title: A multiple hold-out framework for Sparse Partial Least Squares.
abstract: Supervised classification machine learning algorithms may have limitations when studying brain diseases with heterogeneous populations, as the labels might be unreliable. More exploratory approaches, such as Sparse Partial Least Squares (SPLS), may provide insights into the brain's mechanisms by finding relationships between neuroimaging and clinical/demographic data. The identification of these relationships has the potential to improve the current understanding of disease mechanisms, refine clinical assessment tools, and stratify patients. SPLS finds multivariate associative effects in the data by computing pairs of sparse weight vectors, where each pair is used to remove its corresponding associative effect from the data by matrix deflation, before computing additional pairs.
  
  
  
  We propose a novel SPLS framework which selects the adequate number of voxels and clinical variables to describe each associative effect, and tests their reliability by fitting the model to different splits of the data. As a proof of concept, the approach was applied to find associations between grey matter probability maps and individual items of the Mini-Mental State Examination (MMSE) in a clinical sample with various degrees of dementia.
  
  
  
  The framework found two statistically significant associative effects between subsets of brain voxels and subsets of the questions/tasks.
  
  
  
  SPLS was compared with its non-sparse version (PLS). The use of projection deflation versus a classical PLS deflation was also tested in both PLS and SPLS.
  
  
  
  SPLS outperformed PLS, finding statistically significant effects and providing higher correlation values in hold-out data. Moreover, projection deflation provided better results.
authors.affiliation: Department of Computer Science, University College London, London, UK; Max Planck University College London Centre for Computational Psychiatry and Ageing Research, University College London, London, UK. Electronic address: joao.monteiro@ucl.ac.uk.
authors.forename: João M
authors.initials: JM
authors.lastname: Monteiro
authors.affiliation: Department of Computer Science, University College London, London, UK; Max Planck University College London Centre for Computational Psychiatry and Ageing Research, University College London, London, UK.
authors.forename: Anil
authors.initials: A
authors.lastname: Rao
authors.affiliation: Department of Computer Science, University College London, London, UK.
authors.forename: John
authors.initials: J
authors.lastname: Shawe-Taylor
authors.affiliation: Department of Computer Science, University College London, London, UK; Max Planck University College London Centre for Computational Psychiatry and Ageing Research, University College London, London, UK.
authors.forename: Janaina
authors.initials: J
authors.lastname: Mourão-Miranda
mesh_terms: D000368:Aged; D001921:Brain / Q000000981:diagnostic imaging; D003704:Dementia / Q000175:diagnosis; D005260:Female; D066128:Gray Matter / Q000000981:diagnostic imaging; D006801:Humans; D016018:Least-Squares Analysis; D000069550:Machine Learning; D008279:Magnetic Resonance Imaging; D008297:Male; D008609:Mental Status Schedule; D015999:Multivariate Analysis
keywords: Dementia; Machine learning; Mini-Mental State Examination; Neuroimaging; Partial Least Squares; Sparse methods