Search results for "SPARSITY"
showing 4 items of 14 documents
On the sign recovery by LASSO, thresholded LASSO and thresholded Basis Pursuit Denoising
2020
Basis Pursuit (BP), Basis Pursuit DeNoising (BPDN), and LASSO are popular methods for identifyingimportant predictors in the high-dimensional linear regression model Y = Xβ + ε. By definition, whenε = 0, BP uniquely recovers β when Xβ = Xb and β different than b implies L1 norm of β is smaller than the L1 norm of b (identifiability condition). Furthermore, LASSO can recover the sign of β only under a much stronger irrepresentability condition. Meanwhile, it is known that the model selection properties of LASSO can be improved by hard-thresholdingits estimates. This article supports these findings by proving that thresholded LASSO, thresholded BPDNand thresholded BP recover the sign of β in …
Shift-Invariant Canonical Polyadic Decomposition of Complex-Valued Multi-Subject fMRI Data with a Phase Sparsity Constraint
2020
Canonical polyadic decomposition (CPD) of multi-subject complex-valued fMRI data can be used to provide spatially and temporally shared components among groups with both magnitude and phase information. However, the CPD model is not well formulated due to the large subject variability in the spatial and temporal modalities, as well as the high noise level in complex-valued fMRI data. Considering that the shift-invariant CPD can model temporal variability across subjects, we propose to further impose a phase sparsity constraint on the shared spatial maps to denoise the complex-valued components and to model the inter-subject spatial variability as well. More precisely, subject-specific time …
Sparse relative risk survival modelling
2016
Cancer survival is thought to closed linked to the genimic constitution of the tumour. Discovering such signatures will be useful in the diagnosis of the patient and may be used for treatment decisions and perhaps even the development of new treatments. However, genomic data are typically noisy and high-dimensional, often outstripping the number included in the study. Regularized survival models have been proposed to deal with such scenary. These methods typically induce sparsity by means of a coincidental match of the geometry of the convex likelihood and (near) non-convex regularizer.
Using Differential Geometry for Sparse High-Dimensional Risk Regression Models
2023
With the introduction of high-throughput technologies in clinical and epidemiological studies, the need for inferential tools that are able to deal with fat data-structures, i.e., relatively small number of observations compared to the number of features, is becoming more prominent. In this paper we propose an extension of the dgLARS method to high-dimensional risk regression models. The main idea of the proposed method is to use the differential geometric structure of the partial likelihood function in order to select the optimal subset of covariates.