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Jonathan Taylor

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12 papers
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12

AAAI Conference 2016 Conference Paper

Learning Step Size Controllers for Robust Neural Network Training

  • Christian Daniel
  • Jonathan Taylor
  • Sebastian Nowozin

This paper investigates algorithms to automatically adapt the learning rate of neural networks (NNs). Starting with stochastic gradient descent, a large variety of learning methods has been proposed for the NN setting. However, these methods are usually sensitive to the initial learning rate which has to be chosen by the experimenter. We investigate several features and show how an adaptive controller can adjust the learning rate without prior knowledge of the learning problem at hand.

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NeurIPS Conference 2015 Conference Paper

Evaluating the statistical significance of biclusters

  • Jason Lee
  • Yuekai Sun
  • Jonathan Taylor

Biclustering (also known as submatrix localization) is a problem of high practical relevance in exploratory analysis of high-dimensional data. We develop a framework for performing statistical inference on biclusters found by score-based algorithms. Since the bicluster was selected in a data dependent manner by a biclustering or localization algorithm, this is a form of selective inference. Our framework gives exact (non-asymptotic) confidence intervals and p-values for the significance of the selected biclusters. Further, we generalize our approach to obtain exact inference for Gaussian statistics.

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NeurIPS Conference 2014 Conference Paper

Exact Post Model Selection Inference for Marginal Screening

  • Jason Lee
  • Jonathan Taylor

We develop a framework for post model selection inference, via marginal screening, in linear regression. At the core of this framework is a result that characterizes the exact distribution of linear functions of the response $y$, conditional on the model being selected (``condition on selection framework). This allows us to construct valid confidence intervals and hypothesis tests for regression coefficients that account for the selection procedure. In contrast to recent work in high-dimensional statistics, our results are exact (non-asymptotic) and require no eigenvalue-like assumptions on the design matrix $X$. Furthermore, the computational cost of marginal regression, constructing confidence intervals and hypothesis testing is negligible compared to the cost of linear regression, thus making our methods particularly suitable for extremely large datasets. Although we focus on marginal screening to illustrate the applicability of the condition on selection framework, this framework is much more broadly applicable. We show how to apply the proposed framework to several other selection procedures including orthogonal matching pursuit and marginal screening+Lasso. "

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NeurIPS Conference 2013 Conference Paper

On model selection consistency of penalized M-estimators: a geometric theory

  • Jason Lee
  • Yuekai Sun
  • Jonathan Taylor

Penalized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure. Often, the penalties are \emph{geometrically decomposable}, \ie\ can be expressed as a sum of (convex) support functions. We generalize the notion of irrepresentable to geometrically decomposable penalties and develop a general framework for establishing consistency and model selection consistency of M-estimators with such penalties. We then use this framework to derive results for some special cases of interest in bioinformatics and statistical learning.

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NeurIPS Conference 2008 Conference Paper

Bounding Performance Loss in Approximate MDP Homomorphisms

  • Jonathan Taylor
  • Doina Precup
  • Prakash Panagaden

We define a metric for measuring behavior similarity between states in a Markov decision process (MDP), in which action similarity is taken into account. We show that the kernel of our metric corresponds exactly to the classes of states defined by MDP homomorphisms (Ravindran & Barto, 2003). We prove that the difference in the optimal value function of different states can be upper-bounded by the value of this metric, and that the bound is tighter than that provided by bisimulation metrics (Ferns et al. 2004, 2005). Our results hold both for discrete and for continuous actions. We provide an algorithm for constructing approximate homomorphisms, by using this metric to identify states that can be grouped together, as well as actions that can be matched. Previous research on this topic is based mainly on heuristics.

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YNIMG Journal 2003 Journal Article

Deformation-based surface morphometry applied to gray matter deformation

  • Moo K. Chung
  • Keith J. Worsley
  • Steve Robbins
  • Tomáš Paus
  • Jonathan Taylor
  • Jay N. Giedd
  • Judith L. Rapoport
  • Alan C. Evans

We present a unified statistical approach to deformation-based morphometry applied to the cortical surface. The cerebral cortex has the topology of a 2D highly convoluted sheet. As the brain develops over time, the cortical surface area, thickness, curvature, and total gray matter volume change. It is highly likely that such age-related surface changes are not uniform. By measuring how such surface metrics change over time, the regions of the most rapid structural changes can be localized. We avoided using surface flattening, which distorts the inherent geometry of the cortex in our analysis and it is only used in visualization. To increase the signal to noise ratio, diffusion smoothing, which generalizes Gaussian kernel smoothing to an arbitrary curved cortical surface, has been developed and applied to surface data. Afterward, statistical inference on the cortical surface will be performed via random fields theory. As an illustration, we demonstrate how this new surface-based morphometry can be applied in localizing the cortical regions of the gray matter tissue growth and loss in the brain images longitudinally collected in the group of children and adolescents.

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YNIMG Journal 2003 Journal Article

Statistical mapping analysis of lesion location and neurological disability in multiple sclerosis: application to 452 patient data sets

  • Arnaud Charil
  • Alex P Zijdenbos
  • Jonathan Taylor
  • Cyrus Boelman
  • Keith J Worsley
  • Alan C Evans
  • Alain Dagher

In multiple sclerosis (MS), the correlation between disability and the volume of white matter lesions on magnetic resonance imaging (MRI) is usually weak. This may be because lesion location also influences the extent and type of functional disability. We applied an automatic lesion-detection algorithm to 452 MRI scans of patients with relapsing-remitting MS to identify the regions preferentially responsible for different types of clinical deficits. Statistical parametric maps were generated by performing voxel-wise linear regressions between lesion probability and different clinical disability scores. There was a clear distinction between lesion locations causing physical and cognitive disability. Lesion likelihood correlated with the Expanded Disability Status Scale (EDSS) in the left internal capsule and in periventricular white matter mostly in the left hemisphere. Pyramidal deficits correlated with only one area in the left internal capsule that was also present in the EDSS correlation. Cognitive dysfunction correlated with lesion location at the grey-white junction of associative, limbic, and prefrontal cortex. Coordination impairment correlated with areas in interhemispheric and pyramidal periventricular white matter tracts, and in the inferior and superior longitudinal fascicles. Bowel and bladder scores correlated with lesions in the medial frontal lobes, cerebellum, insula, dorsal midbrain, and pons, areas known to be involved in the control of micturition. This study demonstrates for the first time a relationship between the site of lesions and the type of disability in large scale MRI data set in MS.

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v2026.09.13