43 research outputs found
FAASTA: A fast solver for total-variation regularization of ill-conditioned problems with application to brain imaging
The total variation (TV) penalty, as many other analysis-sparsity problems,
does not lead to separable factors or a proximal operatorwith a closed-form
expression, such as soft thresholding for the penalty. As a result,
in a variational formulation of an inverse problem or statisticallearning
estimation, it leads to challenging non-smooth optimization problemsthat are
often solved with elaborate single-step first-order methods. When thedata-fit
term arises from empirical measurements, as in brain imaging, it isoften very
ill-conditioned and without simple structure. In this situation, in proximal
splitting methods, the computation cost of thegradient step can easily dominate
each iteration. Thus it is beneficialto minimize the number of gradient
steps.We present fAASTA, a variant of FISTA, that relies on an internal solver
forthe TV proximal operator, and refines its tolerance to balance
computationalcost of the gradient and the proximal steps. We give benchmarks
andillustrations on "brain decoding": recovering brain maps from
noisymeasurements to predict observed behavior. The algorithm as well as
theempirical study of convergence speed are valuable for any non-exact
proximaloperator, in particular analysis-sparsity problems
An Adversarial Robustness Perspective on the Topology of Neural Networks
In this paper, we investigate the impact of neural networks (NNs) topology on
adversarial robustness. Specifically, we study the graph produced when an input
traverses all the layers of a NN, and show that such graphs are different for
clean and adversarial inputs. We find that graphs from clean inputs are more
centralized around highway edges, whereas those from adversaries are more
diffuse, leveraging under-optimized edges. Through experiments on a variety of
datasets and architectures, we show that these under-optimized edges are a
source of adversarial vulnerability and that they can be used to detect
adversarial inputs
Total Variation meets Sparsity: statistical learning with segmenting penalties
International audiencePrediction from medical images is a valuable aid to diagnosis. For instance, anatomical MR images can reveal certain disease conditions, while their functional counterparts can predict neuropsychi-atric phenotypes. However, a physician will not rely on predictions by black-box models: understanding the anatomical or functional features that underpin decision is critical. Generally, the weight vectors of clas-sifiers are not easily amenable to such an examination: Often there is no apparent structure. Indeed, this is not only a prediction task, but also an inverse problem that calls for adequate regularization. We address this challenge by introducing a convex region-selecting penalty. Our penalty combines total-variation regularization, enforcing spatial conti-guity, and 1 regularization, enforcing sparsity, into one group: Voxels are either active with non-zero spatial derivative or zero with inactive spatial derivative. This leads to segmenting contiguous spatial regions (inside which the signal can vary freely) against a background of zeros. Such segmentation of medical images in a target-informed manner is an important analysis tool. On several prediction problems from brain MRI, the penalty shows good segmentation. Given the size of medical images, computational efficiency is key. Keeping this in mind, we contribute an efficient optimization scheme that brings significant computational gains