Model Search Space Research Articles

Associations between delay discounting and unhealthy behaviors in substance use recovery

BackgroundResearch on delay discounting (DD) is mixed on whether DD is a domain-specific component related to specific behaviors or a domain-general process that cuts across various behaviors. A pivotal group to test the associations between DD and unhealthy behaviors is individuals in recovery from substance use disorders (SUD), as they are moving away from a disorder toward a healthier state. MethodsIndividuals in SUD recovery (n = 317) completed the Temptation Scale, the Health Behaviors Questionnaire, and an Adjusting Delay Discounting Task. An exhaustive model space search was performed using linear regression to examine associations between DD with temptation, engagement in unhealthy behaviors, and the total number of unhealthy behaviors participants engage in. We also tested whether remission status is associated with the total number of unhealthy behaviors participants engage in. ResultsResults revealed that DD was positively associated with poor eating (p<.001), physical inactivity (p=.003), financial irresponsibility (p<.001), risky behaviors (p<.001), lack of personal development goals (p<.001), lack of household savings (p=.004), and lack of health behaviors (p=.003). DD was also positively associated with the total number of unhealthy behaviors participants engage in (p<.001). Participants who were not in remission engaged in more unhealthy behaviors compared to those who were in remission (p<.001). ConclusionIn a sample of individuals in recovery from SUD, DD is not domain-specific and undergirds engagement in several maladaptive health behaviors that can negatively impact recovery. Thus, DD can be a target for interventions aiming to reduce other maladaptive behaviors in SUD recovery.

A strategy of model space search for dynamic causal modeling in task fMRI data exploratory analysis.

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.

Stable Radial Basis Function Selection via Mixture Modelling of the Sample Path

We consider a fully Bayesian treatment of radial basis function regression, and propose a solution to the the instability of basis selection. Indeed, when bases are selected solely according to the magnitude of their posterior inclusion probabilities, it is often the case that many bases in the same neighborhood end up getting selected leading to redundancy and ultimately inaccuracy of the representation. In this paper, we propose a straightforward solution to the problem based on post-processing the sample path yielded by the model space search technique. Specically, we perform an a posteriori model-based clustering of the sample path via a mixture of Gaussians, and then select the points closer to the means of the Gaussians. Our solution is found to be more stable and yields a better performance on simulated and real tasks.

TopoFilter: a MATLAB package for mechanistic model identification in systems biology

BackgroundTo develop mechanistic dynamic models in systems biology, one often needs to identify all (or minimal) representations of the biological processes that are consistent with experimental data, out of a potentially large set of hypothetical mechanisms. However, a simple enumeration of all alternatives becomes quickly intractable when the number of model parameters grows. Selecting appropriate dynamic models out of a large ensemble of models, taking the uncertainty in our biological knowledge and in the experimental data into account, is therefore a key current problem in systems biology.ResultsThe TopoFilter package addresses this problem in a heuristic and automated fashion by implementing the previously described topological filtering method for Bayesian model selection. It includes a core heuristic for searching the space of submodels of a parametrized model, coupled with a sampling-based exploration of the parameter space. Recent developments of the method allow to balance exhaustiveness and speed of the model space search, to efficiently re-sample parameters, to parallelize the search, and to use custom scoring functions. We use a theoretical example to motivate these features and then demonstrate TopoFilter’s applicability for a yeast signaling network with more than 250’000 possible model structures.ConclusionsTopoFilter is a flexible software framework that makes Bayesian model selection and reduction efficient and scalable to network models of a complexity that represents contemporary problems in, for example, cell signaling. TopoFilter is open-source, available under the GPL-3.0 license at https://gitlab.com/csb.ethz/TopoFilter. It includes installation instructions, a quickstart guide, a description of all package options, and multiple examples.

A Mixed Model Approach to Vegetation Condition Prediction Using Artificial Neural Networks (ANN): Case of Kenya’s Operational Drought Monitoring

Droughts, with their increasing frequency of occurrence, especially in the Greater Horn of Africa (GHA), continue to negatively affect lives and livelihoods. For example, the 2011 drought in East Africa caused massive losses, documented to have cost the Kenyan economy over 12 billion US dollars. Consequently, the demand is ever-increasing for ex-ante drought early warning systems with the ability to offer drought forecasts with sufficient lead times The study uses 10 precipitation and vegetation condition indices that are lagged over 1, 2 and 3-month time-steps to predict future values of vegetation condition index aggregated over a 3-month time period (VCI3M) that is a proxy variable for drought monitoring. The study used data covering the period 2001–2015 at a monthly frequency for four arid northern Kenya counties for model training, with data for 2016–2017 used as out-of-sample data for model testing. The study adopted a model space search approach to obtain the most predictive artificial neural network (ANN) model as opposed to the traditional greedy search approach that is based on optimal variable selection at each model building step. The initial large model-space was reduced using the general additive model (GAM) technique together with a set of assumptions. Even though we built a total of 102 GAM models, only 20 had R2 ≥ 0.7, and together with the model with lag of the predicted variable, were subjected to the ANN modelling process. The ANN process itself uses the brute-force approach that automatically partitions the training data into 10 sub-samples, builds the ANN models in these samples and evaluates their performance using multiple metrics. The results show the superiority of 1-month lag of the variables as compared to longer time lags of 2 and 3 months. The best ANN model recorded an R2 of 0.78 between actual and predicted vegetation conditions 1-month ahead using the out-of-sample data. Investigated as a classifier distinguishing five vegetation deficit classes, the best ANN model had a modest accuracy of 67% and a multi-class area under the receiver operating characteristic curve (AUROC) of 89.99%.

A model space search approach to finite-frequency SKS splitting intensity tomography in a reduced parameter space

Here we develop a theoretical and practical framework for the tomographic inversion of shear wave splitting intensity measurements for anisotropic structure in the upper mantle using a model space search approach. Treating the anisotropic scatterers as a first order perturbation to the background isotropic state, we implement the Born approximation to compute the integral sensitivity kernels in a finite frequency framework. We implement a parametrization of the anisotropy based on insights from olivine elasticity and fabric development that involves three parameters (corresponding to the azimuth and dip of the anisotropic symmetry axis, plus a strength parameter). Previous work on finite-frequency shear wave splitting tomography has implemented a linearization technique to invert splitting intensity data for the spatial distribution of anisotropic scatterers. The inverse problem, however, is strongly non-linear in terms of several of the involved parameters (those that describe the orientation of the symmetry axis), and their variation is not of first order. Therefore, in the case of a realistic upper mantle where anisotropic structure varies in a complicated manner, a linearization technique may not be adequate. To ameliorate these problems, we implement a model space search approach (specifically, a Markov chain Monte Carlo with Gibbs sampling algorithm) to the tomographic inversion of splitting intensity data. This approach allows for the visualization of posterior probability distributions for anisotropic parameters in the inversion. We perform a suite of synthetic resolution tests to demonstrate the reliability of our method, using a station distribution from an actual deployment of a dense seismic network. These resolution tests show that anisotropic structure may be resolved up to a length scale of roughly 50 km with teleseismic SKS waves for station spacing of 10–15 km.

The Overfitting Toolbox (TOT): large-scale search in model space for expected neuroimaging effects

The Overfitting Toolbox (TOT): large-scale search in model space for expected neuroimaging effects

A Bayesian approach to assess the importance of crustal corrections in global anisotropic surface wave tomography

Several recent studies have demonstrated the importance of crustal corrections when inverting surface wave data to model lateral variations in mantle radial anisotropy. It has also been shown that the choice of the prior crustal model to correct the data can strongly influence the anisotropy model and potentially lead to different geodynamic interpretations. In comparing tomographic models of radial anisotropy obtained from different crustal corrections, these studies did not, however, determine quantitative model uncertainties. Nevertheless, mantle models resulting from different prior crustal corrections are statistically different only if the posterior model errors stemming from the non-uniqueness of the inverse problem are smaller than the effect of the crustal correction itself. Here, we applied a model space search approach to global fundamental and higher mode Rayleigh and Love wave phase velocity maps to determine reliable, quantitative model uncertainties on seismic velocities and radial anisotropy. The technique employed enabled us to describe the model space with a posterior probability density function, and therefore to test whether models obtained from different crustal corrections are statistically different. We thus assessed the significance of the choice of the crustal model by comparing the posterior model errors to the differences in mantle structure resulting from different crustal corrections. We tested prior crustal models CRUST2.0, CRUST1.0, and 3SMAC. Our study shows that the use of prior crustal corrections from different crustal models yields significant discrepancies in mantle velocities around 50 km depth and in radial anisotropy down to 100 km. The impact of the crustal correction on radial anisotropy can extend down to 250 km in some locations.We found that choosing 3SMAC instead of the other crustal models has a stronger influence on the mantle model, but that CRUST1.0 and CRUST2.0 yield statistically identical anisotropy models at all depths, except at a few grid cells. Importantly, the effect of the crustal model is most significant in continental regions and not so much beneath oceans, which has important consequences for determining the depth of continental roots. Our results therefore suggest that improving constraints on crustal structure in continents is essential for our understanding of continent formation. Our work also demonstrates that the prior crustal model does not significantly affect radial anisotropy and velocities at depths greater than 100 km. This implies that if geodynamic interpretations of radial anisotropy below 100 km depth were to account for tomographic model uncertainties, they would not depend on the choice of the prior crustal model. It is therefore important for geodynamicists and seismologists to work in concert and to put effort into determining quantitative tomographic model uncertainties before interpreting the results. Our results also caution against the use of 3SMAC to correct surface wave data for studies of the continental lithosphere, and suggest that the solid Earth community would benefit from putting some efforts toward building a revised 3SMAC. The discrepancies between mantle models built based on 3SMAC crustal corrections and those based on CRUST1.0 or CRUST2.0 should also help shed light on the validity of the geodynamical assumptions made in the construction of models like 3SMAC.

The distribution function of the Galaxy's dark halo

Starting from the hypothesis that the Galaxy's dark halo responded adiabatically to the infall of baryons, we have constructed a self-consistent dynamical model of the Galaxy that satisfies a large number of observations, including measurements of gas terminal velocities and masers, the kinematics of 180 000 giant stars from the RAVE (RAdial Velocity Experiment) survey and star-count data from the Sloan Digital Sky Survey. The stellar disc and the dark halo are both specified by distribution functions of the action integrals. The model is obtained by extending the work of Piffl et al. from the construction of a single model to a systematic search of model space. Whereas the model of Piffl et al. violated constraints on the terminal-velocity curve, our model respects these constraints by adopting a long scalelength Rd = 3.66 kpc for the thin and thick discs. The model is, however, inconsistent with the measured optical depth for microlensing of bulge stars because it attributes too large a fraction of the density at R ≲ 3 kpc to dark matter rather than stars. Moreover, it now seems likely that the thick disc's scalelength is significantly shorter than the model implies. Shortening this scalelength would cause the constraints from the rotation curve to be violated anew. We conclude that we can now rule out adiabatic compression of our Galaxy's dark halo.

Probabilistic inversion of airborne electromagnetic data under spatial constraints

Probabilistic 1D inversions of airborne electromagnetic (AEM) surveys allow an exhaustive search of model space for each station, but they often assume that there is no spatial correlation between neighboring stations. This can result in abrupt transverse model discontinuities when attempting to construct a 3D model. In contrast to this, fully spatially regularized deterministic inversions can take spatial correlation between 1D models into account, but they do not explore the model space sufficiently to be able to evaluate model robustness. The Bayesian parametric bootstrap (BPB) approach that we developed is a practical compromise between computationally expensive exhaustive search techniques and computationally efficient deterministic inversions. Using a 1D kernel, we inverted for the interfaces, layer properties, and related uncertainties, taking lateral spatial correlations and additional prior information into account. Numerical examples revealed that a BPB technique was likely to explore the model space sufficiently for nonpathological situations. Using a subset of a large AEM survey collected in northwest Australia for aquifer mapping, we show how the BPB approach can be used to produce a spatially coherent map of the base of the Broome sandstone aquifer. The recovered uncertainties, which are likely to be one of the main sources of uncertainty in any groundwater model, exhibited the well-known increase in uncertainty of a depth to interface with increasing depth to the interface.

An explorative study of search of model space in problem-solving

Building on dual-space theories, the three-space theory of problem-solving proposes a search of a model space in addition to search of experiment and hypothesis spaces. This study aimed at exploring the three postulated spaces, especially model space, by means of verbal protocols. Participants (N = 32) were asked to think aloud when working with a computer-based learning program. Through this program, they learned about torques in physics using interactive graphics for conducting experiments with levers and forces. Their knowledge about torques was tested before and after working with the program. Verbal protocols were analysed with regard to the amount of search of the three spaces and the quality of the participants' models for torques. The three postulated spaces could be reliably identified in the protocols. Amount of search of the model space predicted improvement in knowledge beyond prior knowledge and search of the other spaces. Our results add to the validity of model space and will allow us to further explore the three-space theory.

Imaging lithospheric interfaces and 3D structures using receiver functions, gravity, and tomography in a common inversion scheme

Joint inversions are now commonly used in the earth sciences. They have been developed to better understand the structure of the earth, since they provide more constraints on the inverted parameters. We propose a new process to simultaneously invert several data sets in order to better image 3D crustal and upper mantle structures. Our inversion uses three kinds of data that present good complementarity: (1) P-wave receiver functions to provide Moho depth variations, (2) teleseismic delay times of P-waves to retrieve velocity anomalies in the crust and the upper mantle, and (3) gravity anomalies to image density variations at the lithospheric scale. We use a stochastic scheme, where receiver functions are first inverted. The interpolated resulting Moho depths are incorporated as a priori information into the joint inversion of teleseismic delay times and gravity anomalies process. Moreover, velocity and density can be linked by empirical relationships, which justifies the joint inversion of those parameters. In our stochastic approach, we perform a model space search for Moho variations, P-velocity, and density structure to find an acceptable fit to the three data sets. In order to preferentially sample the good data fit regions, we chose the neighborhood algorithm of Sambridge to optimistically survey the model space. We model the delay times with 3D raytracing using evenly spaced velocity–density nodes. We present here the first results given by this method on synthetic tests.

Bayesian flexible modeling of trip durations

Recent advances in Bayesian modeling have led to stunning improvements in our ability to flexibly and easily model complex high-dimensional data. Flexibility comes from the use of a very large number of parameters without fixed dimension. Priors are placed on the parameters to avoid over-fitting and sensibly guide the search in model space for appropriate data-driven model choice. Modern computational, high dimensional search methods (in particular Markov Chain Monte Carlo) then allow us to search the parameter space. This paper introduces the application of BART, Bayesian Additive Regression Trees, to modelling trip durations. We have survey data on characteristics of trips in the Austin area. We seek to relate the trip duration to features of the household and trip characteristics. BART enables one to make inferences about the relationship with minimal assumptions and user decisions.

Global anisotropic phase velocity maps for higher mode Love and Rayleigh waves

SUMMARY It is well established that the Earth’s uppermost mantle is anisotropic, but there are no clear observations of anisotropy in the deeper parts of the mantle. Surface waves are well suited to observe anisotropy since they carry information about both radial and azimuthal anisotropy. Fundamental mode surface waves, for commonly used periods up to 200 s, are sensitive to structure in the first few hundred kilometres, and therefore, do not provide information on anisotropy below. Higher mode surface waves have sensitivities that extend to and beyond the transition zone, and should thus give insight about azimuthal anisotropy at greater depths. We have measured higher mode Love and Rayleigh phase velocities using a model space search approach, which provides us with consistent relative uncertainties from measurement to measurement and from mode to mode. From these phase velocity measurements, we constructed global anisotropic phase velocity maps. Prior to inversion, we determine the optimum relative weighting for anisotropy. We present global azimuthal phase velocity maps for higher mode Rayleigh waves (up to the sixth higher mode) and Love waves (up to the fifth higher mode) with corresponding average model uncertainties. The anisotropy we derive is robust within the uncertainties for all modes. Given the ray theoretical sensitivity kernels of Rayleigh and Love wave modes, the source of anisotropy is complex, but mainly located in the asthenosphere and deeper. Our models show a good correspondence with other studies for the fundamental mode, but we have been able to achieve higher resolution.

Radial anisotropy in seismic reference models of the mantle

Sambridge's Neighborhood Algorithm was applied to normal mode and surface wave phase velocity data to determine the likelihood of radial anisotropy in mantle reference models. This full model space search technique provides probability density functions for each model parameter and therefore reliable estimates of resolution and uncertainty, without having to introduce unnecessary regularization on the model space. Our results for shear wave anisotropy (described by parameter ξ) show a fast decrease with depth with no significant deviation from Preliminary Reference Earth Model (PREM) at any depth. The data do not require strong deviations from PREM for P wave anisotropy either, except between 220 and 400 km depth and in the D″ layer. The intermediate parameter η might depart from PREM between 220 and 670 km depth. This implies a likely deeper P wave anisotropy and η anisotropy than S wave anisotropy. The sign change in the anisotropic parameters across the 670‐km discontinuity found by other authors is not warranted by our data set, which is far more extensive than in previous studies. We found that density needs to be well resolved because we observe a high dependence of the results for P wave‐related parameters on the presence or absence of density in the parameterization. S wave anisotropy and η are less affected by density. A well‐resolved negative density anomaly was found in the uppermost mantle, and a density excess was observed in the transition zone and the lowermost mantle which might be a seismic signature of the recently identified postperovskite phase.

Error bars for the global seismic Q profile

The radial attenuation profile of the Earth is needed to account for dispersion effects when interpreting seismic velocities and can provide important constraints on composition. To date, most radial Q models have been produced using traditional damped inversions of free oscillation and surface wave data. Because such inversions can severely underestimate the model uncertainties that are needed to guide mineralogical and dynamic interpretation, and because the quality of data has continued to improve, we revisit this seismic inverse problem using a model space search approach already proven effective with similar data. We do, indeed, observe model uncertainties at least an order of magnitude greater than earlier estimates. At the same time, we find that Q is determined well enough to confirm that the data favor several important features previously disputed because of questions of consistency. These include shear attenuation that drops significantly in the lower third of the lower mantle and bulk attenuation that is negligible in the inner core but stronger in the outer core and lower mantle than suggested by most models.

Probability density functions for radial anisotropy: implications for the upper 1200 km of the mantle

The presence of radial anisotropy in the upper mantle, transition zone and top of the lower mantle is investigated by applying a model space search technique to Rayleigh and Love wave phase velocity models. Probability density functions are obtained independently for S-wave anisotropy, P-wave anisotropy, intermediate parameter η, V p, V s and density anomalies. The likelihoods for P-wave and S-wave anisotropy beneath continents cannot be explained by a dry olivine-rich upper mantle at depths larger than 220 km. Indeed, while shear-wave anisotropy tends to disappear below 220 km depth in continental areas, P-wave anisotropy is still present but its sign changes compared to the uppermost mantle. This could be due to an increase with depth of the amount of pyroxene relative to olivine in these regions, although the presence of water, partial melt or a change in the deformation mechanism cannot be ruled out as yet. A similar observation is made for old oceans, but not for young ones where V SH> V SV appears likely down to 670 km depth and V PH> V PV down to 400 km depth. The change of sign in P-wave anisotropy seems to be qualitatively correlated with the presence of the Lehmann discontinuity, generally observed beneath continents and some oceans but not beneath ridges. Parameter η shows a similar age-related depth pattern as shear-wave anisotropy in the uppermost mantle and it undergoes the same change of sign as P-wave anisotropy at 220 km depth. The ratio between dln V s and dln V p suggests that a chemical component is needed to explain the anomalies in most places at depths greater than 220 km. More tests are needed to infer the robustness of the results for density, but they do not affect the results for anisotropy.

Robust normal mode constraints on inner-core anisotropy from model space search.

A technique for searching full model space that was applied to measurements of anomalously split normal modes showed a robust pattern of P-wave and S-wave anisotropy in the inner core. The parameter describing P-wave anisotropy changes sign around a radius of 400 kilometers, whereas S-wave anisotropy is small in the upper two-thirds of the inner core and becomes negative at greater depths. Our results agree with observed travel-time anomalies of rays traveling at epicentral distances varying from 150 degrees to 180 degrees. The models may be explained by progressively tilted hexagonal close-packed iron in the upper half of the inner core and could suggest a different iron phase in the center.

P and S tomography using normal-mode and surface waves data with a neighbourhood algorithm

SUMMARY Traditionally P- and S-wave tomography has been based on the inversion of data that are sensitive to the desired Earth structure, and model covariance is estimated from imperfect resolution and data error propagation. This analysis ignores the usually large null-spaces, and hence the significant non-uniqueness of the solution encountered in seismic tomography problems. Here we perform a model space search for P- and S-velocity structure to find acceptable fits to recent normal-mode splitting and fundamental-mode phase velocity data. The survey of the model space employs the neighbourhood algorithm of Sambridge, which preferentially samples the good data-fitting regions. A Bayesian approach is used subsequently to extract robust information from the ensemble of models. We particularly focus on posterior marginal probability density functions and covariances for the various model parameters. The covariance matrix obtained is very useful in providing insights into the trade-offs between the different variables and the uncertainties associated with them. We stay within the framework of perturbation theory, meaning that our emphasis is on the null-space of the linear inverse problem rather than the neglected non-linearity. The whole model space (including the nullspace) is sampled within reasonable parameter bounds, and hence the error bars are determined by all fitting models rather than subjective prior information. We estimated P and S models for spherical harmonic degree two only. The uncertainties are quite large and corresponding relative errors can exceed 100 per cent in the mid-mantle for Vp. We find a good correlation of our most likely S model with previous models but some small changes in amplitude. Our most likely P model differs quite strongly from the recent P model SB10L18 and the correlation between our most likely P and S models is small. Among all the good data-fitting models, there are, however, many that have a significant Vp − Vs correlation. We compute d ln Vs/d ln Vp from the models that correlate significantly. We find an increase with depth in the top 1500 km. Deeper in the mantle, normal-mode data prefer modest values compared with traveltime data.

Probable networks and plausible predictions — a review of practical Bayesian methods for supervised neural networks

Bayesian probability theory provides a unifying framework for data modelling. In this framework the overall aims are to find models that are well-matched to the data, and to use these models to make optimal predictions. Neural network learning is interpreted as an inference of the most probable parameters for the model, given the training data. The search in model space (i.e., the space of architectures, noise models, preprocessings, regularizers and weight decay constants) can then also be treated as an inference problem, in which we infer the relative probability of alternative models, given the data. This review describes practical techniques based on Gaussian approximations for implementation of these powerful methods for controlling, comparing and using adaptive networks.