Spatiotemporal Anatomical Atlas Building
|
|
|
- Elvin Simon
- 5 years ago
- Views:
Transcription
1 Spatiotemporal Anatomical Atlas Building Population Shape Regression For Random Design Data Brad Davis 1, P. Thomas Fletcher 2, Elizabeth Bullitt 1, Sarang Joshi 2 1 The University of North Carolina at Chapel Hill 2 Scientific Computing and Imaging Institute The University of Utah
2 Population Shape Regression 84 Healthy Individuals Age Mortemet et al. Regression in Vector Space Regression on a Shape Manifold 2/36 MICCAI 2007
3 Detailed Anatomical Regression Infer average structural changes Improve understanding of anatomy Indicated in disease detection, understanding Age 3/36 MICCAI 2007
4 Related Work Large-deformation Diffeomorphic 3D Image Matching Younes, Trouve, Joshi, Beg, Avants, Gee, Miller Longitudinal shape change models for individuals Beg, Miller [03, 04]; Clatz et al. [05]; Tompson, Toga eg. [00] Large-deformation Intrinsic Mean Images Avants & Gee [04]; Davis, Lorenzen, Joshi [04,05]; Pennec [06] Regression of scalar function on manifold Nilsson, Sha, Jordan [07] Regression of spherical data Jupp & Kent [87] 4/36 MICCAI 2007
5 Our Work Average anatomical change for population, not individual Anatomical change via large-deformation diffeomorphic transformations Predictor: vector space (e.g., time); Response: point on manifold 5/36 MICCAI 2007
6 Outline Anatomical Shape Change Via Image Mapping Manifold, Intrinsic Mean Nadaraya-Watson Regression Estimator Manifold Kernel Regression Synthetic example Application: Healthy brain aging 6/36 MICCAI 2007
7 Review: Capturing Anatomical Shape Change Detailed local changes via diffeomorphic transformations of underlying coordinate system Ω R 3 Diffeomorphism: smooth mapping with smooth inverse Diff(Ω) h:ω Ω 7/36 MICCAI 2007
8 Review: Capturing Anatomical Shape Change Manifold structure, not vector space: addition is not defined h 1,h 2 Diff(Ω):g=h 1 +h 2 / Diff(Ω) Form a group under composition h 1,h 2 Diff(Ω):g=h 1 h 2 Diff(Ω) Example: Rotations 8/36 MICCAI 2007
9 Review: Capturing Anatomical Shape Change Metric structure on Diff(Ω) Integrate flow of velocity fields h t (x)=x+ t 0 v s (h s (x))ds Induce a metric via Sobolev norm on velocity fields 1 d 2 Diff(Ω) (Id,h)= min Lv t (x) 2 dxdt v:ḣs=v s h s 0 Ω 9/36 MICCAI 2007
10 Review: Capturing Anatomical Shape Change d I Implies a metric on anatomical images: captures severity and amount of shape change required to match images d 2 I(I,J) min v: ḣ s =v s h s σ 2 Ω Ω Lv s (x) 2 dxds ( I(h 1 (x)) J(x) ) 2 dx 10/36 MICCAI 2007
11 Review: Nadaraya-Watson Regression Observations {x i,y i },x i,y i R y i =m(x i )+ε i Regression estimator: m(x) E(Y X=x)= y f(x,y) f X (x) dy 11/36 MICCAI 2007
12 Review: Nadaraya-Watson Regression Replace unknown densities with kernel density estimates ˆf X(x) h 1 h( x xi N K h Joint density estimate via product kernel ) ˆf g,h (x,y) 1 N K h( x xi h ) K g ( y yi g ) 12/36 MICCAI 2007
13 Review: Nadaraya-Watson Regression ˆm h (x)= N i=1 K h(x x i )y i N i=1 K h(x x i ) Assume symmetric kernels Weighted mean of response variables Weights depend on predictor variables 13/36 MICCAI 2007
14 Manifold Kernel Regression How do we define regression on a manifold? m(x) E(Y X=x)= Use Fréchet expectation to define intrinsic mean via the metric d y f(x,y) f X (x) dy µ=argmin q M 1 N N i d 2 (q,p i ) 14/36 MICCAI 2007
15 Fréchet Mean: Averaging Anatomies 15/36 MICCAI 2007
16 Manifold Kernel Regression Image observations and associated age measurements {t i,i i } Manifold Kernel Regression estimator via Fréchet expectation ( N ) K i h (t t i )d 2 I (I,I i) ˆm h (t)=argmin I I N i K h (t t i ) 16/36 MICCAI 2007
17 Manifold Kernel Regression Response: Diff(Ω) X X X X X X X Predictor: t i R 17/36 MICCAI 2007
18 Manifold Kernel Regression Weighted Intrinsic Mean Response: Diff(Ω) X X X X X X X Predictor: t i R N i K h (t t i )d 2 I (I,I i) N i K h (t t i ) 18/36 MICCAI 2007
19 Manifold Kernel Regression Solution Compute weighted, large-deformation Fréchet mean at each age Iterative greedy method Alternately optimize deformations, mean image [Davis, Lorenzen, Joshi ISBI 2004, NeuroImage 2004] Coarse-to-fine 19/36 MICCAI 2007
20 Manifold Kernel Regression Linear in number of observations Multithreaded implementation 5-80 minutes (per predictor) images 8x2-core 3 GHz Processors 64 GB memory 20/36 MICCAI 2007
21 Example: Regression with Known Ground Truth Observations: 100 2D bullseye images random predictor values r i (t) nonlinear, independent r 2 (t) r 3 (t) r 1 (t) Structural Noise: i.i.d. Gaussian noise added to radii Goal: Recover radii functions from images alone via regression 21/36 MICCAI 2007
22 Example: Regression with Known Ground Truth Observations (sorted by t ) X X X X X X X 22/36 MICCAI 2007
23 Example: Regression with Known Ground Truth Regressed Images Ground Truth Overlay (colored) X X X X X X X 23/36 MICCAI 2007
24 Application: Aging Brain How does the brain change over time? Regress image as function of age 84 3T-MR T1 volumes from healthy adults Ages Preprocessing: Intensity calibration Skull stripping Rigid alignment Kernel Bandwidth: 6 years Available Online 24/36 MICCAI 2007
25 Aging Brain: Regressed Image Volume Renderings of 3D Regressed Images 25/36 MICCAI 2007
26 Aging Brain: Regressed Image 26/36 MICCAI 2007
27 Quantifying Change Dense collection regressed images Infer diffeomorphic transformation that encodes change of average anatomy over time h t :Ω Ω h t v ti 27/36 MICCAI 2007
28 Diffeomorphic Growth Model Individual represented by observations [Miller 2005] I t 1 0 v t 2 V dt+ 1 σ I t I 0 h 1 t 2 L 2 dt Measure shape change via Sobolev norm Deformed template I 0 matches image observations I t 28/36 MICCAI 2007
29 Diffeomorphic Growth Model Individual represented by observations [Miller 2005] I t 1 0 v t 2 V dt+ 1 σ I t I 0 h 1 t 2 L 2 dt Apply to population via Fréchet Expectation 1 0 v t 2 V dt+ 1 σ E(I T =t) I 0 h 1 t 2 L 2 dt 29/36 MICCAI 2007
30 Quantifying Change Expansion Contraction 30/36 MICCAI 2007
31 Quantifying Change log D(Id(x)+v t (x)) >0 Expansion: Contraction: log D(Id(x)+v t (x)) <0 31/36 MICCAI 2007
32 Kernel Bandwidth 32/36 MICCAI 2007
33 Kernel Bandwidth Goldie Locks : Too smooth; Too rough; Just right! Cross-Validation based on MISE 33/36 MICCAI 2007
34 Conclusion Anatomical change via regression Manifold Kernel Regression estimator within diffeomorphic image mapping framework Apply to study aging brain via 3D MR image database 34/36 MICCAI 2007
35 Future Work Predictors Compare populations Analyze new observations Healthy Diseased Kernel Regression Parametric; Robust; convergence? Shape Spaces/Metrics? 35/36 MICCAI 2007
36 Acknowledgements Steve Marron, UNC Statistics Martin Styner, UNC Computer Science Benedict Mortamet, UNC Neurosurgery Clement Vachet, UNC Psychiatry Peter Lorenzen, UNC Computer Science Funding: R01 EB NIH-NIBIB, and R01 CA NIH-NCI 36/36 MICCAI 2007
37 Questions? Image database may be downloaded from this URL: Or
Quantitative Neuro-Anatomic and Functional Image Assessment Recent progress on image registration and its applications
Quantitative Neuro-Anatomic and Functional Image Assessment Recent progress on image registration and its applications Guido Gerig Sarang Joshi Tom Fletcher Applications of image registration in neuroimaging
Population Shape Regression From Random Design Data
Population Shape Regression From Random Design Data B. C. Davis University of North Carolina at Chapel Hill Chapel Hill, NC, USA Kitware, Inc. Clifton Park, NY, USA brad.davis@unc.edu E. Bullitt University
Multivariate Statistical Analysis of Deformation Momenta Relating Anatomical Shape to Neuropsychological Measures
Multivariate Statistical Analysis of Deformation Momenta Relating Anatomical Shape to Neuropsychological Measures Nikhil Singh, Tom Fletcher, Sam Preston, Linh Ha, J. Stephen Marron, Michael Wiener, and
Fast Geodesic Regression for Population-Based Image Analysis
Fast Geodesic Regression for Population-Based Image Analysis Yi Hong 1, Polina Golland 2, and Miaomiao Zhang 2 1 Computer Science Department, University of Georgia 2 Computer Science and Artificial Intelligence
Analysis of Longitudinal Shape Variability via Subject Specific Growth Modeling
Analysis of Longitudinal Shape Variability via Subject Specific Growth Modeling James Fishbaugh 1, Marcel Prastawa 1, Stanley Durrleman 2, Joseph Piven 3 for the IBIS Network, and Guido Gerig 1 1 Scientific
Metamorphic Geodesic Regression
Metamorphic Geodesic Regression Yi Hong, Sarang Joshi 3, Mar Sanchez 4, Martin Styner, and Marc Niethammer,2 UNC-Chapel Hill/ 2 BRIC, 3 University of Utah, 4 Emory University Abstract. We propose a metamorphic
Registration of anatomical images using geodesic paths of diffeomorphisms parameterized with stationary vector fields
Registration of anatomical images using geodesic paths of diffeomorphisms parameterized with stationary vector fields Monica Hernandez, Matias N. Bossa, and Salvador Olmos Communication Technologies Group
Template estimation form unlabeled point set data and surfaces for Computational Anatomy
Template estimation form unlabeled point set data and surfaces for Computational Anatomy Joan Glaunès 1 and Sarang Joshi 1 Center for Imaging Science, Johns Hopkins University, joan@cis.jhu.edu SCI, University
Symmetric Image Normalization in the Diffeomorphic Space
Symmetric Image Normalization in the Diffeomorphic Space Brian Avants, Charles Epstein, James Gee Penn Image Computing & Science Lab Departments of Radiology and Mathematics University of Pennsylvania
Diffeomorphic Shape Trajectories for Improved Longitudinal Segmentation and Statistics
Diffeomorphic Shape Trajectories for Improved Longitudinal Segmentation and Statistics Prasanna Muralidharan 1, James Fishbaugh 1, Hans J. Johnson 2, Stanley Durrleman 3, Jane S. Paulsen 2, Guido Gerig
Bayesian Principal Geodesic Analysis in Diffeomorphic Image Registration
Bayesian Principal Geodesic Analysis in Diffeomorphic Image Registration Miaomiao Zhang and P. Thomas Fletcher School of Computing, University of Utah, Salt Lake City, USA Abstract. Computing a concise
Computational Brain Anatomy
Computational Brain Anatomy John Ashburner Wellcome Trust Centre for Neuroimaging, 12 Queen Square, London, UK. Overview Voxel-Based Morphometry Morphometry in general Volumetrics VBM preprocessing followed
Morphometry. John Ashburner. Wellcome Trust Centre for Neuroimaging, 12 Queen Square, London, UK. Voxel-Based Morphometry
Morphometry John Ashburner Wellcome Trust Centre for Neuroimaging, 12 Queen Square, London, UK. Overview Voxel-Based Morphometry Morphometry in general Volumetrics VBM preprocessing followed by SPM Tissue
Spatiotemporal Atlas Estimation for Developmental Delay Detection in Longitudinal Datasets
Spatiotemporal Atlas Estimation for Developmental Delay Detection in Longitudinal Datasets Stanley Durrleman 1,2, Xavier Pennec 1, Alain Trouvé 2, Guido Gerig 3, and Nicholas Ayache 1 1 INRIA - Asclepios
Uncertainty Quantification for LDDMM Using a Low-rank Hessian Approximation
Uncertainty Quantification for LDDMM Using a Low-rank Hessian Approximation Xiao Yang, Marc Niethammer, Department of Computer Science and Biomedical Research Imaging Center University of North Carolina
Improved Correspondence for DTI Population Studies via Unbiased Atlas Building
Improved Correspondence for DTI Population Studies via Unbiased Atlas Building Casey Goodlett 1, Brad Davis 1,2, Remi Jean 3, John Gilmore 3, and Guido Gerig 1,3 1 Department of Computer Science, University
Deformation Morphometry: Basics and Applications
Deformation Morphometry: Basics and Applications Valerie Cardenas Nicolson, Ph.D. Assistant Adjunct Professor NCIRE, UCSF, SFVA Center for Imaging of Neurodegenerative Diseases VA Challenge Clinical studies
Morphometrics with SPM12
Morphometrics with SPM12 John Ashburner Wellcome Trust Centre for Neuroimaging, 12 Queen Square, London, UK. What kind of differences are we looking for? Usually, we try to localise regions of difference.
Neuroimage Processing
Neuroimage Processing Instructor: Moo K. Chung mkchung@wisc.edu Lecture 10-11. Deformation-based morphometry (DBM) Tensor-based morphometry (TBM) November 13, 2009 Image Registration Process of transforming
Construction of a Deformable Spatiotemporal MRI Atlas of the Fetal Brain: Evaluation of Similarity Metrics and Deformation Models
Construction of a Deformable Spatiotemporal MRI Atlas of the Fetal Brain: Evaluation of Similarity Metrics and Deformation Models Ali Gholipour 1, Catherine Limperopoulos 2, Sean Clancy 1, Cedric Clouchoux
Geodesic Refinement Using James-Stein Estimators
Geodesic Refinement Using James-Stein Estimators Greg M. Fleishman 1,2, P. Thomas Fletcher 3, Boris A. Gutman 2, Gautam Prasad 2, Yingnian Wu 4, and Paul M. Thompson 2 1 UC Los Angeles, Department of Bioengineering
PDiff: Irrotational Diffeomorphisms for Computational Anatomy
PDiff: Irrotational Diffeomorphisms for Computational Anatomy Jacob Hinkle and Sarang Joshi Scientific Computing and Imaging Institute, Department of Bioengineering, University of Utah, Salt Lake City,
Multivariate models of inter-subject anatomical variability
Multivariate models of inter-subject anatomical variability Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, 12 Queen Square, London WC1N 3BG, UK. Prediction Binary Classification Curse
Medical Image Synthesis via Monte Carlo Simulation
Medical Image Synthesis via Monte Carlo Simulation An Application of Statistics in Geometry & Building a Geometric Model with Correspondence James Z. Chen, Stephen M. Pizer, Edward L. Chaney, Sarang Joshi,
Morphometrics with SPM12
Morphometrics with SPM12 John Ashburner Wellcome Trust Centre for Neuroimaging, 12 Queen Square, London, UK. What kind of differences are we looking for? Usually, we try to localise regions of difference.
Introduction. Linear Regression. coefficient estimates for the wage equation: E(Y X) = X 1 β X d β d = X β
Introduction - Introduction -2 Introduction Linear Regression E(Y X) = X β +...+X d β d = X β Example: Wage equation Y = log wages, X = schooling (measured in years), labor market experience (measured
Geodesic Regression on Riemannian Manifolds
Geodesic Regression on Riemannian Manifolds Thomas Fletcher To cite this version: Thomas Fletcher. Geodesic Regression on Riemannian Manifolds. Pennec, Xavier and Joshi, Sarang and Nielsen, Mads. Proceedings
Kernel-Based Contrast Functions for Sufficient Dimension Reduction
Kernel-Based Contrast Functions for Sufficient Dimension Reduction Michael I. Jordan Departments of Statistics and EECS University of California, Berkeley Joint work with Kenji Fukumizu and Francis Bach
T xi (M) n i. x i b 1xi. x j. h j. x p j b 2x i
Gaussian Random Fields for Statistical Characterization of Brain Submanifolds. Sarang Joshi Department of Radiation Oncology and Biomedical Enginereing University of North Carolina at Chapel Hill Sarang
Statistical Analysis of Tensor Fields
Statistical Analysis of Tensor Fields Yuchen Xie Baba C. Vemuri Jeffrey Ho Department of Computer and Information Sciences and Engineering University of Florida Abstract. In this paper, we propose a Riemannian
Longitudinal growth analysis of early childhood brain using deformation based morphometry
Longitudinal growth analysis of early childhood brain using deformation based morphometry Junki Lee 1, Yasser Ad-Dab'bagh 2, Vladimir Fonov 1, Alan C. Evans 1 and the Brain Development Cooperative Group
Time-Warped Geodesic Regression
Time-Warped Geodesic Regression Yi Hong 1, Nikhil Singh 1, Roland Kwitt 3, and Marc Niethammer 1,2 1 University of North Carolina (UNC) at Chapel Hill, NC, USA 2 Biomedical Research Imaging Center, UNC-Chapel
A new algorithm for the computation of the group logarithm of diffeomorphisms
A new algorithm for the computation of the group logarithm of diffeomorphisms Matias Bossa and Salvador Olmos GTC, I3A, University of Zaragoza, Spain, {bossa,olmos}@unizar.es Abstract. There is an increasing
Statistics on Anatomic Objects Reflecting Inter-Object Relations
Statistics on Anatomic Objects Reflecting Inter-Object Relations Ja-Yeon Jeong, Stephen M.Pizer, and Surajit Ray Medical Image Display & Analysis Group (MIDAG) University of North Carolina, Chapel Hill
Nonparametric Methods
Nonparametric Methods Michael R. Roberts Department of Finance The Wharton School University of Pennsylvania July 28, 2009 Michael R. Roberts Nonparametric Methods 1/42 Overview Great for data analysis
Topological Data Analysis for Brain Networks
Topological Data Analysis for Brain Networks Relating Functional Brain Network Topology to Clinical Measures of Behavior Bei Wang Phillips 1,2 University of Utah Joint work with Eleanor Wong 1,2, Sourabh
Improved Correspondence for DTI Population Studies Via Unbiased Atlas Building
Improved Correspondence for DTI Population Studies Via Unbiased Atlas Building Casey Goodlett 1,BradDavis 1,2,RemiJean 3, John Gilmore 3, and Guido Gerig 1,3 1 Department of Computer Science, University
The Euler-Lagrange Equation for Interpolating Sequence of Landmark Datasets
The Euler-Lagrange Equation for Interpolating Sequence of Landmark Datasets Mirza Faisal Beg 1, Michael Miller 1, Alain Trouvé 2, and Laurent Younes 3 1 Center for Imaging Science & Department of Biomedical
Tract-Specific Analysis for DTI of Brain White Matter
Tract-Specific Analysis for DTI of Brain White Matter Paul Yushkevich, Hui Zhang, James Gee Penn Image Computing & Science Lab Department of Radiology University of Pennsylvania IPAM Summer School July
Morphometry. John Ashburner. Wellcome Trust Centre for Neuroimaging, 12 Queen Square, London, UK.
Morphometry John Ashburner Wellcome Trust Centre for Neuroimaging, 12 Queen Square, London, UK. Morphometry is defined as: Measurement of the form of organisms or of their parts. The American Heritage
Alternatives to Basis Expansions. Kernels in Density Estimation. Kernels and Bandwidth. Idea Behind Kernel Methods
Alternatives to Basis Expansions Basis expansions require either choice of a discrete set of basis or choice of smoothing penalty and smoothing parameter Both of which impose prior beliefs on data. Alternatives
Rapid, Robust, and Reliable Blind Deconvolution via Nonconvex Optimization
Rapid, Robust, and Reliable Blind Deconvolution via Nonconvex Optimization Shuyang Ling Department of Mathematics, UC Davis Oct.18th, 2016 Shuyang Ling (UC Davis) 16w5136, Oaxaca, Mexico Oct.18th, 2016
Motion Estimation (I)
Motion Estimation (I) Ce Liu celiu@microsoft.com Microsoft Research New England We live in a moving world Perceiving, understanding and predicting motion is an important part of our daily lives Motion
A Riemannian Framework for Denoising Diffusion Tensor Images
A Riemannian Framework for Denoising Diffusion Tensor Images Manasi Datar No Institute Given Abstract. Diffusion Tensor Imaging (DTI) is a relatively new imaging modality that has been extensively used
Kernel metrics on normal cycles for the matching of geometrical structures.
Kernel metrics on normal cycles for the matching of geometrical structures. Pierre Roussillon University Paris Descartes July 18, 2016 1 / 34 Overview Introduction Matching of geometrical structures Kernel
An Anatomical Equivalence Class Based Joint Transformation-Residual Descriptor for Morphological Analysis
An Anatomical Equivalence Class Based Joint Transformation-Residual Descriptor for Morphological Analysis Sajjad Baloch, Ragini Verma, and Christos Davatzikos University of Pennsylvania, Philadelphia,
FRÉCHET REGRESSION FOR RANDOM OBJECTS WITH EUCLIDEAN PREDICTORS
Submitted to the Annals of Statistics FRÉCHET REGRESSION FOR RANDOM OBJECTS WITH EUCLIDEAN PREDICTORS By Alexander Petersen and Hans-Georg Müller, Department of Statistics, University of California, Santa
arxiv: v1 [cs.cv] 23 Nov 2017
![arxiv: v1 [cs.cv] 23 Nov 2017](/thumbs/82/85716691.jpg "arxiv: v1 [cs.cv] 23 Nov 2017")
Parallel transport in shape analysis: a scalable numerical scheme arxiv:1711.08725v1 [cs.cv] 23 Nov 2017 Maxime Louis 12, Alexandre Bône 12, Benjamin Charlier 23, Stanley Durrleman 12, and the Alzheimer
Multi-Atlas Tensor-Based Morphometry and its Application to a Genetic Study of 92 Twins
Multi-Atlas Tensor-Based Morphometry and its Application to a Genetic Study of 92 Twins Natasha Leporé 1, Caroline Brun 1, Yi-Yu Chou 1, Agatha D. Lee 1, Marina Barysheva 1, Greig I. de Zubicaray 2, Matthew
Motion Estimation (I) Ce Liu Microsoft Research New England
Motion Estimation (I) Ce Liu celiu@microsoft.com Microsoft Research New England We live in a moving world Perceiving, understanding and predicting motion is an important part of our daily lives Motion
Additive Isotonic Regression
Additive Isotonic Regression Enno Mammen and Kyusang Yu 11. July 2006 INTRODUCTION: We have i.i.d. random vectors (Y 1, X 1 ),..., (Y n, X n ) with X i = (X1 i,..., X d i ) and we consider the additive
MAP Examples. Sargur Srihari
MAP Examples Sargur srihari@cedar.buffalo.edu 1 Potts Model CRF for OCR Topics Image segmentation based on energy minimization 2 Examples of MAP Many interesting examples of MAP inference are instances
Symmetric Log-Domain Diffeomorphic Registration: A Demons-Based Approach
Symmetric Log-Domain Diffeomorphic Registration: A Demons-Based Approach Tom Vercauteren 1, Xavier Pennec 2,AymericPerchant 1, and Nicholas Ayache 2 1 Mauna Kea Technologies, France 2 Asclepios, INRIA
Welcome to Copenhagen!
Welcome to Copenhagen! Schedule: Monday Tuesday Wednesday Thursday Friday 8 Registration and welcome 9 Crash course on Crash course on Introduction to Differential and Differential and Information Geometry
Using Estimating Equations for Spatially Correlated A
Using Estimating Equations for Spatially Correlated Areal Data December 8, 2009 Introduction GEEs Spatial Estimating Equations Implementation Simulation Conclusion Typical Problem Assess the relationship
Directional Statistics
Directional Statistics Kanti V. Mardia University of Leeds, UK Peter E. Jupp University of St Andrews, UK I JOHN WILEY & SONS, LTD Chichester New York Weinheim Brisbane Singapore Toronto Contents Preface
Mixed effect model for the spatiotemporal analysis of longitudinal manifold value data
Mixed effect model for the spatiotemporal analysis of longitudinal manifold value data Stéphanie Allassonnière with J.B. Schiratti, O. Colliot and S. Durrleman Université Paris Descartes & Ecole Polytechnique
Density estimation Nonparametric conditional mean estimation Semiparametric conditional mean estimation. Nonparametrics. Gabriel Montes-Rojas
0 0 5 Motivation: Regression discontinuity (Angrist&Pischke) Outcome.5 1 1.5 A. Linear E[Y 0i X i] 0.2.4.6.8 1 X Outcome.5 1 1.5 B. Nonlinear E[Y 0i X i] i 0.2.4.6.8 1 X utcome.5 1 1.5 C. Nonlinearity
1.1 Basis of Statistical Decision Theory
ECE598: Information-theoretic methods in high-dimensional statistics Spring 2016 Lecture 1: Introduction Lecturer: Yihong Wu Scribe: AmirEmad Ghassami, Jan 21, 2016 [Ed. Jan 31] Outline: Introduction of
Schild s Ladder for the parallel transport of deformations in time series of images
Schild s Ladder for the parallel transport of deformations in time series of images Lorenzi Marco 1,2, Nicholas Ayache 1, Xavier Pennec 1, and the Alzheimer s Disease Neuroimaging Initiative 1 Project
Web Appendix for Hierarchical Adaptive Regression Kernels for Regression with Functional Predictors by D. B. Woodard, C. Crainiceanu, and D.
Web Appendix for Hierarchical Adaptive Regression Kernels for Regression with Functional Predictors by D. B. Woodard, C. Crainiceanu, and D. Ruppert A. EMPIRICAL ESTIMATE OF THE KERNEL MIXTURE Here we
Optimized Conformal Parameterization of Cortical Surfaces Using Shape Based Matching of Landmark Curves
Optimized Conformal Parameterization of Cortical Surfaces Using Shape Based Matching of Landmark Curves Lok Ming Lui 1, Sheshadri Thiruvenkadam 1, Yalin Wang 1,2,TonyChan 1, and Paul Thompson 2 1 Department
Diffeomorphic Warping. Ben Recht August 17, 2006 Joint work with Ali Rahimi (Intel)
Diffeomorphic Warping Ben Recht August 17, 2006 Joint work with Ali Rahimi (Intel) What Manifold Learning Isn t Common features of Manifold Learning Algorithms: 1-1 charting Dense sampling Geometric Assumptions
17th Annual Meeting of the Organization for Human Brain Mapping. Multivariate cortical shape modeling based on sparse representation
17th Annual Meeting of the Organization for Human Brain Mapping Multivariate cortical shape modeling based on sparse representation Abstract No: 2207 Authors: Seongho Seo 1, Moo K. Chung 1,2, Kim M. Dalton
Introduction to machine learning and pattern recognition Lecture 2 Coryn Bailer-Jones
Introduction to machine learning and pattern recognition Lecture 2 Coryn Bailer-Jones http://www.mpia.de/homes/calj/mlpr_mpia2008.html 1 1 Last week... supervised and unsupervised methods need adaptive
Generated Covariates in Nonparametric Estimation: A Short Review.
Generated Covariates in Nonparametric Estimation: A Short Review. Enno Mammen, Christoph Rothe, and Melanie Schienle Abstract In many applications, covariates are not observed but have to be estimated
Fast Template-based Shape Analysis using Diffeomorphic Iterative Centroid
Fast Template-based Shape Analysis using Diffeomorphic Iterative Centroid Claire Cury, Joan Alexis Glaunès, Marie Chupin, Olivier Colliot To cite this version: Claire Cury, Joan Alexis Glaunès, Marie Chupin,
Construction of Neuroanatomical Shape Complex Atlas from 3D Brain MRI
Construction of Neuroanatomical Shape Complex Atlas from 3D Brain MRI Ting Chen 1, Anand Rangarajan 1, Stephan J. Eisenschenk 2, and Baba C. Vemuri 1 1 Department of CISE, University of Florida, Gainesville,
DT-REFinD: Diffusion Tensor Registration With Exact Finite-Strain Differential
DT-REFinD: Diffusion Tensor Registration With Exact Finite-Strain Differential The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation
Non-parametric Inference and Resampling
Non-parametric Inference and Resampling Exercises by David Wozabal (Last update 3. Juni 2013) 1 Basic Facts about Rank and Order Statistics 1.1 10 students were asked about the amount of time they spend
Riemannian Metrics on the Space of Solid Shapes
Riemannian Metrics on the Space of Solid Shapes P. Thomas Fletcher and Ross T. Whitaker School of Computing University of Utah fletcher@sci.utah.edu, whitaker@cs.utah.edu Abstract. We present a new framework
Nonparametric Econometrics
Applied Microeconometrics with Stata Nonparametric Econometrics Spring Term 2011 1 / 37 Contents Introduction The histogram estimator The kernel density estimator Nonparametric regression estimators Semi-
Local Polynomial Regression
VI Local Polynomial Regression (1) Global polynomial regression We observe random pairs (X 1, Y 1 ),, (X n, Y n ) where (X 1, Y 1 ),, (X n, Y n ) iid (X, Y ). We want to estimate m(x) = E(Y X = x) based
Local Polynomial Modelling and Its Applications
Local Polynomial Modelling and Its Applications J. Fan Department of Statistics University of North Carolina Chapel Hill, USA and I. Gijbels Institute of Statistics Catholic University oflouvain Louvain-la-Neuve,
Chapter 9. Non-Parametric Density Function Estimation
9-1 Density Estimation Version 1.1 Chapter 9 Non-Parametric Density Function Estimation 9.1. Introduction We have discussed several estimation techniques: method of moments, maximum likelihood, and least
Modelling Non-linear and Non-stationary Time Series
Modelling Non-linear and Non-stationary Time Series Chapter 2: Non-parametric methods Henrik Madsen Advanced Time Series Analysis September 206 Henrik Madsen (02427 Adv. TS Analysis) Lecture Notes September
CS 468. Differential Geometry for Computer Science. Lecture 17 Surface Deformation
CS 468 Differential Geometry for Computer Science Lecture 17 Surface Deformation Outline Fundamental theorem of surface geometry. Some terminology: embeddings, isometries, deformations. Curvature flows
Sparse Scale-Space Decomposition of Volume Changes in Deformations Fields
Sparse Scale-Space Decomposition of Volume Changes in Deformations Fields Lorenzi Marco 1, Bjoern H Menze 1,2, Marc Niethammer 3, Nicholas Ayache 1, and Xavier Pennec 1 for the Alzheimer's Disease Neuroimaging
An Optimal Control Approach for the Registration of Image Time-Series
An Optimal Control Approach for the Registration of Image Time-Series Marc Niethammer Gabriel L. Hart Christopher Zach Abstract This paper discusses an optimal control approach for the registration of
Exploiting k-nearest Neighbor Information with Many Data
Exploiting k-nearest Neighbor Information with Many Data 2017 TEST TECHNOLOGY WORKSHOP 2017. 10. 24 (Tue.) Yung-Kyun Noh Robotics Lab., Contents Nonparametric methods for estimating density functions Nearest
Lecture Notes 15 Prediction Chapters 13, 22, 20.4.
Lecture Notes 15 Prediction Chapters 13, 22, 20.4. 1 Introduction Prediction is covered in detail in 36-707, 36-701, 36-715, 10/36-702. Here, we will just give an introduction. We observe training data
Nonparametric Regression Härdle, Müller, Sperlich, Werwarz, 1995, Nonparametric and Semiparametric Models, An Introduction
Härdle, Müller, Sperlich, Werwarz, 1995, Nonparametric and Semiparametric Models, An Introduction Tine Buch-Kromann Univariate Kernel Regression The relationship between two variables, X and Y where m(
Discrete geodesic regression in shape space
Discrete geodesic regression in shape space Benjamin Berkels 1, P. Thomas Fletcher 2, Behrend Heeren 1, Martin Rumpf 1, and Benedikt Wirth 3 1 Institute for Numerical Simulation, Universität Bonn, benjamin.berkels,behrend.heeren,martin.rumpf@ins.uni-bonn.de
Geodesics, Parallel Transport & One-parameter Subgroups for Diffeomorphic Image Registration
Geodesics, Parallel Transport & One-parameter Subgroups for Diffeomorphic Image Registration Marco Lorenzi 1,2 and Xavier Pennec 1 1 Project Team Asclepios, INRIA Sophia Antipolis, France 2 LENITEM, IRCCS
The momentum map representation of images
The momentum map representation of images M. Bruveris 1, F. Gay-Balmaz, D. D. Holm 1, and T. S. Ratiu 3 Revised version August 1, 1 arxiv:91.99v [nlin.cd] 8 Apr 15 Abstract This paper discusses the mathematical
ECE521 week 3: 23/26 January 2017
ECE521 week 3: 23/26 January 2017 Outline Probabilistic interpretation of linear regression - Maximum likelihood estimation (MLE) - Maximum a posteriori (MAP) estimation Bias-variance trade-off Linear
Discriminative Direction for Kernel Classifiers
Discriminative Direction for Kernel Classifiers Polina Golland Artificial Intelligence Lab Massachusetts Institute of Technology Cambridge, MA 02139 polina@ai.mit.edu Abstract In many scientific and engineering
Dictionary Learning on Riemannian Manifolds
Dictionary Learning on Riemannian Manifolds Yuchen Xie Baba C. Vemuri Jeffrey Ho Department of CISE, University of Florida, Gainesville FL, 32611, USA {yxie,vemuri,jho}@cise.ufl.edu Abstract. Existing
Nonlinear Registration of Diffusion MR Images Based on Fiber Bundles
Nonlinear Registration of Diffusion MR Images Based on Fiber Bundles Ulas Ziyan 1, Mert R. Sabuncu 1, Lauren J. O Donnell 2,3, and Carl-Fredrik Westin 1,3 1 MIT Computer Science and Artificial Intelligence
A Hamiltonian Particle Method for Diffeomorphic Image Registration
A Hamiltonian Particle Method for Diffeomorphic Image Registration Stephen Marsland and Robert McLachlan Massey University, Private Bag 11-222 Palmerston North, New Zealand {s.r.marsland,r.mchlachlan}@massey.ac.nz
The geometry of Gaussian processes and Bayesian optimization. Contal CMLA, ENS Cachan
The geometry of Gaussian processes and Bayesian optimization. Contal CMLA, ENS Cachan Background: Global Optimization and Gaussian Processes The Geometry of Gaussian Processes and the Chaining Trick Algorithm
Sparse Nonparametric Density Estimation in High Dimensions Using the Rodeo
Outline in High Dimensions Using the Rodeo Han Liu 1,2 John Lafferty 2,3 Larry Wasserman 1,2 1 Statistics Department, 2 Machine Learning Department, 3 Computer Science Department, Carnegie Mellon University
Error distribution function for parametrically truncated and censored data
Error distribution function for parametrically truncated and censored data Géraldine LAURENT Jointly with Cédric HEUCHENNE QuantOM, HEC-ULg Management School - University of Liège Friday, 14 September
4 Nonparametric Regression
4 Nonparametric Regression 4.1 Univariate Kernel Regression An important question in many fields of science is the relation between two variables, say X and Y. Regression analysis is concerned with the
Nonparametric regression for topology. applied to brain imaging data
, applied to brain imaging data Cleveland State University October 15, 2010 Motivation from Brain Imaging MRI Data Topology Statistics Application MRI Data Topology Statistics Application Cortical surface
Nonparametric Regression. Badr Missaoui
Badr Missaoui Outline Kernel and local polynomial regression. Penalized regression. We are given n pairs of observations (X 1, Y 1 ),...,(X n, Y n ) where Y i = r(x i ) + ε i, i = 1,..., n and r(x) = E(Y
Local Polynomial Regression with Application to Sea Surface Temperatures
Clemson University TigerPrints All Theses Theses 8-2012 Local Polynomial Regression with Application to Sea Surface Temperatures Michael Finney Clemson University, finney2@clemson.edu Follow this and additional
Transformations and Bayesian Density Estimation
Transformations and Bayesian Density Estimation Andrew Bean 1, Steve MacEachern, Xinyi Xu The Ohio State University 10 th Conference on Bayesian Nonparametrics June 25, 2015 1 bean.243@osu.edu Transformations
Persistent homology and nonparametric regression
Cleveland State University March 10, 2009, BIRS: Data Analysis using Computational Topology and Geometric Statistics joint work with Gunnar Carlsson (Stanford), Moo Chung (Wisconsin Madison), Peter Kim
Boundary Correction Methods in Kernel Density Estimation Tom Alberts C o u(r)a n (t) Institute joint work with R.J. Karunamuni University of Alberta
Boundary Correction Methods in Kernel Density Estimation Tom Alberts C o u(r)a n (t) Institute joint work with R.J. Karunamuni University of Alberta November 29, 2007 Outline Overview of Kernel Density