A Model Selection Method for Nonlinear System Identification Based fMRI Effective Connectivity Analysis

The Hayling Sentence Completion Task (HSCT) is known to activate left hemisphere frontal and temporal language regions. However, the effective connectivity between frontal and temporal language regions associated with the task has yet to be examined. The aims of the study were to examine activation and effective connectivity during the HSCT using a functional magnetic resonance imaging (fMRI) paradigm in which participants made overt verbal responses. We predicted that producing an incongruent response (response suppression), compared to a congruent one (response initiation), would be associated with greater activation in the left prefrontal cortex and an increase in the effective connectivity between temporal and frontal regions. Fifteen participants were scanned while completing 80 sentence stems. The congruency and constraint of sentences varied across trials. Dynamic Causal Modeling (DCM) and Bayesian Model Selection (BMS) were used to compare a set of alternative DCMs of fronto-temporal connectivity. The HSCT activated regions in the left temporal and prefrontal cortices, and the cuneus. Response suppression was associated with greater activation in the left middle and orbital frontal gyri and the bilateral precuneus than response initiation. Left middle temporal and frontal regions identified by the conventional fMRI analyses were entered into the DCM analysis. Using a systematic BMS procedure, the optimal DCM showed that the connection from the left middle temporal gyrus, which was driven by verbal stimuli per se, was significantly increased in strength during response suppression compared to initiation. Greater effective connectivity between left temporal and prefrontal regions during response suppression may reflect the transfer of information from posterior temporal regions where semantic and lexical information is stored to prefrontal regions where it is manipulated in preparation for an appropriate response.

Evidence suggests that obsessive compulsive disorder (OCD) is associated with an overactive error control system. A key role in error detection and control has been ascribed to the fronto-cingulate system. However, the exact functional interplay between the single components of this network in OCD is largely unknown. Therefore, the present study combined a univariate data analysis and effective connectivity analysis using dynamic causal modeling (DCM) to examine error control in 21 patients with OCD and 21 matched healthy controls. All subjects performed an adapted version of the Stroop color-word task while undergoing fMRI scans. Enhanced activation in the fronto-cingulate system could be detected in OCD patients during the incongruent task condition. Additionally, task-related modulation of effective connectivity from the dorsal ACC to left DLPFC was significantly stronger in OCD patients. These findings are consistent with an overactive error control system in OCD subserving suppression of prepotent responses during decision-making.

Effective connectivity (EC) refers to directional or causal influences between interacting neuronal populations or brain regions and can be estimated from functional magnetic resonance imaging (fMRI) data via dynamic causal modeling (DCM). In contrast to functional connectivity, the impact of data processing varieties on DCM estimates of task‐evoked EC has hardly ever been addressed. We therefore investigated how task‐evoked EC is affected by choices made for data processing. In particular, we considered the impact of global signal regression (GSR), block/event‐related design of the general linear model (GLM) used for the first‐level task‐evoked fMRI analysis, type of activation contrast, and significance thresholding approach. Using DCM, we estimated individual and group‐averaged task‐evoked EC within a brain network related to spatial conflict processing for all the parameters considered and compared the differences in task‐evoked EC between any two data processing conditions via between‐group parametric empirical Bayes (PEB) analysis and Bayesian data comparison (BDC). We observed strongly varying patterns of the group‐averaged EC depending on the data processing choices. In particular, task‐evoked EC and parameter certainty were strongly impacted by GLM design and type of activation contrast as revealed by PEB and BDC, respectively, whereas they were little affected by GSR and the type of significance thresholding. The event‐related GLM design appears to be more sensitive to task‐evoked modulations of EC, but provides model parameters with lower certainty than the block‐based design, while the latter is more sensitive to the type of activation contrast than is the event‐related design. Our results demonstrate that applying different reasonable data processing choices can substantially alter task‐evoked EC as estimated by DCM. Such choices should be made with care and, whenever possible, varied across parallel analyses to evaluate their impact and identify potential convergence for robust outcomes.

Corporate Bond Spreads and Real Activity in the Euro Area - Least Angle Regression Forecasting and the Probability of the Recession

In this study, we examined regions in the left and right hemisphere language network that were altered in terms of the underlying neural activation and effective connectivity subsequent to language rehabilitation. Eight persons with chronic post-stroke aphasia and eight normal controls participated in the current study. Patients received a 10 week semantic feature-based rehabilitation program to improve their skills. Therapy was provided on atypical examples of one trained category while two control categories were monitored; the categories were counterbalanced across patients. In each fMRI session, two experimental tasks were conducted: (a) picture naming and (b) semantic feature verification of trained and untrained categories. Analysis of treatment effect sizes revealed that all patients showed greater improvements on the trained category relative to untrained categories. Results from this study show remarkable patterns of consistency despite the inherent variability in lesion size and activation patterns across patients. Across patients, activation that emerged as a function of rehabilitation on the trained category included bilateral IFG, bilateral SFG, LMFG, and LPCG for picture naming; and bilateral IFG, bilateral MFG, LSFG, and bilateral MTG for semantic feature verification. Analysis of effective connectivity using Dynamic Causal Modeling (DCM) indicated that LIFG was the consistently significantly modulated region after rehabilitation across participants. These results indicate that language networks in patients with aphasia resemble normal language control networks and that this similarity is accentuated by rehabilitation.

In public health research, it has been well established that geographic location plays an important role in influencing health outcomes. In recent years, there has been an increased emphasis on the impact of neighborhood or contextual factors as potential risk factors for childhood obesity. Some neighborhood factors relevant to childhood obesity include access to food sources, access to recreational facilities, neighborhood safety, and socioeconomic status (SES) variables. It is common for neighborhood or area-level variables to be available at multiple spatial scales (SS) or geographic units, such as the census block group and census tract, and selection of the spatial scale for area-level variables can be considered as a model selection problem. In this paper, we model the variation in body mass index (BMI) in a study of pediatric patients of the Virginia Commonwealth University (VCU) Medical Center, while considering the selection of spatial scale for a set of neighborhood-level variables available at multiple spatial scales using four recently proposed spatial scale selection algorithms: SS forward stepwise regression, SS incremental forward stagewise regression, SS least angle regression (LARS), and SS lasso. For pediatric BMI, we found evidence of significant positive associations with visit age and black race at the individual level, percent Hispanic white at the census block group level, percent Hispanic black at the census tract level, and percent vacant housing at the census tract level. We also found significant negative associations with population density at the census tract level, median household income at the census tract level, percent renter at the census tract level, and exercise equipment expenditures at the census block group level. The SS algorithms selected covariates at different spatial scales, producing better goodness-of-fit in comparison to traditional models, where all area-level covariates were modeled at the same scale. These findings underscore the importance of considering spatial scale when performing model selection.

An elastic net (EN) is an algorithm for fitting penalized regression models using a convex combination of the LASSO and ridge penalty norms. The algorithm takes advantage of both the sparsity property of the LASSO and variable grouping property of the ridge, making it a natural choice for model selection. EN estimates can be computed using LASSO‐based estimation methods, such as Least Angle Regression (LARS) or coordinate descent, and computational implementations of these methods are available in open‐source software packages.

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.

Sparse and redundant representation of data assumes an ability to describe signals as linear combinations of a few atoms from a dictionary. If the model of the signal is unknown, the dictionary can be learned from a set of training signals. Like the K-SVD, many of the practical dictionary learning algorithms are composed of two main parts: sparse-coding and dictionary-update. This paper first proposes a Stagewise least angle regression (St-LARS) method for performing the sparse-coding operation. The St-LARS applies a hard-thresholding strategy into the original least angle regression (LARS) algorithm, which enables it to select many atoms at each iteration and thus results in fast solutions while still provides good results. Then, a dictionary update method named approximated singular value decomposition (ASVD) is used on the dictionary update stage. It is a quick approximation of the exact SVD computation and can reduce the complexity of it. Experiments on both synthetic data and 3-D image denoising demonstrate the advantages of the proposed algorithm over other dictionary learning methods not only in terms of better trained dictionary but also in terms of computation time.

The classical model of blood oxygen level-dependent (BOLD) responses by Buxton et al. [Buxton, R.B., Wong, E.C., Frank, L.R., 1998. Dynamics of blood flow and oxygenation changes during brain activation: the Balloon model. Magn. Reson. Med. 39, 855–864] has been very important in providing a biophysically plausible framework for explaining different aspects of hemodynamic responses. It also plays an important role in the hemodynamic forward model for dynamic causal modeling (DCM) of fMRI data. A recent study by Obata et al. [Obata, T., Liu, T.T., Miller, K.L., Luh, W.M., Wong, E.C., Frank, L.R., Buxton, R.B., 2004. Discrepancies between BOLD and flow dynamics in primary and supplementary motor areas: application of the Balloon model to the interpretation of BOLD transients. NeuroImage 21, 144–153] linearized the BOLD signal equation and suggested a revised form for the model coefficients. In this paper, we show that the classical and revised models are special cases of a generalized model. The BOLD signal equation of this generalized model can be reduced to that of the classical Buxton model by simplifying the coefficients or can be linearized to give the Obata model. Given the importance of hemodynamic models for investigating BOLD responses and analyses of effective connectivity with DCM, the question arises which formulation is the best model for empirically measured BOLD responses. In this article, we address this question by embedding different variants of the BOLD signal equation in a well-established DCM of functional interactions among visual areas. This allows us to compare the ensuing models using Bayesian model selection. Our model comparison approach had a factorial structure, comparing eight different hemodynamic models based on (i) classical vs. revised forms for the coefficients, (ii) linear vs. non-linear output equations, and (iii) fixed vs. free parameters, ε, for region-specific ratios of intra- and extravascular signals. Using fMRI data from a group of twelve subjects, we demonstrate that the best model is a non-linear model with a revised form for the coefficients, in which ε is treated as a free parameter.

Only unstructured single-path model selection techniques, i.e., Information Criteria, are used by Bounds test of cointegration for model selection. The aim of this paper was twofold; one was to evaluate the performance of these five routinely used information criteria {Akaike Information Criterion (AIC), Akaike Information Criterion Corrected (AICC), Schwarz/Bayesian Information Criterion (SIC/BIC), Schwarz/Bayesian Information Criterion Corrected (SICC/BICC), and Hannan and Quinn Information Criterion (HQC)} and three structured approaches (Forward Selection, Backward Elimination, and Stepwise) by assessing their size and power properties at different sample sizes based on Monte Carlo simulations, and second was the assessment of the same based on real economic data. The second aim was achieved by the evaluation of the long-run relationship between three pairs of macroeconomic variables, i.e., Energy Consumption and GDP, Oil Price and GDP, and Broad Money and GDP for BRICS (Brazil, Russia, India, China and South Africa) countries using Bounds cointegration test. It was found that information criteria and structured procedures have the same powers for a sample size of 50 or greater. However, BICC and Stepwise are better at small sample sizes. In the light of simulation and real data results, a modified Bounds test with Stepwise model selection procedure may be used as it is strongly theoretically supported and avoids noise in the model selection process.

PurposeWith the prosperity of grey extension models, the form and structure of grey forecasting models tend to be complicated. How to select the appropriate model structure according to the data characteristics has become an important topic. The purpose of this paper is to design a structure selection method for the grey multivariate model.Design/methodology/approachThe linear correction term is introduced into the grey model, then the nonhomogeneous grey multivariable model with convolution integral [NGMC(1,N)] is proposed. Then, by incorporating the least absolute shrinkage and selection operator (LASSO), the model parameters are compressed and estimated based on the least angle regression (LARS) algorithm.FindingsBy adjusting the values of the parameters, the NGMC(1,N) model can derive various structures of grey models, which shows the structural adaptability of the NGMC(1,N) model. Based on the geometric interpretation of the LASSO method, the structure selection of the grey model can be transformed into sparse parameter estimation, and the structure selection can be realized by LASSO estimation.Practical implicationsThis paper not only provides an effective method to identify the key factors of the agricultural drought vulnerability, but also presents a practical model to predict the agricultural drought vulnerability.Originality/valueBased on the LASSO method, a structure selection algorithm for the NGMC(1,N) model is designed, and the structure selection method is applied to the vulnerability prediction of agricultural drought in Puyang City, Henan Province.

This article is part of the Focus Theme of Methods of Information in Medicine on "Biosignal Interpretation: Advanced Methods for Neural Signals and Images". Dynamic Causal Modelling (DCM) is a generic formalism to study effective brain connectivity based on neuroimaging data, particularly functional Magnetic Resonance Imaging (fMRI). Recently, there have been attempts at modifying this model to allow for stochastic disturbances in the states of the model. This paper proposes the Multiple-Model Kalman Filtering (MMKF) technique as a stochastic identification model discriminating among different hypothetical connectivity structures in the DCM framework; moreover, the performance compared to a similar deterministic identification model is assessed. The integration of the stochastic DCM equations is first presented, and a MMKF algorithm is then developed to perform model selection based on these equations. Monte Carlo simulations are performed in order to investigate the ability of MMKF to distinguish between different connectivity structures and to estimate hidden states under both deterministic and stochastic DCM. The simulations show that the proposed MMKF algorithm was able to successfully select the correct connectivity model structure from a set of pre-specified plausible alternatives. Moreover, the stochastic approach by MMKF was more effective compared to its deterministic counterpart, both in the selection of the correct connectivity structure and in the estimation of the hidden states. These results demonstrate the applicability of a MMKF approach to the study of effective brain connectivity using DCM, particularly when a stochastic formulation is desirable.

Variable selection plays a significant role in statistics. There are many variable selection methods. Forward stagewise regression takes a different approach among those. In this thesis Least Angle Regression (LAR) is discussed in detail. This approach has similar principles as forward stagewise regression but does not suffer from its computational difficulties. By using a small artificial data set and the well-known Longley data set, the LAR algorithm is illustrated in detail and the coefficient profiles are obtained. Furthermore a penalized approach to variable reduction called the LASSO is discussed, and it is shown how to compute its coefficient profiles efficiently using the LAR algorithm with a small modification. Finally, a method called K-fold cross validation used to select the constraint parameter for the LASSO is presented and illustrated with the Longley data.

Dynamic causal modeling (DCM) is a tool used for effective connectivity (EC) estimation in neuroimage analysis. But it is a model-driven analysis method, and the structure of the EC network needs to be determined in advance based on a large amount of prior knowledge. This characteristic makes it difficult to apply DCM to the exploratory brain network analysis. The exploratory analysis of DCM can be realized from two perspectives: one is to reduce the computational cost of the model; the other is to reduce the model space. From the perspective of model space reduction, a model space exploration strategy is proposed, including two algorithms. One algorithm, named GreedyEC, starts with reducing EC from full model, and the other, named GreedyROI, start with adding EC from one node model. Then the two algorithms were applied to the task state functional magnetic resonance imaging (fMRI) data of visual object recognition and selected the best DCM model from the perspective of model comparison based on Bayesian model compare method. Results show that combining the results of the two algorithms can further improve the effect of DCM exploratory analysis. For convenience in application, the algorithms were encapsulated into MATLAB function based on SPM to help neuroscience researchers to analyze the brain causal information flow network. The strategy provides a model space exploration tool that may obtain the best model from the perspective of model comparison and lower the threshold of DCM analysis.