Cassio Polpo de Campos

Genome wide DNA-profiling of marginal zone lymphomas identifies subtype-specific lesions with an impact on the clinical outcome

Marginal zone B-cell lymphomas (MZLs) have been divided into 3 distinct subtypes (extranodal MZLs of mucosa-associated lymphoid tissue [MALT] type, nodal MZLs, and splenic MZLs). Nevertheless, the relationship between the subtypes is still unclear. We performed a comprehensive analysis of genomic DNA copy number changes in a very large series of MZL cases with the aim of addressing this question. Samples from 218 MZL patients (25 nodal, 57 MALT, 134 splenic, and 2 not better specified MZLs) were analyzed with the Affymetrix Human Mapping 250K SNP arrays, and the data combined with matched gene expression in 33 of 218 cases. MALT lymphoma presented significantly more frequently gains at 3p, 6p, 18p, and del(6q23) (TNFAIP3/A20), whereas splenic MZLs was associated with del(7q31), del(8p). Nodal MZLs did not show statistically significant differences compared with MALT lymphoma while lacking the splenic MZLs-related 7q losses. Gains of 3q and 18q were common to all 3 subtypes. del(8p) was often present together with del(17p) (TP53). Although del(17p) did not determine a worse outcome and del(8p) was only of borderline significance, the presence of both deletions had a highly significant negative impact on the outcome of splenic MZLs.

Structure learning of Bayesian networks using constraints

This paper addresses exact learning of Bayesian network structure from data and experts knowledge based on score functions that are decomposable. First, it describes useful properties that strongly reduce the time and memory costs of many known methods such as hill-climbing, dynamic programming and sampling variable orderings. Secondly, a branch and bound algorithm is presented that integrates parameter and structural constraints with data in a way to guarantee global optimality with respect to the score function. It is an any-time procedure because, if stopped, it provides the best current solution and an estimation about how far it is from the global solution. We show empirically the advantages of the properties and the constraints, and the applicability of the algorithm to large data sets (up to one hundred variables) that cannot be handled by other current methods (limited to around 30 variables).

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.

Computing lower and upper expectations under epistemic independence

This paper investigates the computation of lower/upper expectations that must cohere with a collection of probabilistic assessments and a collection of judgements of epistemic independence. New algorithms, based on multilinear programming, are presented, both for independence among events and among random variables. Separation properties of graphical models are also investigated.

Probabilistic logic with independence

This paper investigates probabilistic logics endowed with independence relations. We review propositional probabilistic languages without and with independence. We then consider graph-theoretic representations for propositional probabilistic logic with independence; complexity is analyzed, algorithms are derived, and examples are discussed. Finally, we examine a restricted first-order probabilistic logic that generalizes relational Bayesian networks.

Constrained Maximum Likelihood Learning of Bayesian Networks for Facial Action Recognition

Probabilistic graphical models such as Bayesian Networks have been increasingly applied to many computer vision problems. Accuracy of inferences in such models depends on the quality of network parameters. Learning reliable parameters of Bayesian networks often requires a large amount of training data, which may be hard to acquire and may contain missing values. On the other hand, qualitative knowledge is available in many computer vision applications, and incorporating such knowledge can improve the accuracy of parameter learning. This paper describes a general framework based on convex optimization to incorporate constraints on parameters with training data to perform Bayesian network parameter estimation. For complete data, a global optimum solution to maximum likelihood estimation is obtained in polynomial time, while for incomplete data, a modified expectation-maximization method is proposed. This framework is applied to real image data from a facial action unit recognition problem and produces results that are similar to those of state-of-the-art methods.

Solving limited memory influence diagrams

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.

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). Retrospective clinical datasets have often small sample size and many missing data.We use Bayesian networks to impute missing data enhancing survival tree analysis.The Bayesian network is learned from incomplete data and used for the imputation.Our method generally achieved more accurate predictions than widely used approaches.

Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)]@?E[g(Y)], where E[@?] denotes interval-valued expectation and @? denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

Approximating credal network inferences by linear programming

An algorithm for approximate credal network updating is presented. The problem in its general formulation is a multilinear optimization task, which can be linearized by an appropriate rule for fixing all the local models apart from those of a single variable. This simple idea can be iterated and quickly leads to very accurate inferences. The approach can also be specialized to classification with credal networks based on the maximality criterion. A complexity analysis for both the problem and the algorithm is reported together with numerical experiments, which confirm the good performance of the method. While the inner approximation produced by the algorithm gives rise to a classifier which might return a subset of the optimal class set, preliminary empirical results suggest that the accuracy of the optimal class set is seldom affected by the approximate probabilities.