A forward modeling approach to analyzing galaxy clustering with SimBIG.

We present cosmological constraints from a simulation-based inference (SBI) analysis of galaxy clustering from the SimBIG forward modeling framework. SimBIG leverages the predictive power of high-fidelity simulations and provides an inference framework that can extract cosmological information on small nonlinear scales. In this work, we apply SimBIG to the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS galaxy sample and analyze the power spectrum, [Formula: see text], to [Formula: see text]. We construct 20,000 simulated galaxy samples using our forward model, which is based on 2,000 high-resolution Quijote[Formula: see text]-body simulations and includes detailed survey realism for a more complete treatment of observational systematics. We then conduct SBI by training normalizing flows using the simulated samples and infer the posterior distribution of [Formula: see text]CDM cosmological parameters: [Formula: see text]. We derive significant constraints on [Formula: see text] and [Formula: see text], which are consistent with previous works. Our constraint on [Formula: see text] is 27% more precise than standard [Formula: see text] analyses because we exploit additional cosmological information on nonlinear scales beyond the limit of current analytic models, [Formula: see text]. This improvement is equivalent to the statistical gain expected from a standard [Formula: see text] analysis of galaxy sample [Formula: see text]60% larger than CMASS. While we focus on [Formula: see text] in this work for validation and comparison to the literature, SimBIG provides a framework for analyzing galaxy clustering using any summary statistic. We expect further improvements on cosmological constraints from subsequent SimBIG analyses of summary statistics beyond [Formula: see text].

Population heterogeneity in clinical cohorts affects the predictive accuracy of brain imaging.

Brain imaging research enjoys increasing adoption of supervised machine learning for single-participant disease classification. Yet, the success of these algorithms likely depends on population diversity, including demographic differences and other factors that may be outside of primary scientific interest. Here, we capitalize on propensity scores as a composite confound index to quantify diversity due to major sources of population variation. We delineate the impact of population heterogeneity on the predictive accuracy and pattern stability in 2 separate clinical cohorts: the Autism Brain Imaging Data Exchange (ABIDE, n = 297) and the Healthy Brain Network (HBN, n = 551). Across various analysis scenarios, our results uncover the extent to which cross-validated prediction performances are interlocked with diversity. The instability of extracted brain patterns attributable to diversity is located preferentially in regions part of the default mode network. Collectively, our findings highlight the limitations of prevailing deconfounding practices in mitigating the full consequences of population diversity.

Feature-space selection with banded ridge regression.

Encoding models provide a powerful framework to identify the information represented in brain recordings. In this framework, a stimulus representation is expressed within a feature space and is used in a regularized linear regression to predict brain activity. To account for a potential complementarity of different feature spaces, a joint model is fit on multiple feature spaces simultaneously. To adapt regularization strength to each feature space, ridge regression is extended to banded ridge regression, which optimizes a different regularization hyperparameter per feature space. The present paper proposes a method to decompose over feature spaces the variance explained by a banded ridge regression model. It also describes how banded ridge regression performs a feature-space selection, effectively ignoring non-predictive and redundant feature spaces. This feature-space selection leads to better prediction accuracy and to better interpretability. Banded ridge regression is then mathematically linked to a number of other regression methods with similar feature-space selection mechanisms. Finally, several methods are proposed to address the computational challenge of fitting banded ridge regressions on large numbers of voxels and feature spaces. All implementations are released in an open-source Python package called Himalaya.

Solid harmonic wavelet scattering for predictions of molecule properties.

We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory (DFT). Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which we compute invariant "solid harmonic scattering coefficients" that account for different types of interactions at different scales. Multilinear regressions of various physical properties of molecules are computed from these invariant coefficients. Numerical experiments show that these regressions have near state-of-the-art performance, even with relatively few training examples. Predictions over small sets of scattering coefficients can reach a DFT precision while being interpretable.

Seeing it all: Convolutional network layers map the function of the human visual system.

Convolutional networks used for computer vision represent candidate models for the computations performed in mammalian visual systems. We use them as a detailed model of human brain activity during the viewing of natural images by constructing predictive models based on their different layers and BOLD fMRI activations. Analyzing the predictive performance across layers yields characteristic fingerprints for each visual brain region: early visual areas are better described by lower level convolutional net layers and later visual areas by higher level net layers, exhibiting a progression across ventral and dorsal streams. Our predictive model generalizes beyond brain responses to natural images. We illustrate this on two experiments, namely retinotopy and face-place oppositions, by synthesizing brain activity and performing classical brain mapping upon it. The synthesis recovers the activations observed in the corresponding fMRI studies, showing that this deep encoding model captures representations of brain function that are universal across experimental paradigms.

Formal Models of the Network Co-occurrence Underlying Mental Operations.

Systems neuroscience has identified a set of canonical large-scale networks in humans. These have predominantly been characterized by resting-state analyses of the task-unconstrained, mind-wandering brain. Their explicit relationship to defined task performance is largely unknown and remains challenging. The present work contributes a multivariate statistical learning approach that can extract the major brain networks and quantify their configuration during various psychological tasks. The method is validated in two extensive datasets (n = 500 and n = 81) by model-based generation of synthetic activity maps from recombination of shared network topographies. To study a use case, we formally revisited the poorly understood difference between neural activity underlying idling versus goal-directed behavior. We demonstrate that task-specific neural activity patterns can be explained by plausible combinations of resting-state networks. The possibility of decomposing a mental task into the relative contributions of major brain networks, the "network co-occurrence architecture" of a given task, opens an alternative access to the neural substrates of human cognition.

Data-driven HRF estimation for encoding and decoding models.

Despite the common usage of a canonical, data-independent, hemodynamic response function (HRF), it is known that the shape of the HRF varies across brain regions and subjects. This suggests that a data-driven estimation of this function could lead to more statistical power when modeling BOLD fMRI data. However, unconstrained estimation of the HRF can yield highly unstable results when the number of free parameters is large. We develop a method for the joint estimation of activation and HRF by means of a rank constraint, forcing the estimated HRF to be equal across events or experimental conditions, yet permitting it to differ across voxels. Model estimation leads to an optimization problem that we propose to solve with an efficient quasi-Newton method, exploiting fast gradient computations. This model, called GLM with Rank-1 constraint (R1-GLM), can be extended to the setting of GLM with separate designs which has been shown to improve decoding accuracy in brain activity decoding experiments. We compare 10 different HRF modeling methods in terms of encoding and decoding scores on two different datasets. Our results show that the R1-GLM model outperforms competing methods in both encoding and decoding settings, positioning it as an attractive method both from the points of view of accuracy and computational efficiency.

Individual Brain Charting dataset extension, third release for movie watching and retinotopy data.

The Individual Brain Charting (IBC) is a multi-task functional Magnetic Resonance Imaging dataset acquired at high spatial-resolution and dedicated to the cognitive mapping of the human brain. It consists in the deep phenotyping of twelve individuals, covering a broad range of psychological domains suitable for functional-atlasing applications. Here, we present the inclusion of task data from both naturalistic stimuli and trial-based designs, to uncover structures of brain activation. We rely on the Fast Shared Response Model (FastSRM) to provide a data-driven solution for modelling naturalistic stimuli, typically containing many features. We show that data from left-out runs can be reconstructed using FastSRM, enabling the extraction of networks from the visual, auditory and language systems. We also present the topographic organization of the visual system through retinotopy. In total, six new tasks were added to IBC, wherein four trial-based retinotopic tasks contributed with a mapping of the visual field to the cortex. IBC is open access: source plus derivatives imaging data and meta-data are available in public repositories.

Characterizing responses of translation-invariant neurons to natural stimuli: maximally informative invariant dimensions.

The human visual system is capable of recognizing complex objects even when their appearances change drastically under various viewing conditions. Especially in the higher cortical areas, the sensory neurons reflect such functional capacity in their selectivity for complex visual features and invariance to certain object transformations, such as image translation. Due to the strong nonlinearities necessary to achieve both the selectivity and invariance, characterizing and predicting the response patterns of these neurons represents a formidable computational challenge. A related problem is that such neurons are poorly driven by randomized inputs, such as white noise, and respond strongly only to stimuli with complex high-order correlations, such as natural stimuli. Here we describe a novel two-step optimization technique that can characterize both the shape selectivity and the range and coarseness of position invariance from neural responses to natural stimuli. One step in the optimization is finding the template as the maximally informative dimension given the estimated spatial location where the response could have been triggered within each image. The estimates of the locations that triggered the response are updated in the next step. Under the assumption of a monotonic relationship between the firing rate and stimulus projections on the template at a given position, the most likely location is the one that has the largest projection on the estimate of the template. The algorithm shows quick convergence during optimization, and the estimation results are reliable even in the regime of small signal-to-noise ratios. When we apply the algorithm to responses of complex cells in the primary visual cortex (V1) to natural movies, we find that responses of the majority of cells were significantly better described by translation-invariant models based on one template compared with position-specific models with several relevant features.

Arrhythmia classification of 12-lead and reduced-lead electrocardiograms via recurrent networks, scattering, and phase harmonic correlation.

We describe an automatic classifier of arrhythmias based on 12-lead and reduced-lead electrocardiograms. Our classifier comprises four modules: scattering transform (ST), phase harmonic correlation (PHC), depthwise separable convolutions (DSC), and a long short-term memory (LSTM) network. It is trained on PhysioNet/Computing in Cardiology Challenge 2021 data. The ST captures short-term temporal ECG modulations while the PHC characterizes the phase dependence of coherent ECG components. Both reduce the sampling rate to a few samples per typical heart beat. We pass the output of the ST and PHC to a depthwise-separable convolution layer (DSC) which combines lead responses separately for each ST or PHC coefficient and then combines resulting values across all coefficients. At a deeper level, two LSTM layers integrate local variations of the input over long time scales. We train in an end-to-end fashion as a multilabel classification problem with a normal and 25 arrhythmia classes. Lastly, we use canonical correlation analysis (CCA) for transfer learning from 12-lead ST and PHC representations to reduced-lead ones. After local cross-validation on the public data from the challenge, our team 'BitScattered' achieved the following results: 0.682 ± 0.0095 for 12-lead; 0.666 ± 0.0257 for 6-lead; 0.674 ± 0.0185 for 4-lead; 0.661 ± 0.0098 for 3-lead; and 0.662 ± 0.0151 for 2-lead.

Hierarchical Region-Network Sparsity for High-Dimensional Inference in Brain Imaging.

Structured sparsity penalization has recently improved statistical models applied to high-dimensional data in various domains. As an extension to medical imaging, the present work incorporates priors on network hierarchies of brain regions into logistic-regression to distinguish neural activity effects. These priors bridge two separately studied levels of brain architecture: functional segregation into regions and functional integration by networks. Hierarchical region-network priors are shown to better classify and recover 18 psychological tasks than other sparse estimators. Varying the relative importance of region and network structure within the hierarchical tree penalty captured complementary aspects of the neural activity patterns. Local and global priors of neurobiological knowledge are thus demonstrated to offer advantages in generalization performance, sample complexity, and domain interpretability.

Machine learning for neuroimaging with scikit-learn.

Statistical machine learning methods are increasingly used for neuroimaging data analysis. Their main virtue is their ability to model high-dimensional datasets, e.g., multivariate analysis of activation images or resting-state time series. Supervised learning is typically used in decoding or encoding settings to relate brain images to behavioral or clinical observations, while unsupervised learning can uncover hidden structures in sets of images (e.g., resting state functional MRI) or find sub-populations in large cohorts. By considering different functional neuroimaging applications, we illustrate how scikit-learn, a Python machine learning library, can be used to perform some key analysis steps. Scikit-learn contains a very large set of statistical learning algorithms, both supervised and unsupervised, and its application to neuroimaging data provides a versatile tool to study the brain.