Multimodal Deep Learning for Predicting Survival from Breast Cancer
|
|
- Shonda Craig
- 6 years ago
- Views:
Transcription
1 Multimodal Deep Learning for Predicting Survival from Breast Cancer Heather Couture Deep Learning Journal Club Nov. 16, 2016
2 Outline Background on tumor histology & genetic data Background on survival analysis Deep survival models Katzman et al., Deep Survival: A Deep Cox Proportional Hazards Network, 2016 Yousefi et al., Learning Genomic Representations to Predict Clinical Outcomes in Cancer, ICLR, 2016 Multimodal deep learning Wang et al., On Deep Multi-View Representation Learning, ICML, 2015 My work: predicting survival from tumor histology & genetics 2
3 Tissue Microarray microarray assembly gene expression tumor area identified on slide genetic subtype immunohistochemistry receptor status Sauter, Tissue microarrays in drug discovery, 2003 H&E histology histologic subtype, grade 3
4 Applications of Tumor Analysis Prognosis More favorable outcome if: few mitoses less nuclear pleomorphism (irregularity of nuclear size and shape) well differentiated (cell specialization) Abnormal cells Personalized treatment Target tumors based on molecular analysis: treatment 1 molecular analysis + image analysis? treatment 2 treatment 3 4
5 Motivation Improve predictions by using automated image analysis Faster More repeatable Capture properties that humans cannot Capture spatial properties in a way that genetics cannot vs Complement genetic analysis by integrating image and genetic data into a single model Predict survival to identify high and low risk patients 5
6 Approach Deep survival model with multimodal data + risk score image features gene expression 6
7 Survival Data Event time T, event indicator E E=1 (e.g., death) T is time to death E=0 (e.g., last contact with patient) T is time of last followup (right-censored) Predicting survival: Standard regression methods Must discard right-censored data Binary discriminative methods (e.g., death by time T) Must discard time to death Solution: proportional hazards model 7
8 Survival Analysis Survival function S(t) = Pr(T > t) Hazard function λ(t )=lim δ 0 Pr (t T <t +δ T t) δ Proportional hazards model λ(t x)=λ 0 (t )e h(x) Cox proportional hazards model λ 0 (t) baseline hazard function h(x) risk function x covariates h β (x)=β T x Cox partial likelihood maximize partial log likelihood L c (β)= i ϵ{i E i =1} e h β(x i ) e h β(x j ) j ϵ{j T j >T i } 8
9 Model Performance Concordance index pairwise agreement of risk predictions CI (β, X)= P I (i, j) P I (i, j)={ 1 if h(βt x i )>h(β T x j ) and T j >T i 0 otherwise P set of orderable pairs (X i,x j ) i.e., if E i =1 and E j =1 or E j =0 and T j > T i 9
10 Deep Survival Network Katzman et al., Deep Survival: A Deep Cox Proportional Hazards Network, 2016 Yousefi et al., Learning Genomic Representations to Predict Clinical Outcomes in Cancer, 2016 Approach: replace h(x) with a DNN risk score h θ (x i ) network weights θ input features x i Cost function: Cox partial log likelihood L(θ)= iϵ{i E i =1} h θ (x i ) log e h θ(x j ) j ϵ{j T j >T i } 10
11 Experiments Katzman et al., Deep Survival: A Deep Cox Proportional Hazards Network, 2016 Worcester Heart Attack Study 1638 observations 5 features (age, sex, BMI, left heart failure complications, order of MI) Linear Cox regression C-index: (95% CI: ) DeepSurv C-index: (95% CI: ) Molecular Taxonomy of Breast Cancer 1981 patients expression level for 14 manually selected genes clinical features: age, number of positive nodes, tumor size, receptor status, treatment Linear Cox regression C-index: (95% CI: ) Deep Surv C-index: (95% CI: ) 11
12 Experiments Yousefi et al., Learning Genomic Representations to Predict Clinical Outcomes in Cancer, ICLR, 2016 TCGA brain tumors 628 samples, 183 genomic features 10 random sets: 70% training, 30% testing 2 fully connected layers of 250 hidden units each 12
13 Multimodal Deep Learning Wang et al., On Deep Multi-View Representation Learning, ICML, 2015 Access to multiple unlabeled views of data for representation learning but only one view at test time Examples Audio + video Images + text Parallel text in two languages Words + context Two approaches Canonical correlation analysis (CCA) Learn features in two views that are maximally correlated Autoencoder Learn a representation that best reconstructs the inputs 13
14 Multimodal Data Given (xi,y i ), i=1,,n Wish to learn f(xi ) and g(y i ) such that f(x i ) and g(y i ) are highly correlated and/or Possible to reconstruct y i from x i through f(x i ) and vice versa 14
15 Canonical Correlation Analysis (CCA) Find projections u and v such that the data are maximally correlated u T Σ xy v (u, v)=argmax u, v maximize: u T Σ xy v corr(u T X, v T Y )=argmax u,v Constrain projections to have unit variance subject to: u T Σ xx u=v T Σ yy v=1 maximize: tr(u T Σ xy V ) subject to: U T Σ xx U =V T Σ yy V =I u T Σ xx u v T Σ yy v Find multiple pairs (u i, v i ) such that u i Σ xx u j = v i Σ yy v j = 0 for i < j U = [u 1,,u k ] and V = [v 1,,v k ] 15
16 Deep Canonical Correlation Analysis (DCCA) Andrew et al., Deep Canonical Correlation Analysis, ICML, 2013 maximize: 1 N tr (U T f ( X) g(y ) T V ) subject to: U T ( 1 N f (X )f ( X)T +r x I ) U =I features within modality are uncorrelated V T ( 1 N g(y ) g(y )T +r y I ) V =I u i T f ( X )g(y ) T v j =0 for i j r x, r y regularization parameters 16
17 Split Autoencoder (SplitAE) minimize: 1 N i=1 N ( x i p(f (x i )) 2 + y i q (f (x i )) 2 ) 17
18 Deep Canonically Correlated Autoencoder (DCCAE) Wang et al., On Deep Multi-View Representation Learning, ICML, 2015 minimize: 1 N tr (U T f ( X) g(y ) T V ) + subject to: U T ( 1 N f ( X)f ( X )T +r x I ) U =I λ N N ( x i p(f (x i )) 2 + y i q(g( y i )) 2 ) i=1 autoencoder regularization DCCA V T ( 1 N g(y )g(y )T +r y I ) V =I u i f ( X) g(y ) T v j =0 for i j 18
19 Correlated Autoencoder (CorrAE) Wang et al., On Deep Multi-View Representation Learning, ICML, 2015 minimize: 1 N tr(u T f ( X )g(y ) T V )+ λ N i=1 N ( x i p(f (x i )) 2 + y i q(g( y i )) 2 ) subject to: u i T f ( X )f ( X) T u i =v i T g(y ) g(y ) T v i =N, 1 i L Relaxation of DCCAE: feature dimensions within each view not constrained to be uncorrelated with each other 19
20 Experiments: Speech Recognition Wang et al., On Deep Multi-View Representation Learning, ICML, 2015 Recorded speech & articulatory measurements from 47 American English speakers 39 acoustic & 16 articulatory features from each of 7 frames Roughly 50k frames/speaker 1.43M frames Apply representation learning to frames Use original & learned features in standard HMM-based recognizer PER = phone error rates 20
21 Experiments: Multilingual Word Embeddings Wang et al., On Deep Multi-View Representation Learning, ICML, 2015 Learn representation of English words from pairs of English-German word embeddings 640D monolingual word vectors trained via LSA 36K English-German word pairs Evaluated on 180k English word embeddings Add projections of the two words in each bigram Cosine similarity between bigram pairs Order pairs by similarity Measure Spearman s correlation between model s and human s rankings AN: adjective-noun VN: verb-object 21
22 Experiments: Diagnosis of Schizophrenia Qi and Tejedor, Deep Multi-view Representation Learning for Multi-modal Features of Schizophrenia and Schizo-affective Disorder, ICASSP, 2016 Features from MRI: Source-based morphometric loading: 32 Functional network connectivity: labeled, 119,748 unlabeled samples Train SVM on learned features 22
23 My Work: Predicting Survival from Breast Cancer SPECS: breast tumors tissue microarray 145 patients 2 cores per patient 512 image features from VGG16 14,570 gene expression levels
24 Multimodal Deep Survival Network risk score h θ (x i ) network weights θ input image features x i 1 input genetic features x i 2 L Cox (θ)= i ϵ{i E i =1} h θ (x i ) log e h θ(x j ) jϵ{j T j >T i } 24
25 Multiple Outputs for Regularization subtype risk score grade, receptor status, etc. network weights θ input image features x i 1 input genetic features x i 2 L(θ, X, E,T,Y subtype,y grade )= α L Cox (θ, X, E,T )+ L cross entropy (θ, X,Y subtype )+ L cross entropy (θ, X,Y grade ) 25
26 Implementation Details/Tricks Batch normalization Drop out L2 regularization 26
27 5-fold cross-validation x4 Results
28 Questions?
Building a Prognostic Biomarker
Building a Prognostic Biomarker Noah Simon and Richard Simon July 2016 1 / 44 Prognostic Biomarker for a Continuous Measure On each of n patients measure y i - single continuous outcome (eg. blood pressure,
More informationarxiv: v1 [cs.lg] 25 Mar 2019
Gene Expression based Survival Prediction for Cancer Patients A Topic Modeling Approach Luke Kumar 1,2, Russell Greiner 1,2, arxiv:1903.10536v1 [cs.lg] 25 Mar 2019 1 Department of Computing Science, University
More informationβ j = coefficient of x j in the model; β = ( β1, β2,
Regression Modeling of Survival Time Data Why regression models? Groups similar except for the treatment under study use the nonparametric methods discussed earlier. Groups differ in variables (covariates)
More informationStochastic Optimization for Deep CCA via Nonlinear Orthogonal Iterations
Stochastic Optimization for Deep CCA via Nonlinear Orthogonal Iterations Weiran Wang Toyota Technological Institute at Chicago * Joint work with Raman Arora (JHU), Karen Livescu and Nati Srebro (TTIC)
More informationREGRESSION ANALYSIS FOR TIME-TO-EVENT DATA THE PROPORTIONAL HAZARDS (COX) MODEL ST520
REGRESSION ANALYSIS FOR TIME-TO-EVENT DATA THE PROPORTIONAL HAZARDS (COX) MODEL ST520 Department of Statistics North Carolina State University Presented by: Butch Tsiatis, Department of Statistics, NCSU
More informationConditional Random Fields and beyond DANIEL KHASHABI CS 546 UIUC, 2013
Conditional Random Fields and beyond DANIEL KHASHABI CS 546 UIUC, 2013 Outline Modeling Inference Training Applications Outline Modeling Problem definition Discriminative vs. Generative Chain CRF General
More informationRelative-risk regression and model diagnostics. 16 November, 2015
Relative-risk regression and model diagnostics 16 November, 2015 Relative risk regression More general multiplicative intensity model: Intensity for individual i at time t is i(t) =Y i (t)r(x i, ; t) 0
More informationSequential Supervised Learning
Sequential Supervised Learning Many Application Problems Require Sequential Learning Part-of of-speech Tagging Information Extraction from the Web Text-to to-speech Mapping Part-of of-speech Tagging Given
More informationWhy DNN Works for Acoustic Modeling in Speech Recognition?
Why DNN Works for Acoustic Modeling in Speech Recognition? Prof. Hui Jiang Department of Computer Science and Engineering York University, Toronto, Ont. M3J 1P3, CANADA Joint work with Y. Bao, J. Pan,
More informationSparse Models for Speech Recognition
Sparse Models for Speech Recognition Weibin Zhang and Pascale Fung Human Language Technology Center Hong Kong University of Science and Technology Outline Introduction to speech recognition Motivations
More informationHidden Markov Models in Language Processing
Hidden Markov Models in Language Processing Dustin Hillard Lecture notes courtesy of Prof. Mari Ostendorf Outline Review of Markov models What is an HMM? Examples General idea of hidden variables: implications
More informationOptimal Treatment Regimes for Survival Endpoints from a Classification Perspective. Anastasios (Butch) Tsiatis and Xiaofei Bai
Optimal Treatment Regimes for Survival Endpoints from a Classification Perspective Anastasios (Butch) Tsiatis and Xiaofei Bai Department of Statistics North Carolina State University 1/35 Optimal Treatment
More informationMulti-state Models: An Overview
Multi-state Models: An Overview Andrew Titman Lancaster University 14 April 2016 Overview Introduction to multi-state modelling Examples of applications Continuously observed processes Intermittently observed
More informationMAS3301 / MAS8311 Biostatistics Part II: Survival
MAS3301 / MAS8311 Biostatistics Part II: Survival M. Farrow School of Mathematics and Statistics Newcastle University Semester 2, 2009-10 1 13 The Cox proportional hazards model 13.1 Introduction In the
More informationPairwise rank based likelihood for estimating the relationship between two homogeneous populations and their mixture proportion
Pairwise rank based likelihood for estimating the relationship between two homogeneous populations and their mixture proportion Glenn Heller and Jing Qin Department of Epidemiology and Biostatistics Memorial
More informationLecture 7 Time-dependent Covariates in Cox Regression
Lecture 7 Time-dependent Covariates in Cox Regression So far, we ve been considering the following Cox PH model: λ(t Z) = λ 0 (t) exp(β Z) = λ 0 (t) exp( β j Z j ) where β j is the parameter for the the
More informationDynamic Prediction of Disease Progression Using Longitudinal Biomarker Data
Dynamic Prediction of Disease Progression Using Longitudinal Biomarker Data Xuelin Huang Department of Biostatistics M. D. Anderson Cancer Center The University of Texas Joint Work with Jing Ning, Sangbum
More informationMachine Learning. Module 3-4: Regression and Survival Analysis Day 2, Asst. Prof. Dr. Santitham Prom-on
Machine Learning Module 3-4: Regression and Survival Analysis Day 2, 9.00 16.00 Asst. Prof. Dr. Santitham Prom-on Department of Computer Engineering, Faculty of Engineering King Mongkut s University of
More informationSupport Vector Hazard Regression (SVHR) for Predicting Survival Outcomes. Donglin Zeng, Department of Biostatistics, University of North Carolina
Support Vector Hazard Regression (SVHR) for Predicting Survival Outcomes Introduction Method Theoretical Results Simulation Studies Application Conclusions Introduction Introduction For survival data,
More informationKernel Methods. Lecture 4: Maximum Mean Discrepancy Thanks to Karsten Borgwardt, Malte Rasch, Bernhard Schölkopf, Jiayuan Huang, Arthur Gretton
Kernel Methods Lecture 4: Maximum Mean Discrepancy Thanks to Karsten Borgwardt, Malte Rasch, Bernhard Schölkopf, Jiayuan Huang, Arthur Gretton Alexander J. Smola Statistical Machine Learning Program Canberra,
More informationInformation Extraction from Text
Information Extraction from Text Jing Jiang Chapter 2 from Mining Text Data (2012) Presented by Andrew Landgraf, September 13, 2013 1 What is Information Extraction? Goal is to discover structured information
More informationMultistate models and recurrent event models
Multistate models Multistate models and recurrent event models Patrick Breheny December 10 Patrick Breheny Survival Data Analysis (BIOS 7210) 1/22 Introduction Multistate models In this final lecture,
More informationKnowledge Extraction from DBNs for Images
Knowledge Extraction from DBNs for Images Son N. Tran and Artur d Avila Garcez Department of Computer Science City University London Contents 1 Introduction 2 Knowledge Extraction from DBNs 3 Experimental
More informationIntroduction to Machine Learning. PCA and Spectral Clustering. Introduction to Machine Learning, Slides: Eran Halperin
1 Introduction to Machine Learning PCA and Spectral Clustering Introduction to Machine Learning, 2013-14 Slides: Eran Halperin Singular Value Decomposition (SVD) The singular value decomposition (SVD)
More informationComputational Genomics and Molecular Biology, Fall
Computational Genomics and Molecular Biology, Fall 2011 1 HMM Lecture Notes Dannie Durand and Rose Hoberman October 11th 1 Hidden Markov Models In the last few lectures, we have focussed on three problems
More informationComputational Genomics
Computational Genomics http://www.cs.cmu.edu/~02710 Introduction to probability, statistics and algorithms (brief) intro to probability Basic notations Random variable - referring to an element / event
More informationA fast routine for fitting Cox models with time varying effects
Chapter 3 A fast routine for fitting Cox models with time varying effects Abstract The S-plus and R statistical packages have implemented a counting process setup to estimate Cox models with time varying
More informationA Least Squares Formulation for Canonical Correlation Analysis
A Least Squares Formulation for Canonical Correlation Analysis Liang Sun, Shuiwang Ji, and Jieping Ye Department of Computer Science and Engineering Arizona State University Motivation Canonical Correlation
More informationMultimodal Machine Learning
Multimodal Machine Learning Louis-Philippe (LP) Morency CMU Multimodal Communication and Machine Learning Laboratory [MultiComp Lab] 1 CMU Course 11-777: Multimodal Machine Learning 2 Lecture Objectives
More informationStatistics in medicine
Statistics in medicine Lecture 4: and multivariable regression Fatma Shebl, MD, MS, MPH, PhD Assistant Professor Chronic Disease Epidemiology Department Yale School of Public Health Fatma.shebl@yale.edu
More informationClassification Based on Probability
Logistic Regression These slides were assembled by Byron Boots, with only minor modifications from Eric Eaton s slides and grateful acknowledgement to the many others who made their course materials freely
More informationMultistate models and recurrent event models
and recurrent event models Patrick Breheny December 6 Patrick Breheny University of Iowa Survival Data Analysis (BIOS:7210) 1 / 22 Introduction In this final lecture, we will briefly look at two other
More informationYou know I m not goin diss you on the internet Cause my mama taught me better than that I m a survivor (What?) I m not goin give up (What?
You know I m not goin diss you on the internet Cause my mama taught me better than that I m a survivor (What?) I m not goin give up (What?) I m not goin stop (What?) I m goin work harder (What?) Sir David
More informationSurvival Prediction Under Dependent Censoring: A Copula-based Approach
Survival Prediction Under Dependent Censoring: A Copula-based Approach Yi-Hau Chen Institute of Statistical Science, Academia Sinica 2013 AMMS, National Sun Yat-Sen University December 7 2013 Joint work
More informationADVANCED STATISTICAL ANALYSIS OF EPIDEMIOLOGICAL STUDIES. Cox s regression analysis Time dependent explanatory variables
ADVANCED STATISTICAL ANALYSIS OF EPIDEMIOLOGICAL STUDIES Cox s regression analysis Time dependent explanatory variables Henrik Ravn Bandim Health Project, Statens Serum Institut 4 November 2011 1 / 53
More informationA Bayesian Nonparametric Approach to Causal Inference for Semi-competing risks
A Bayesian Nonparametric Approach to Causal Inference for Semi-competing risks Y. Xu, D. Scharfstein, P. Mueller, M. Daniels Johns Hopkins, Johns Hopkins, UT-Austin, UF JSM 2018, Vancouver 1 What are semi-competing
More informationSurvival SVM: a Practical Scalable Algorithm
Survival SVM: a Practical Scalable Algorithm V. Van Belle, K. Pelckmans, J.A.K. Suykens and S. Van Huffel Katholieke Universiteit Leuven - Dept. of Electrical Engineering (ESAT), SCD Kasteelpark Arenberg
More information10 : HMM and CRF. 1 Case Study: Supervised Part-of-Speech Tagging
10-708: Probabilistic Graphical Models 10-708, Spring 2018 10 : HMM and CRF Lecturer: Kayhan Batmanghelich Scribes: Ben Lengerich, Michael Kleyman 1 Case Study: Supervised Part-of-Speech Tagging We will
More informationLecture 5 Models and methods for recurrent event data
Lecture 5 Models and methods for recurrent event data Recurrent and multiple events are commonly encountered in longitudinal studies. In this chapter we consider ordered recurrent and multiple events.
More informationUniversität Potsdam Institut für Informatik Lehrstuhl Maschinelles Lernen. Linear Classifiers. Blaine Nelson, Tobias Scheffer
Universität Potsdam Institut für Informatik Lehrstuhl Linear Classifiers Blaine Nelson, Tobias Scheffer Contents Classification Problem Bayesian Classifier Decision Linear Classifiers, MAP Models Logistic
More informationProbabilistic Graphical Models for Image Analysis - Lecture 1
Probabilistic Graphical Models for Image Analysis - Lecture 1 Alexey Gronskiy, Stefan Bauer 21 September 2018 Max Planck ETH Center for Learning Systems Overview 1. Motivation - Why Graphical Models 2.
More informationTMA 4275 Lifetime Analysis June 2004 Solution
TMA 4275 Lifetime Analysis June 2004 Solution Problem 1 a) Observation of the outcome is censored, if the time of the outcome is not known exactly and only the last time when it was observed being intact,
More informationPackage SimSCRPiecewise
Package SimSCRPiecewise July 27, 2016 Type Package Title 'Simulates Univariate and Semi-Competing Risks Data Given Covariates and Piecewise Exponential Baseline Hazards' Version 0.1.1 Author Andrew G Chapple
More informationUndirected Graphical Models
Outline Hong Chang Institute of Computing Technology, Chinese Academy of Sciences Machine Learning Methods (Fall 2012) Outline Outline I 1 Introduction 2 Properties Properties 3 Generative vs. Conditional
More informationSurvival Regression Models
Survival Regression Models David M. Rocke May 18, 2017 David M. Rocke Survival Regression Models May 18, 2017 1 / 32 Background on the Proportional Hazards Model The exponential distribution has constant
More informationECLT 5810 Linear Regression and Logistic Regression for Classification. Prof. Wai Lam
ECLT 5810 Linear Regression and Logistic Regression for Classification Prof. Wai Lam Linear Regression Models Least Squares Input vectors is an attribute / feature / predictor (independent variable) The
More informationAn Introduction to Bioinformatics Algorithms Hidden Markov Models
Hidden Markov Models Outline 1. CG-Islands 2. The Fair Bet Casino 3. Hidden Markov Model 4. Decoding Algorithm 5. Forward-Backward Algorithm 6. Profile HMMs 7. HMM Parameter Estimation 8. Viterbi Training
More informationChapter 4 Dynamic Bayesian Networks Fall Jin Gu, Michael Zhang
Chapter 4 Dynamic Bayesian Networks 2016 Fall Jin Gu, Michael Zhang Reviews: BN Representation Basic steps for BN representations Define variables Define the preliminary relations between variables Check
More informationAcoustic Unit Discovery (AUD) Models. Leda Sarı
Acoustic Unit Discovery (AUD) Models Leda Sarı Lucas Ondel and Lukáš Burget A summary of AUD experiments from JHU Frederick Jelinek Summer Workshop 2016 lsari2@illinois.edu November 07, 2016 1 / 23 The
More informationDimension Reduction (PCA, ICA, CCA, FLD,
Dimension Reduction (PCA, ICA, CCA, FLD, Topic Models) Yi Zhang 10-701, Machine Learning, Spring 2011 April 6 th, 2011 Parts of the PCA slides are from previous 10-701 lectures 1 Outline Dimension reduction
More informationA Variance Modeling Framework Based on Variational Autoencoders for Speech Enhancement
A Variance Modeling Framework Based on Variational Autoencoders for Speech Enhancement Simon Leglaive 1 Laurent Girin 1,2 Radu Horaud 1 1: Inria Grenoble Rhône-Alpes 2: Univ. Grenoble Alpes, Grenoble INP,
More informationAssociation studies and regression
Association studies and regression CM226: Machine Learning for Bioinformatics. Fall 2016 Sriram Sankararaman Acknowledgments: Fei Sha, Ameet Talwalkar Association studies and regression 1 / 104 Administration
More informationECLT 5810 Linear Regression and Logistic Regression for Classification. Prof. Wai Lam
ECLT 5810 Linear Regression and Logistic Regression for Classification Prof. Wai Lam Linear Regression Models Least Squares Input vectors is an attribute / feature / predictor (independent variable) The
More informationMultiplex network inference
(using hidden Markov models) University of Cambridge Bioinformatics Group Meeting 11 February 2016 Words of warning Disclaimer These slides have been produced by combining & translating two of my previous
More informationHidden Markov Models
Hidden Markov Models Outline 1. CG-Islands 2. The Fair Bet Casino 3. Hidden Markov Model 4. Decoding Algorithm 5. Forward-Backward Algorithm 6. Profile HMMs 7. HMM Parameter Estimation 8. Viterbi Training
More informationOther likelihoods. Patrick Breheny. April 25. Multinomial regression Robust regression Cox regression
Other likelihoods Patrick Breheny April 25 Patrick Breheny High-Dimensional Data Analysis (BIOS 7600) 1/29 Introduction In principle, the idea of penalized regression can be extended to any sort of regression
More informationLogistic Regression. Robot Image Credit: Viktoriya Sukhanova 123RF.com
Logistic Regression These slides were assembled by Eric Eaton, with grateful acknowledgement of the many others who made their course materials freely available online. Feel free to reuse or adapt these
More informationMidterm: CS 6375 Spring 2015 Solutions
Midterm: CS 6375 Spring 2015 Solutions The exam is closed book. You are allowed a one-page cheat sheet. Answer the questions in the spaces provided on the question sheets. If you run out of room for an
More informationPhilosophy and Features of the mstate package
Introduction Mathematical theory Practice Discussion Philosophy and Features of the mstate package Liesbeth de Wreede, Hein Putter Department of Medical Statistics and Bioinformatics Leiden University
More informationBeyond GLM and likelihood
Stat 6620: Applied Linear Models Department of Statistics Western Michigan University Statistics curriculum Core knowledge (modeling and estimation) Math stat 1 (probability, distributions, convergence
More information] Automatic Speech Recognition (CS753)
] Automatic Speech Recognition (CS753) Lecture 17: Discriminative Training for HMMs Instructor: Preethi Jyothi Sep 28, 2017 Discriminative Training Recall: MLE for HMMs Maximum likelihood estimation (MLE)
More informationSpeaker Representation and Verification Part II. by Vasileios Vasilakakis
Speaker Representation and Verification Part II by Vasileios Vasilakakis Outline -Approaches of Neural Networks in Speaker/Speech Recognition -Feed-Forward Neural Networks -Training with Back-propagation
More informationCanonical Correlation Analysis with Kernels
Canonical Correlation Analysis with Kernels Florian Markowetz Max-Planck-Institute for Molecular Genetics Computational Molecular Biology Berlin Computational Diagnostics Group Seminar 2003 Mar 10 1 Overview
More informationPart IV Extensions: Competing Risks Endpoints and Non-Parametric AUC(t) Estimation
Part IV Extensions: Competing Risks Endpoints and Non-Parametric AUC(t) Estimation Patrick J. Heagerty PhD Department of Biostatistics University of Washington 166 ISCB 2010 Session Four Outline Examples
More informationGraph Wavelets to Analyze Genomic Data with Biological Networks
Graph Wavelets to Analyze Genomic Data with Biological Networks Yunlong Jiao and Jean-Philippe Vert "Emerging Topics in Biological Networks and Systems Biology" symposium, Swedish Collegium for Advanced
More informationSegmental Recurrent Neural Networks for End-to-end Speech Recognition
Segmental Recurrent Neural Networks for End-to-end Speech Recognition Liang Lu, Lingpeng Kong, Chris Dyer, Noah Smith and Steve Renals TTI-Chicago, UoE, CMU and UW 9 September 2016 Background A new wave
More informationUnivariate shrinkage in the Cox model for high dimensional data
Univariate shrinkage in the Cox model for high dimensional data Robert Tibshirani January 6, 2009 Abstract We propose a method for prediction in Cox s proportional model, when the number of features (regressors)
More informationLow-Dimensional Discriminative Reranking. Jagadeesh Jagarlamudi and Hal Daume III University of Maryland, College Park
Low-Dimensional Discriminative Reranking Jagadeesh Jagarlamudi and Hal Daume III University of Maryland, College Park Discriminative Reranking Useful for many NLP tasks Enables us to use arbitrary features
More informationBrief Introduction of Machine Learning Techniques for Content Analysis
1 Brief Introduction of Machine Learning Techniques for Content Analysis Wei-Ta Chu 2008/11/20 Outline 2 Overview Gaussian Mixture Model (GMM) Hidden Markov Model (HMM) Support Vector Machine (SVM) Overview
More informationSTAT 6350 Analysis of Lifetime Data. Failure-time Regression Analysis
STAT 6350 Analysis of Lifetime Data Failure-time Regression Analysis Explanatory Variables for Failure Times Usually explanatory variables explain/predict why some units fail quickly and some units survive
More informationSTAT 730 Chapter 1 Background
STAT 730 Chapter 1 Background Timothy Hanson Department of Statistics, University of South Carolina Stat 730: Multivariate Analysis 1 / 27 Logistics Course notes hopefully posted evening before lecture,
More informationBits of Machine Learning Part 1: Supervised Learning
Bits of Machine Learning Part 1: Supervised Learning Alexandre Proutiere and Vahan Petrosyan KTH (The Royal Institute of Technology) Outline of the Course 1. Supervised Learning Regression and Classification
More informationCOMP 551 Applied Machine Learning Lecture 13: Dimension reduction and feature selection
COMP 551 Applied Machine Learning Lecture 13: Dimension reduction and feature selection Instructor: Herke van Hoof (herke.vanhoof@cs.mcgill.ca) Based on slides by:, Jackie Chi Kit Cheung Class web page:
More informationarxiv: v1 [stat.ml] 16 Jan 2018
Deep Canonically Correlated LSTMs Mallinar, Neil nmallinar@gmail.com Rosset, Corbin corbyrosset@gmail.com arxiv:1801.05407v1 [stat.ml] 16 Jan 2018 Abstract We examine Deep Canonically Correlated LSTMs
More informationSurvival Analysis for Case-Cohort Studies
Survival Analysis for ase-ohort Studies Petr Klášterecký Dept. of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, harles University, Prague, zech Republic e-mail: petr.klasterecky@matfyz.cz
More informationStructural Learning and Integrative Decomposition of Multi-View Data
Structural Learning and Integrative Decomposition of Multi-View Data, Department of Statistics, Texas A&M University JSM 2018, Vancouver, Canada July 31st, 2018 Dr. Gen Li, Columbia University, Mailman
More informationPh.D. course: Regression models. Introduction. 19 April 2012
Ph.D. course: Regression models Introduction PKA & LTS Sect. 1.1, 1.2, 1.4 19 April 2012 www.biostat.ku.dk/~pka/regrmodels12 Per Kragh Andersen 1 Regression models The distribution of one outcome variable
More informationMixtures of Gaussians with Sparse Structure
Mixtures of Gaussians with Sparse Structure Costas Boulis 1 Abstract When fitting a mixture of Gaussians to training data there are usually two choices for the type of Gaussians used. Either diagonal or
More informationMaster s Written Examination - Solution
Master s Written Examination - Solution Spring 204 Problem Stat 40 Suppose X and X 2 have the joint pdf f X,X 2 (x, x 2 ) = 2e (x +x 2 ), 0 < x < x 2
More informationLecture 3. Truncation, length-bias and prevalence sampling
Lecture 3. Truncation, length-bias and prevalence sampling 3.1 Prevalent sampling Statistical techniques for truncated data have been integrated into survival analysis in last two decades. Truncation in
More informationComparison of Shannon, Renyi and Tsallis Entropy used in Decision Trees
Comparison of Shannon, Renyi and Tsallis Entropy used in Decision Trees Tomasz Maszczyk and W lodzis law Duch Department of Informatics, Nicolaus Copernicus University Grudzi adzka 5, 87-100 Toruń, Poland
More informationMaking Deep Learning Understandable for Analyzing Sequential Data about Gene Regulation
Making Deep Learning Understandable for Analyzing Sequential Data about Gene Regulation Dr. Yanjun Qi Department of Computer Science University of Virginia Tutorial @ ACM BCB-2018 8/29/18 Yanjun Qi / UVA
More informationSTATS 306B: Unsupervised Learning Spring Lecture 13 May 12
STATS 306B: Unsupervised Learning Spring 2014 Lecture 13 May 12 Lecturer: Lester Mackey Scribe: Jessy Hwang, Minzhe Wang 13.1 Canonical correlation analysis 13.1.1 Recap CCA is a linear dimensionality
More informationThe coxvc_1-1-1 package
Appendix A The coxvc_1-1-1 package A.1 Introduction The coxvc_1-1-1 package is a set of functions for survival analysis that run under R2.1.1 [81]. This package contains a set of routines to fit Cox models
More informationDeep Learning Basics Lecture 7: Factor Analysis. Princeton University COS 495 Instructor: Yingyu Liang
Deep Learning Basics Lecture 7: Factor Analysis Princeton University COS 495 Instructor: Yingyu Liang Supervised v.s. Unsupervised Math formulation for supervised learning Given training data x i, y i
More informationMachine learning - HT Maximum Likelihood
Machine learning - HT 2016 3. Maximum Likelihood Varun Kanade University of Oxford January 27, 2016 Outline Probabilistic Framework Formulate linear regression in the language of probability Introduce
More informationPh.D. course: Regression models. Regression models. Explanatory variables. Example 1.1: Body mass index and vitamin D status
Ph.D. course: Regression models Introduction PKA & LTS Sect. 1.1, 1.2, 1.4 25 April 2013 www.biostat.ku.dk/~pka/regrmodels13 Per Kragh Andersen Regression models The distribution of one outcome variable
More informationPower and Sample Size Calculations with the Additive Hazards Model
Journal of Data Science 10(2012), 143-155 Power and Sample Size Calculations with the Additive Hazards Model Ling Chen, Chengjie Xiong, J. Philip Miller and Feng Gao Washington University School of Medicine
More informationLecture 12. Multivariate Survival Data Statistics Survival Analysis. Presented March 8, 2016
Statistics 255 - Survival Analysis Presented March 8, 2016 Dan Gillen Department of Statistics University of California, Irvine 12.1 Examples Clustered or correlated survival times Disease onset in family
More informationMachine Learning 2nd Edition
INTRODUCTION TO Lecture Slides for Machine Learning 2nd Edition ETHEM ALPAYDIN, modified by Leonardo Bobadilla and some parts from http://www.cs.tau.ac.il/~apartzin/machinelearning/ The MIT Press, 2010
More informationMultivariable Fractional Polynomials
Multivariable Fractional Polynomials Axel Benner September 7, 2015 Contents 1 Introduction 1 2 Inventory of functions 1 3 Usage in R 2 3.1 Model selection........................................ 3 4 Example
More informationCIMAT Taller de Modelos de Capture y Recaptura Known Fate Survival Analysis
CIMAT Taller de Modelos de Capture y Recaptura 2010 Known Fate urvival Analysis B D BALANCE MODEL implest population model N = λ t+ 1 N t Deeper understanding of dynamics can be gained by identifying variation
More informationMultimodal context analysis and prediction
Multimodal context analysis and prediction Valeria Tomaselli (valeria.tomaselli@st.com) Sebastiano Battiato Giovanni Maria Farinella Tiziana Rotondo (PhD student) Outline 2 Context analysis vs prediction
More informationDiscriminative 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
More informationThe influence of categorising survival time on parameter estimates in a Cox model
The influence of categorising survival time on parameter estimates in a Cox model Anika Buchholz 1,2, Willi Sauerbrei 2, Patrick Royston 3 1 Freiburger Zentrum für Datenanalyse und Modellbildung, Albert-Ludwigs-Universität
More informationSpeech and Language Processing. Chapter 9 of SLP Automatic Speech Recognition (II)
Speech and Language Processing Chapter 9 of SLP Automatic Speech Recognition (II) Outline for ASR ASR Architecture The Noisy Channel Model Five easy pieces of an ASR system 1) Language Model 2) Lexicon/Pronunciation
More informationWhat s an HMM? Extraction with Finite State Machines e.g. Hidden Markov Models (HMMs) Hidden Markov Models (HMMs) for Information Extraction
Hidden Markov Models (HMMs) for Information Extraction Daniel S. Weld CSE 454 Extraction with Finite State Machines e.g. Hidden Markov Models (HMMs) standard sequence model in genomics, speech, NLP, What
More informationPackage CoxRidge. February 27, 2015
Type Package Title Cox Models with Dynamic Ridge Penalties Version 0.9.2 Date 2015-02-12 Package CoxRidge February 27, 2015 Author Aris Perperoglou Maintainer Aris Perperoglou
More informationLecture 18: Kernels Risk and Loss Support Vector Regression. Aykut Erdem December 2016 Hacettepe University
Lecture 18: Kernels Risk and Loss Support Vector Regression Aykut Erdem December 2016 Hacettepe University Administrative We will have a make-up lecture on next Saturday December 24, 2016 Presentations
More informationExtensions of Cox Model for Non-Proportional Hazards Purpose
PhUSE Annual Conference 2013 Paper SP07 Extensions of Cox Model for Non-Proportional Hazards Purpose Author: Jadwiga Borucka PAREXEL, Warsaw, Poland Brussels 13 th - 16 th October 2013 Presentation Plan
More information