Joris M. Mooij

MAGMA: Generalized Gene-Set Analysis of GWAS Data

By aggregating data for complex traits in a biologically meaningful way, gene and gene-set analysis constitute a valuable addition to single-marker analysis. However, although various methods for gene and gene-set analysis currently exist, they generally suffer from a number of issues. Statistical power for most methods is strongly affected by linkage disequilibrium between markers, multi-marker associations are often hard to detect, and the reliance on permutation to compute p-values tends to make the analysis computationally very expensive. To address these issues we have developed MAGMA, a novel tool for gene and gene-set analysis. The gene analysis is based on a multiple regression model, to provide better statistical performance. The gene-set analysis is built as a separate layer around the gene analysis for additional flexibility. This gene-set analysis also uses a regression structure to allow generalization to analysis of continuous properties of genes and simultaneous analysis of multiple gene sets and other gene properties. Simulations and an analysis of Crohn’s Disease data are used to evaluate the performance of MAGMA and to compare it to a number of other gene and gene-set analysis tools. The results show that MAGMA has significantly more power than other tools for both the gene and the gene-set analysis, identifying more genes and gene sets associated with Crohn’s Disease while maintaining a correct type 1 error rate. Moreover, the MAGMA analysis of the Crohn’s Disease data was found to be considerably faster as well.

Sufficient Conditions for Convergence of the Sum–Product Algorithm

Novel conditions are derived that guarantee convergence of the sum-product algorithm (also known as loopy belief propagation or simply belief propagation (BP)) to a unique fixed point, irrespective of the initial messages, for parallel (synchronous) updates. The computational complexity of the conditions is polynomial in the number of variables. In contrast with previously existing conditions, our results are directly applicable to arbitrary factor graphs (with discrete variables) and are shown to be valid also in the case of factors containing zeros, under some additional conditions. The conditions are compared with existing ones, numerically and, if possible, analytically. For binary variables with pairwise interactions, sufficient conditions are derived that take into account local evidence (i.e., single-variable factors) and the type of pair interactions (attractive or repulsive). It is shown empirically that this bound outperforms existing bounds.

Remote Sensing Feature Selection by Kernel Dependence Measures

This letter introduces a nonlinear measure of independence between random variables for remote sensing supervised feature selection. The so-called Hilbert-Schmidt independence criterion (HSIC) is a kernel method for evaluating statistical dependence and it is based on computing the Hilbert-Schmidt norm of the cross-covariance operator of mapped samples in the corresponding Hilbert spaces. The HSIC empirical estimator is easy to compute and has good theoretical and practical properties. Rather than using this estimate for maximizing the dependence between the selected features and the class labels, we propose the more sensitive criterion of minimizing the associated HSIC p-value. Results in multispectral, hyperspectral, and SAR data feature selection for classification show the good performance of the proposed approach.

On the properties of the Bethe approximation and loopy belief propagation on binary networks

We analyse the local stability of the high-temperature fixed point of the loopy belief propagation (LBP) algorithm and how this relates to the properties of the Bethe free energy which LBP tries to minimize. We focus on the case of binary networks with pairwise interactions. In particular, we state sufficient conditions for convergence of LBP to a unique fixed point and show that these are sharp for purely ferromagnetic interactions. In contrast, in the purely antiferromagnetic case, the undamped parallel LBP algorithm is suboptimal in the sense that the stability of the fixed point breaks down much earlier than for damped or sequential LBP; we observe that the onset of instability for the latter algorithms is related to the properties of the Bethe free energy. For spin-glass interactions, damping LBP only helps slightly. We estimate analytically the temperature at which the high-temperature LBP fixed point becomes unstable for random graphs with arbitrary degree distributions and random interactions.

Regression by dependence minimization and its application to causal inference in additive noise models

Motivated by causal inference problems, we propose a novel method for regression that minimizes the statistical dependence between regressors and residuals. The key advantage of this approach to regression is that it does not assume a particular distribution of the noise, i.e., it is non-parametric with respect to the noise distribution. We argue that the proposed regression method is well suited to the task of causal inference in additive noise models. A practical disadvantage is that the resulting optimization problem is generally non-convex and can be difficult to solve. Nevertheless, we report good results on one of the tasks of the NIPS 2008 Causality Challenge, where the goal is to distinguish causes from effects in pairs of statistically dependent variables. In addition, we propose an algorithm for efficiently inferring causal models from observational data for more than two variables. The required number of regressions and independence tests is quadratic in the number of variables, which is a significant improvement over the simple method that tests all possible DAGs.

Inference in the Promedas Medical Expert System

In the current paper, the Promedas model for internal medicine, developed by our team, is introduced. The model is based on up-to-date medical knowledge and consists of approximately 2000 diagnoses, 1000 findings and 8600 connections between diagnoses and findings, covering a large part of internal medicine. We show that Belief Propagation (BP) can be successfully applied as approximate inference algorithm in the Promedas network. In some cases, however, we find errors that are too large for this application. We apply a recently developed method that improves the BP results by means of a loop expansion scheme. This method, termed Loop Corrected (LC) BP, is able to improve the marginal probabilities significantly, leaving a remaining error which is acceptable for the purpose of medical diagnosis.

Methods for causal inference from gene perturbation experiments and validation

Inferring causal effects from observational and interventional data is a highly desirable but ambitious goal. Many of the computational and statistical methods are plagued by fundamental identifiability issues, instability, and unreliable performance, especially for large-scale systems with many measured variables. We present software and provide some validation of a recently developed methodology based on an invariance principle, called invariant causal prediction (ICP). The ICP method quantifies confidence probabilities for inferring causal structures and thus leads to more reliable and confirmatory statements for causal relations and predictions of external intervention effects. We validate the ICP method and some other procedures using large-scale genome-wide gene perturbation experiments in Saccharomyces cerevisiae. The results suggest that prediction and prioritization of future experimental interventions, such as gene deletions, can be improved by using our statistical inference techniques.

Quantitative imaging through a spectrograph. 1. Principles and theory.

Laser-based optical diagnostics, such as planar laser-induced fluorescence and, especially, Raman imaging, often require selective spectral filtering. We advocate the use of an imaging spectrograph with a broad entrance slit as a spectral filter for two-dimensional imaging. A spectrograph in this mode of operation produces output that is a convolution of the spatial and spectral information that is present in the incident light. We describe an analytical deconvolution procedure, based on Bayesian statistics, that retrieves the spatial information while it avoids excessive noise blowup. The method permits direct imaging through a spectrograph, even under broadband illumination. We introduce the formalism and discuss the underlying assumptions. The performance of the procedure is demonstrated on an artificial but pathological example. In a companion paper [Appl. Opt. 43, 5682-5690 (2004)] the method is applied to the practical case of fuel equivalence ratio Raman imaging in a combustible methane-air mixture.

Semi-supervised Learning in Causal and Anticausal Settings

We consider the problem of learning in the case where an underlying causal model can be inferred. Causal knowledge may facilitate some approaches for a given problem, and rule out others. We formulate the hypothesis that semi-supervised learning can help in an anti-causal setting, but not in a causal setting, and corroborate it with empirical results.

A graphical model framework for decoding in the visual erp-based bci speller

We present a graphical model framework for decoding in the visual ERP-based speller system. The proposed framework allows researchers to build generative models from which the decoding rules are obtained in a straightforward manner. We suggest two models for generating brain signals conditioned on the stimulus events. Both models incorporate letter frequency information but assume different dependencies between brain signals and stimulus events. For both models, we derive decoding rules and perform a discriminative training. We show on real visual speller data how decoding performance improves by incorporating letter frequency information and using a more realistic graphical model for the dependencies between the brain signals and the stimulus events. Furthermore, we discuss how the standard approach to decoding can be seen as a special case of the graphical model framework. The letter also gives more insight into the discriminative approach for decoding in the visual speller system.