Storyline approach to the construction of regional climate change information

Climate science seeks to make statements of confidence about what has happened, and what will happen (conditional on scenario). The approach is effective for the global, thermodynamic aspects of climate change, but is ineffective when it comes to aspects of climate change related to atmospheric circulation, which are highly uncertain. Yet atmospheric circulation strongly mediates climate impacts at the regional scale. In this way the confidence framework, which focuses on avoiding Type 1 errors (false alarms), raises the prospect of committing Type 2 errors (missed warnings). This has ethical implications. At the regional scale, however, where information on climate change has to be combined with many other factors affecting vulnerability and exposure — most of which are highly uncertain — the societally relevant question is not “What will happen?” but rather “What is the impact of particular actions under an uncertain regional climate change?” This re-framing of the question can cut the Gordian Knot of regional climate-change information, provided one distinguishes between epistemic and aleatoric uncertainties — something that is generally not done in climate projections. It is argued that the storyline approach to climate change — the identification of physically self-consistent, plausible pathways — has the potential to accomplish precisely this

Bayesian optimization of the PC algorithm for learning Gaussian Bayesian networks

The PC algorithm is a popular method for learning the structure of Gaussian Bayesian networks. It carries out statistical tests to determine absent edges in the network. It is hence governed by two parameters: (i) The type of test, and (ii) its significance level. These parameters are usually set to values recommended by an expert. Nevertheless, such an approach can suffer from human bias, leading to suboptimal reconstruction results. In this paper we consider a more principled approach for choosing these parameters in an automatic way. For this we optimize a reconstruction score evaluated on a set of different Gaussian Bayesian networks. This objective is expensive to evaluate and lacks a closed-form expression, which means that Bayesian optimization (BO) is a natural choice. BO methods use a model to guide the search and are hence able to exploit smoothness properties of the objective surface. We show that the parameters found by a BO method outperform those found by a random search strategy and the expert recommendation. Importantly, we have found that an often overlooked statistical test provides the best over-all reconstruction results

Challenges for Efficient Query Evaluation on Structured Probabilistic Data

Query answering over probabilistic data is an important task but is generally intractable. However, a new approach for this problem has recently been proposed, based on structural decompositions of input databases, following, e.g., tree decompositions. This paper presents a vision for a database management system for probabilistic data built following this structural approach. We review our existing and ongoing work on this topic and highlight many theoretical and practical challenges that remain to be addressed.Comment: 9 pages, 1 figure, 23 references. Accepted for publication at SUM 201

Case-control association testing by graphical modeling for the Genetic Analysis Workshop 17 mini-exome sequence data

We generalize recent work on graphical models for linkage disequilibrium to estimate the conditional independence structure between all variables for individuals in the Genetic Analysis Workshop 17 unrelated individuals data set. Using a stepwise approach for computational efficiency and an extension of our previously described methods, we estimate a model that describes the relationships between the disease trait, all quantitative variables, all covariates, ethnic origin, and the loci most strongly associated with these variables. We performed our analysis for the first 50 replicate data sets. We found that our approach was able to describe the relationships between the outcomes and covariates and that it could correctly detect associations of disease with several loci and with a reasonable false-positive detection rate

Bayesian Networks for Max-linear Models

We study Bayesian networks based on max-linear structural equations as introduced in Gissibl and Kl\"uppelberg [16] and provide a summary of their independence properties. In particular we emphasize that distributions for such networks are generally not faithful to the independence model determined by their associated directed acyclic graph. In addition, we consider some of the basic issues of estimation and discuss generalized maximum likelihood estimation of the coefficients, using the concept of a generalized likelihood ratio for non-dominated families as introduced by Kiefer and Wolfowitz [21]. Finally we argue that the structure of a minimal network asymptotically can be identified completely from observational data.Comment: 18 page

The IBMAP approach for Markov networks structure learning

In this work we consider the problem of learning the structure of Markov networks from data. We present an approach for tackling this problem called IBMAP, together with an efficient instantiation of the approach: the IBMAP-HC algorithm, designed for avoiding important limitations of existing independence-based algorithms. These algorithms proceed by performing statistical independence tests on data, trusting completely the outcome of each test. In practice tests may be incorrect, resulting in potential cascading errors and the consequent reduction in the quality of the structures learned. IBMAP contemplates this uncertainty in the outcome of the tests through a probabilistic maximum-a-posteriori approach. The approach is instantiated in the IBMAP-HC algorithm, a structure selection strategy that performs a polynomial heuristic local search in the space of possible structures. We present an extensive empirical evaluation on synthetic and real data, showing that our algorithm outperforms significantly the current independence-based algorithms, in terms of data efficiency and quality of learned structures, with equivalent computational complexities. We also show the performance of IBMAP-HC in a real-world application of knowledge discovery: EDAs, which are evolutionary algorithms that use structure learning on each generation for modeling the distribution of populations. The experiments show that when IBMAP-HC is used to learn the structure, EDAs improve the convergence to the optimum

Discovering a junction tree behind a Markov network by a greedy algorithm

In an earlier paper we introduced a special kind of k-width junction tree, called k-th order t-cherry junction tree in order to approximate a joint probability distribution. The approximation is the best if the Kullback-Leibler divergence between the true joint probability distribution and the approximating one is minimal. Finding the best approximating k-width junction tree is NP-complete if k>2. In our earlier paper we also proved that the best approximating k-width junction tree can be embedded into a k-th order t-cherry junction tree. We introduce a greedy algorithm resulting very good approximations in reasonable computing time. In this paper we prove that if the Markov network underlying fullfills some requirements then our greedy algorithm is able to find the true probability distribution or its best approximation in the family of the k-th order t-cherry tree probability distributions. Our algorithm uses just the k-th order marginal probability distributions as input. We compare the results of the greedy algorithm proposed in this paper with the greedy algorithm proposed by Malvestuto in 1991.Comment: The paper was presented at VOCAL 2010 in Veszprem, Hungar