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Demian Wassermann

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12 papers

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TMLR Journal 2023 Journal Article

PAVI: Plate-Amortized Variational Inference

Louis Rouillard
Alexandre Le Bris
Thomas Moreau
Demian Wassermann

Given observed data and a probabilistic generative model, Bayesian inference searches for the distribution of the model's parameters that could have yielded the data. Inference is challenging for large population studies where millions of measurements are performed over a cohort of hundreds of subjects, resulting in a massive parameter space. This large cardinality renders off-the-shelf Variational Inference (VI) computationally impractical. In this work, we design structured VI families that efficiently tackle large population studies. Our main idea is to share the parameterization and learning across the different i.i.d. variables in a generative model -symbolized by the model's $\textit{plates}$. We name this concept $\textit{plate amortization}$. Contrary to off-the-shelf stochastic VI --which slows down inference-- plate amortization results in orders of magnitude faster to train variational distributions. Applied to large-scale hierarchical problems, PAVI yields expressive, parsimoniously parameterized VI with an affordable training time --effectively unlocking inference in those regimes. We illustrate the practical utility of PAVI through a challenging Neuroimaging example featuring 400 million latent parameters, demonstrating a significant step towards scalable and expressive Variational Inference.

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ICLR Conference 2022 Conference Paper

ADAVI: Automatic Dual Amortized Variational Inference Applied To Pyramidal Bayesian Models

Louis Rouillard
Demian Wassermann

Frequently, population studies feature pyramidally-organized data represented using Hierarchical Bayesian Models (HBM) enriched with plates. These models can become prohibitively large in settings such as neuroimaging, where a sample is composed of a functional MRI signal measured on 300 brain locations, across 4 measurement sessions, and 30 subjects, resulting in around 1 million latent parameters. Such high dimensionality hampers the usage of modern, expressive flow-based techniques. To infer parameter posterior distributions in this challenging class of problems, we designed a novel methodology that automatically produces a variational family dual to a target HBM. This variational family, represented as a neural network, consists in the combination of an attention-based hierarchical encoder feeding summary statistics to a set of normalizing flows. Our automatically-derived neural network exploits exchangeability in the plate-enriched HBM and factorizes its parameter space. The resulting architecture reduces by orders of magnitude its parameterization with respect to that of a typical flow-based representation, while maintaining expressivity. Our method performs inference on the specified HBM in an amortized setup: once trained, it can readily be applied to a new data sample to compute the parameters' full posterior. We demonstrate the capability and scalability of our method on simulated data, as well as a challenging high-dimensional brain parcellation experiment. We also open up several questions that lie at the intersection between normalizing flows, SBI, structured Variational Inference, and inference amortization.

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AAAI Conference 2021 Conference Paper

Complex Coordinate-Based Meta-Analysis with Probabilistic Programming

Valentin Iovene
Gaston E Zanitti
Demian Wassermann

With the growing number of published functional magnetic resonance imaging (fMRI) studies, meta-analysis databases and models have become an integral part of brain mapping research. Coordinate-based meta-analysis (CBMA) databases are built by extracting both coordinates of reported peak activations and term associations using natural language processing techniques from neuroimaging studies. Solving termbased queries on these databases makes it possible to obtain statistical maps of the brain related to specific cognitive processes. However, existing tools for analysing CBMA data are limited in their expressivity to propositional logic, restricting the variety of their queries. Moreover, with tools like Neurosynth, term-based queries on multiple terms often lead to power failure, because too few studies from the database contribute to the statistical estimations. We design a probabilistic domain-specific language (DSL) standing on Datalog and one of its probabilistic extensions, CP-Logic, for expressing and solving complex logic-based queries. We show how CBMA databases can be encoded as probabilistic programs. Using the joint distribution of their Bayesian network translation, we show that solutions of queries on these programs compute the right probability distributions of voxel activations. We explain how recent lifted query processing algorithms make it possible to scale to the size of large neuroimaging data, where knowledge compilation techniques fail to solve queries fast enough for practical applications. Finally, we introduce a method for relating studies to terms probabilistically, leading to better solutions for two-term conjunctive queries (CQs) on smaller databases. We demonstrate results for two-term CQs, both on simulated meta-analysis databases and on the widely used Neurosynth database.

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YNIMG Journal 2021 Journal Article

Machine learning based white matter models with permeability: An experimental study in cuprizone treated in-vivo mouse model of axonal demyelination

Ioana Hill
Marco Palombo
Mathieu Santin
Francesca Branzoli
Anne-Charlotte Philippe
Demian Wassermann
Marie-Stephane Aigrot
Bruno Stankoff

The intra-axonal water exchange time (τi), a parameter associated with axonal permeability, could be an important biomarker for understanding and treating demyelinating pathologies such as Multiple Sclerosis. Diffusion-Weighted MRI (DW-MRI) is sensitive to changes in permeability; however, the parameter has so far remained elusive due to the lack of general biophysical models that incorporate it. Machine learning based computational models can potentially be used to estimate such parameters. Recently, for the first time, a theoretical framework using a random forest (RF) regressor suggests that this is a promising new approach for permeability estimation. In this study, we adopt such an approach and for the first time experimentally investigate it for demyelinating pathologies through direct comparison with histology. We construct a computational model using Monte Carlo simulations and an RF regressor in order to learn a mapping between features derived from DW-MRI signals and ground truth microstructure parameters. We test our model in simulations, and find strong correlations between the predicted and ground truth parameters (intra-axonal volume fraction f: R 2 =0. 99, τi: R 2 =0. 84, intrinsic diffusivity d: R2 =0. 99). We then apply the model in-vivo, on a controlled cuprizone (CPZ) mouse model of demyelination, comparing the results from two cohorts of mice, CPZ (N=8) and healthy age-matched wild-type (WT, N=8). We find that the RF model estimates sensible microstructure parameters for both groups, matching values found in literature. Furthermore, we perform histology for both groups using electron microscopy (EM), measuring the thickness of the myelin sheath as a surrogate for exchange time. Histology results show that our RF model estimates are very strongly correlated with the EM measurements (ρ = 0. 98 for f, ρ = 0. 82 for τi ). Finally, we find a statistically significant decrease in τi in all three regions of the corpus callosum (splenium/genu/body) of the CPZ cohort (<τi >=310ms/330ms/350ms) compared to the WT group (<τi>=370ms/370ms/380ms). This is in line with our expectations that τi is lower in regions where the myelin sheath is damaged, as axonal membranes become more permeable. Overall, these results demonstrate, for the first time experimentally and in vivo, that a computational model learned from simulations can reliably estimate microstructure parameters, including the axonal permeability.

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YNIMG Journal 2021 Journal Article

Towards linking diffusion MRI based macro- and microstructure measures with cortico-cortical transmission in brain tumor patients

Patryk Filipiak
Fabien Almairac
Théodore Papadopoulo
Denys Fontaine
Lydiane Mondot
Stéphane Chanalet
Rachid Deriche
Maureen Clerc

We aimed to link macro- and microstructure measures of brain white matter obtained from diffusion MRI with effective connectivity measures based on a propagation of cortico-cortical evoked potentials induced with intrasurgical direct electrical stimulation. For this, we compared streamline lengths and log-transformed ratios of streamlines computed from presurgical diffusion-weighted images, and the delays and amplitudes of N1 peaks recorded intrasurgically with electrocorticography electrodes in a pilot study of 9 brain tumor patients. Our results showed positive correlation between these two modalities in the vicinity of the stimulation sites (Pearson coefficient 0.54±0.13 for N1 delays, and 0.47±0.23 for N1 amplitudes), which could correspond to the neural propagation via U-fibers. In addition, we reached high sensitivities (0.78±0.07) and very high specificities (0.93±0.03) in a binary variant of our comparison. Finally, we used the structural connectivity measures to predict the effective connectivity using a multiple linear regression model, and showed a significant role of brain microstructure-related indices in this relation.

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YNIMG Journal 2020 Journal Article

Diffusion MRI simulation of realistic neurons with SpinDoctor and the Neuron Module

Chengran Fang
Van-Dang Nguyen
Demian Wassermann
Jing-Rebecca Li

The diffusion MRI signal arising from neurons can be numerically simulated by solving the Bloch-Torrey partial differential equation. In this paper we present the Neuron Module that we implemented within the Matlab-based diffusion MRI simulation toolbox SpinDoctor. SpinDoctor uses finite element discretization and adaptive time integration to solve the Bloch-Torrey partial differential equation for general diffusion-encoding sequences, at multiple b-values and in multiple diffusion directions. In order to facilitate the diffusion MRI simulation of realistic neurons by the research community, we constructed finite element meshes for a group of 36 pyramidal neurons and a group of 29 spindle neurons whose morphological descriptions were found in the publicly available neuron repository NeuroMorpho. Org. These finite elements meshes range from having 15, 163 nodes to 622, 553 nodes. We also broke the neurons into the soma and dendrite branches and created finite elements meshes for these cell components. Through the Neuron Module, these neuron and cell components finite element meshes can be seamlessly coupled with the functionalities of SpinDoctor to provide the diffusion MRI signal attributable to spins inside neurons. We make these meshes and the source code of the Neuron Module available to the public as an open-source package. To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated diffusion MRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches, and include a comparison of the high b-value behavior between dendrite branches and whole neurons. In addition, we demonstrate that the neuron meshes can be used to perform Monte-Carlo diffusion MRI simulations as well. We show that at equivalent accuracy, if only one gradient direction needs to be simulated, SpinDoctor is faster than a GPU implementation of Monte-Carlo, but if many gradient directions need to be simulated, there is a break-even point when the GPU implementation of Monte-Carlo becomes faster than SpinDoctor. Furthermore, we numerically compute the eigenfunctions and the eigenvalues of the Bloch-Torrey and the Laplace operators on the neuron geometries using a finite elements discretization, in order to give guidance in the choice of the space and time discretization parameters for both finite elements and Monte-Carlo approaches. Finally, we perform a statistical study on the set of 65 neurons to test some candidate biomakers that can potentially indicate the soma size. This preliminary study exemplifies the possible research that can be conducted using the Neuron Module.

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YNIMG Journal 2020 Journal Article

Fine-grain atlases of functional modes for fMRI analysis

Kamalaker Dadi
Gaël Varoquaux
Antonia Machlouzarides-Shalit
Krzysztof J. Gorgolewski
Demian Wassermann
Bertrand Thirion
Arthur Mensch

Population imaging markedly increased the size of functional-imaging datasets, shedding new light on the neural basis of inter-individual differences. Analyzing these large data entails new scalability challenges, computational and statistical. For this reason, brain images are typically summarized in a few signals, for instance reducing voxel-level measures with brain atlases or functional modes. A good choice of the corresponding brain networks is important, as most data analyses start from these reduced signals. We contribute finely-resolved atlases of functional modes, comprising from 64 to 1024 networks. These dictionaries of functional modes (DiFuMo) are trained on millions of fMRI functional brain volumes of total size 2. 4 TB, spanned over 27 studies and many research groups. We demonstrate the benefits of extracting reduced signals on our fine-grain atlases for many classic functional data analysis pipelines: stimuli decoding from 12, 334 brain responses, standard GLM analysis of fMRI across sessions and individuals, extraction of resting-state functional-connectomes biomarkers for 2500 individuals, data compression and meta-analysis over more than 15, 000 statistical maps. In each of these analysis scenarii, we compare the performance of our functional atlases with that of other popular references, and to a simple voxel-level analysis. Results highlight the importance of using high-dimensional “soft” functional atlases, to represent and analyze brain activity while capturing its functional gradients. Analyses on high-dimensional modes achieve similar statistical performance as at the voxel level, but with much reduced computational cost and higher interpretability. In addition to making them available, we provide meaningful names for these modes, based on their anatomical location. It will facilitate reporting of results.

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NeurIPS Conference 2020 Conference Paper

PEP: Parameter Ensembling by Perturbation

Alireza Mehrtash
Purang Abolmaesumi
Polina Golland
Tina Kapur
Demian Wassermann
William Wells

Ensembling is now recognized as an effective approach for increasing the predictive performance and calibration of deep networks. We introduce a new approach, Parameter Ensembling by Perturbation (PEP), that constructs an ensemble of parameter values as random perturbations of the optimal parameter set from training by a Gaussian with a single variance parameter. The variance is chosen to maximize the log-likelihood of the ensemble average (𝕃) on the validation data set. Empirically, and perhaps surprisingly, 𝕃 has a well-defined maximum as the variance grows from zero (which corresponds to the baseline model). Conveniently, calibration level of predictions also tends to grow favorably until the peak of 𝕃 is reached. In most experiments, PEP provides a small improvement in performance, and, in some cases, a substantial improvement in empirical calibration. We show that this "PEP effect'' (the gain in log-likelihood) is related to the mean curvature of the likelihood function and the empirical Fisher information. Experiments on ImageNet pre-trained networks including ResNet, DenseNet, and Inception showed improved calibration and likelihood. We further observed a mild improvement in classification accuracy on these networks. Experiments on classification benchmarks such as MNIST and CIFAR-10 showed improved calibration and likelihood, as well as the relationship between the PEP effect and overfitting; this demonstrates that PEP can be used to probe the level of overfitting that occurred during training. In general, no special training procedure or network architecture is needed, and in the case of pre-trained networks, no additional training is needed.

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YNIMG Journal 2018 Journal Article

A comparison of three fiber tract delineation methods and their impact on white matter analysis

Valerie J. Sydnor
Ana María Rivas-Grajales
Amanda E. Lyall
Fan Zhang
Sylvain Bouix
Sarina Karmacharya
Martha E. Shenton
Carl-Fredrik Westin

Diffusion magnetic resonance imaging (dMRI) is an important method for studying white matter connectivity in the brain in vivo in both healthy and clinical populations. Improvements in dMRI tractography algorithms, which reconstruct macroscopic three-dimensional white matter fiber pathways, have allowed for methodological advances in the study of white matter; however, insufficient attention has been paid to comparing post-tractography methods that extract white matter fiber tracts of interest from whole-brain tractography. Here we conduct a comparison of three representative and conceptually distinct approaches to fiber tract delineation: 1) a manual multiple region of interest-based approach, 2) an atlas-based approach, and 3) a groupwise fiber clustering approach, by employing methods that exemplify these approaches to delineate the arcuate fasciculus, the middle longitudinal fasciculus, and the uncinate fasciculus in 10 healthy male subjects. We enable qualitative comparisons across methods, conduct quantitative evaluations of tract volume, tract length, mean fractional anisotropy, and true positive and true negative rates, and report measures of intra-method and inter-method agreement. We discuss methodological similarities and differences between the three approaches and the major advantages and drawbacks of each, and review research and clinical contexts for which each method may be most apposite. Emphasis is given to the means by which different white matter fiber tract delineation approaches may systematically produce variable results, despite utilizing the same input tractography and reliance on similar anatomical knowledge.

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YNIMG Journal 2018 Journal Article

Groupwise structural parcellation of the whole cortex: A logistic random effects model based approach

Guillermo Gallardo
William Wells
Rachid Deriche
Demian Wassermann

Current theories hold that brain function is highly related to long-range physical connections through axonal bundles, namely extrinsic connectivity. However, obtaining a groupwise cortical parcellation based on extrinsic connectivity remains challenging. Current parcellation methods are computationally expensive; need tuning of several parameters or rely on ad-hoc constraints. Furthermore, none of these methods present a model for the cortical extrinsic connectivity of the cortex. To tackle these problems, we propose a parsimonious model for the extrinsic connectivity and an efficient parceling technique based on clustering of tractograms. Our technique allows the creation of single subject and groupwise parcellations of the whole cortex. The parcellations obtained with our technique are in agreement with structural and functional parcellations in the literature. In particular, the motor and sensory cortex are subdivided in agreement with the human homunculus of Penfield. We illustrate this by comparing our resulting parcels with the motor strip mapping included in the Human Connectome Project data.

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YNIMG Journal 2016 Journal Article

MAPL: Tissue microstructure estimation using Laplacian-regularized MAP-MRI and its application to HCP data

Rutger H.J. Fick
Demian Wassermann
Emmanuel Caruyer
Rachid Deriche

The recovery of microstructure-related features of the brain's white matter is a current challenge in diffusion MRI. To robustly estimate these important features from multi-shell diffusion MRI data, we propose to analytically regularize the coefficient estimation of the Mean Apparent Propagator (MAP)-MRI method using the norm of the Laplacian of the reconstructed signal. We first compare our approach, which we call MAPL, with competing, state-of-the-art functional basis approaches. We show that it outperforms the original MAP-MRI implementation and the recently proposed modified Spherical Polar Fourier (mSPF) basis with respect to signal fitting and reconstruction of the Ensemble Average Propagator (EAP) and Orientation Distribution Function (ODF) in noisy, sparsely sampled data of a physical phantom with reference gold standard data. Then, to reduce the variance of parameter estimation using multi-compartment tissue models, we propose to use MAPL's signal fitting and extrapolation as a preprocessing step. We study the effect of MAPL on the estimation of axon diameter using a simplified Axcaliber model and axonal dispersion using the Neurite Orientation Dispersion and Density Imaging (NODDI) model. We show the positive effect of using it as a preprocessing step in estimating and reducing the variances of these parameters in the Corpus Callosum of six different subjects of the MGH Human Connectome Project. Finally, we correlate the estimated axon diameter, dispersion and restricted volume fractions with Fractional Anisotropy (FA) and clearly show that changes in FA significantly correlate with changes in all estimated parameters. Overall, we illustrate the potential of using a well-regularized functional basis together with multi-compartment approaches to recover important microstructure tissue parameters with much less variability, thus contributing to the challenge of better understanding microstructure-related features of the brain's white matter.

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YNIMG Journal 2015 Journal Article

Robust and efficient linear registration of white-matter fascicles in the space of streamlines

Eleftherios Garyfallidis
Omar Ocegueda
Demian Wassermann
Maxime Descoteaux

The neuroscientific community today is very much interested in analyzing specific white matter bundles like the arcuate fasciculus, the corticospinal tract, or the recently discovered Aslant tract to study sex differences, lateralization and many other connectivity applications. For this reason, experts spend time manually segmenting these fascicles and bundles using streamlines obtained from diffusion MRI tractography. However, to date, there are very few computational tools available to register these fascicles directly so that they can be analyzed and their differences quantified across populations. In this paper, we introduce a novel, robust and efficient framework to align bundles of streamlines directly in the space of streamlines. We call this framework Streamline-based Linear Registration. We first show that this method can be used successfully to align individual bundles as well as whole brain streamlines. Additionally, if used as a piecewise linear registration across many bundles, we show that our novel method systematically provides higher overlap (Jaccard indices) than state-of-the-art nonlinear image-based registration in the white matter. We also show how our novel method can be used to create bundle-specific atlases in a straightforward manner and we give an example of a probabilistic atlas construction of the optic radiation. In summary, Streamline-based Linear Registration provides a solid registration framework for creating new methods to study the white matter and perform group-level tractometry analysis.

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