Decoding, i.e. prediction from brain images or signals, calls for empirical evaluation of its predictive power. Such evaluation is achieved via cross-validation, a method also used to tune decoders' hyper-parameters. This paper is a review on cross-validation procedures for decoding in neuroimaging. It includes a didactic overview of the relevant theoretical considerations. Practical aspects are highlighted with an extensive empirical study of the common decoders in within- and across-subject predictions, on multiple datasets -anatomical and functional MRI and MEG- and simulations. Theory and experiments outline that the popular "leave-one-out" strategy leads to unstable and biased estimates, and a repeated random splits method should be preferred. Experiments outline the large error bars of cross-validation in neuroimaging settings: typical confidence intervals of 10%. Nested cross-validation can tune decoders' parameters while avoiding circularity bias. However we find that it can be favorable to use sane defaults, in particular for non-sparse decoders.
In this work, we revisit fast dimension reduction approaches, as with random projections and random sampling. Our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis. Such dimension reduction can be very efficient when the signals of interest have a strong structure, such as with images. We focus on this setting and investigate feature clustering schemes for data reductions that capture this structure. An impediment to fast dimension reduction is then that good clustering comes with large algorithmic costs. We address it by contributing a linear-time agglomerative clustering scheme, Recursive Nearest Agglomeration (ReNA). Unlike existing fast agglomerative schemes, it avoids the creation of giant clusters. We empirically validate that it approximates the data as well as traditional variance-minimizing clustering schemes that have a quadratic complexity. In addition, we analyze signal approximation with feature clustering and show that it can remove noise, improving subsequent analysis steps. As a consequence, data reduction by clustering features with ReNA yields very fast and accurate models, enabling to process large datasets on budget. Our theoretical analysis is backed by extensive experiments on publicly-available data that illustrate the computation efficiency and the denoising properties of the resulting dimension reduction scheme.
Abstract-The identification of image regions associated with external variables through discriminative approaches yields illposed estimation problems. This estimation challenge can be tackled by imposing sparse solutions. However, the sensitivity of sparse estimators to correlated variables leads to nonreproducible results, and only a subset of the important variables are selected. In this paper, we explore an approach based on bagging clustering-based data compression in order to alleviate the instability of sparse models. Specifically, we design a new framework in which the estimator is built by averaging multiple models estimated after feature clustering, to improve the conditioning of the model. We show that this combination of model averaging with spatially consistent compression can have the virtuous effect of increasing the stability of the weight maps, allowing a better interpretation of the results. Finally, we demonstrate the benefit of our approach on several predictive modeling problems.
Brain decoding relates behavior to brain activity through predictive models. These are also used to identify brain regions involved in the cognitive operations related to the observed behavior. Training such multivariate models is a high-dimensional statistical problem that calls for suitable priors. State of the art priors -eg small total-variation- enforce spatial structure on the maps to stabilize them and improve prediction. However, they come with a hefty computational cost. We build upon very fast dimension reduction with spatial structure and model ensembling to achieve decoders that are fast on large datasets and increase the stability of the predictions and the maps. Our approach, fast regularized ensemble of models (FReM), includes an implicit spatial regularization by using a voxel grouping with a fast clustering algorithm. In addition, it aggregates different estimators obtained across splits of a cross-validation loop, each time keeping the best possible model. Experiments on a large number of brain imaging datasets show that our combination of voxel clustering and model ensembling improves decoding maps stability and reduces the variance of prediction accuracy. Importantly, our method requires less samples than state-of-the-art methods to achieve a given level of prediction accuracy. Finally, FreM is much faster than other spatially-regularized methods and, in addition, it can better exploit parallel computing resources.
Abstract-In neuroimaging, multi-subject statistical analysis is an essential step, as it makes it possible to draw conclusions for the population under study. However, the lack of power in neuroimaging studies combined with the lack of stability and sensitivity of voxel-based methods may lead to non-reproducible results. A method designed to tackle this problem is Randomized Parcellation-Based Inference (RPBI), which has shown good empirical performance. Nevertheless, the use of an agglomerative clustering algorithm proposed in the initial RPBI formulation to build the parcellations entails a large computation cost. In this paper, we explore two strategies to speedup RPBI: Firstly, we use a fast clustering algorithm called Recursive Nearest Agglomeration (ReNA), to find the parcellations. Secondly, we consider the aggregation of p-values over multiple parcellations to avoid a permutation test. We evaluate their the computation time, as well as their recovery performance. As a main conclusion, we advocate the use of (permuted) RPBI with ReNA, as it yields very fast models, while keeping the performance of slower methods.
Optimal transport (OT)-based methods have a wide range of applications and have attracted a tremendous amount of attention in recent years. However, most of the computational approaches of OT do not learn the underlying transport map. Although some algorithms have been proposed to learn this map, they rely on kernel-based methods, which makes them prohibitively slow when the number of samples increases. Here, we propose a way to learn an approximate transport map and a parametric approximation of the Wasserstein barycenter. We build an approximated transport mapping by leveraging the closed-form of Gaussian (Bures-Wasserstein) transport; we compute local transport plans between matched pairs of the Gaussian components of each density. The learned map generalizes to out-of-sample examples. We provide experimental results on simulated and real data, comparing our proposed method with other mapping estimation algorithms. Preliminary experiments suggest that our proposed method is not only faster, with a factor 80 overall running time, but it also requires fewer components than state-of-the-art methods to recover the support of the barycenter. From a practical standpoint, it is straightforward to implement and can be used with a conventional machine learning pipeline.
Abstract-Machine learning from brain images is a central tool for image-based diagnosis and diseases characterization. Predicting behavior from functional imaging, brain decoding, analyzes brain activity in terms of the behavior that it implies. While these multivariate techniques are becoming standard brain mapping tools, like mass-univariate analysis, they entail much larger computational costs. In an time of growing data sizes, with larger cohorts and higher-resolutions imaging, this cost is increasingly a burden. Here we consider the use of random sampling and projections as fast data approximation techniques for brain images. We evaluate their prediction accuracy and computation time on various datasets and discrimination tasks. We show that the weight maps obtained after random sampling are highly consistent with those obtained with the whole feature space, while having a fair prediction performance. Altogether, we present the practical advantage of random sampling methods in neuroimaging, showing a simple way to embed back the reduced coefficients, with only a small loss of information.
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