As a result, any interpretation based on them is vulnerable to spurious correlation problems. What does this mean for soil geochemistry mapping, baseline quality documentation, soil resource assessment or risk evaluation? Despite the limitation of relative abundances, individual raw geochemical maps are deemed fundamental to several applications of geochemical maps including environmental assessments. However, element toxicity is related to its bioavailable concentration, which is lowered if its source is mixed with another source. Elements interact, for example under reducing conditions with iron oxides, its solid state is lost and arsenic becomes soluble and mobile. Both of these matters may be more adequately dealt with if a single component map is not interpreted in isolation to determine baseline and threshold assessments. A range of alternative compositionally compliant representations based on log-ratio and log-contrast approaches are explored to supplement the classical single component maps for environmental assessment. Case study examples are shown based on the Tellus soil geochemical dataset, covering Northern Ireland and the results of in vitro oral bioaccessibility testing carried out on a sub-set of archived Tellus Survey shallow soils following the Unified BARGE (Bioaccessibility Research Group of Europe).

The Complexity of MAP Inference in Bayesian Networks Specified Through Logical Languages

We study the computational complexity of finding maximum a posteriori configurations in Bayesian networks whose probabilities are specified by logical formulas. This approach leads to a fine grained study in which local information such as context-sensitive independence and determinism can be considered. It also allows us to characterize more precisely the jump from tractability to NP-hardness and beyond, and to consider the complexity introduced by evidence alone.

Praying for Salvation: A Map of Relatedness

This article attempts to push Mauss’ work on the sociality of prayer (1909) to its fullest conclusion by arguing that prayer can be viewed anthropologically as providing a map for social and emotional relatedness. Based on fieldwork among deep-sea fisher families living in Gamrie, North-East Scotland (home to 700 people and six Protestant churches), the author takes as his primary ethnographic departure the ritual of the ‘mid-week prayer meeting’. Among the self-proclaimed ‘fundamentalists’ of Gamrie’s Brethren and Presbyterian churches, attending the prayer meeting means praying for salvation. Yet, contrary to the stereotype of Protestant soteriology as highly individualist, in the context of Gamrie, salvation is not principally focused upon the self, but is instead sought on behalf of the ‘unconverted’ other. Locally, this ‘other’ is made sense of with reference to three different categories of relatedness: the family, the village and the nation. The author’s argument is that each category of relatedness carries with it a different affective quality: anguish for one’s family, resentment toward one’s village, and resignation towards one’s nation. As such, prayers for salvation establish and maintain not only vertical – human-divine – relatedness, but also horizontal relatedness between persons, while also giving them their emotional tenor. In ‘fundamentalist’ Gamrie, these human relationships, and crucially their affective asymmetries, may be mapped, therefore, by treating prayers as social phenomena that seek to engage with a world dichotomised into vice and virtue, rebellion and submission, and, ultimately, damnation and salvation.