Multimodal Deep Learning for Predicting Survival from Breast Cancer

Size: px
Start display at page:

Download "Multimodal Deep Learning for Predicting Survival from Breast Cancer"

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 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 information

arxiv: v1 [cs.lg] 25 Mar 2019

arxiv: 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 information

β j = coefficient of x j in the model; β = ( β1, β2,

β 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 information

Stochastic Optimization for Deep CCA via Nonlinear Orthogonal Iterations

Stochastic 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 information

REGRESSION 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 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 information

Conditional Random Fields and beyond DANIEL KHASHABI CS 546 UIUC, 2013

Conditional 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 information

Relative-risk regression and model diagnostics. 16 November, 2015

Relative-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 information

Sequential Supervised Learning

Sequential 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 information

Why DNN Works for Acoustic Modeling in Speech Recognition?

Why 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 information

Sparse Models for Speech Recognition

Sparse 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 information

Hidden Markov Models in Language Processing

Hidden 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 information

Optimal 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 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 information

Multi-state Models: An Overview

Multi-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 information

MAS3301 / MAS8311 Biostatistics Part II: Survival

MAS3301 / 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 information

Pairwise 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 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 information

Lecture 7 Time-dependent Covariates in Cox Regression

Lecture 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 information

Dynamic Prediction of Disease Progression Using Longitudinal Biomarker Data

Dynamic 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 information

Machine 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, 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 information

Support 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. 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 information

Kernel 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 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 information

Information Extraction from Text

Information 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 information

Multistate models and recurrent event models

Multistate 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 information

Knowledge Extraction from DBNs for Images

Knowledge 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 information

Introduction to Machine Learning. PCA and Spectral Clustering. Introduction to Machine Learning, Slides: Eran Halperin

Introduction 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 information

Computational Genomics and Molecular Biology, Fall

Computational 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 information

Computational Genomics

Computational 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 information

A fast routine for fitting Cox models with time varying effects

A 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 information

A Least Squares Formulation for Canonical Correlation Analysis

A 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 information

Multimodal Machine Learning

Multimodal 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 information

Statistics in medicine

Statistics 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 information

Classification Based on Probability

Classification 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 information

Multistate models and recurrent event models

Multistate 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 information

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?

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? 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 information

Survival Prediction Under Dependent Censoring: A Copula-based Approach

Survival 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 information

ADVANCED 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 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 information

A Bayesian Nonparametric Approach to Causal Inference for Semi-competing risks

A 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 information

Survival SVM: a Practical Scalable Algorithm

Survival 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 information

10 : HMM and CRF. 1 Case Study: Supervised Part-of-Speech Tagging

10 : 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 information

Lecture 5 Models and methods for recurrent event data

Lecture 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 information

Universität Potsdam Institut für Informatik Lehrstuhl Maschinelles Lernen. Linear Classifiers. Blaine Nelson, Tobias Scheffer

Universität 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 information

Probabilistic Graphical Models for Image Analysis - Lecture 1

Probabilistic 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 information

TMA 4275 Lifetime Analysis June 2004 Solution

TMA 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 information

Package SimSCRPiecewise

Package 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 information

Undirected Graphical Models

Undirected 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 information

Survival Regression Models

Survival 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 information

ECLT 5810 Linear Regression and Logistic Regression for Classification. Prof. Wai Lam

ECLT 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 information

An Introduction to Bioinformatics Algorithms Hidden Markov Models

An 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 information

Chapter 4 Dynamic Bayesian Networks Fall Jin Gu, Michael Zhang

Chapter 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 information

Acoustic Unit Discovery (AUD) Models. Leda Sarı

Acoustic 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 information

Dimension Reduction (PCA, ICA, CCA, FLD,

Dimension 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 information

A Variance Modeling Framework Based on Variational Autoencoders for Speech Enhancement

A 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 information

Association studies and regression

Association 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 information

ECLT 5810 Linear Regression and Logistic Regression for Classification. Prof. Wai Lam

ECLT 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 information

Multiplex network inference

Multiplex 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 information

Hidden Markov Models

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 information

Other likelihoods. Patrick Breheny. April 25. Multinomial regression Robust regression Cox regression

Other 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 information

Logistic Regression. Robot Image Credit: Viktoriya Sukhanova 123RF.com

Logistic 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 information

Midterm: CS 6375 Spring 2015 Solutions

Midterm: 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 information

Philosophy and Features of the mstate package

Philosophy 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 information

Beyond GLM and likelihood

Beyond 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) ] 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 information

Speaker Representation and Verification Part II. by Vasileios Vasilakakis

Speaker 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 information

Canonical Correlation Analysis with Kernels

Canonical 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 information

Part IV Extensions: Competing Risks Endpoints and Non-Parametric AUC(t) Estimation

Part 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 information

Graph Wavelets to Analyze Genomic Data with Biological Networks

Graph 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 information

Segmental Recurrent Neural Networks for End-to-end Speech Recognition

Segmental 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 information

Univariate shrinkage in the Cox model for high dimensional data

Univariate 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 information

Low-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 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 information

Brief Introduction of Machine Learning Techniques for Content Analysis

Brief 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 information

STAT 6350 Analysis of Lifetime Data. Failure-time Regression Analysis

STAT 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 information

STAT 730 Chapter 1 Background

STAT 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 information

Bits of Machine Learning Part 1: Supervised Learning

Bits 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 information

COMP 551 Applied Machine Learning Lecture 13: Dimension reduction and feature selection

COMP 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 information

arxiv: v1 [stat.ml] 16 Jan 2018

arxiv: 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 information

Survival Analysis for Case-Cohort Studies

Survival 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 information

Structural Learning and Integrative Decomposition of Multi-View Data

Structural 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 information

Ph.D. course: Regression models. Introduction. 19 April 2012

Ph.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 information

Mixtures of Gaussians with Sparse Structure

Mixtures 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 information

Master s Written Examination - Solution

Master 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 information

Lecture 3. Truncation, length-bias and prevalence sampling

Lecture 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 information

Comparison of Shannon, Renyi and Tsallis Entropy used in Decision Trees

Comparison 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 information

Making Deep Learning Understandable for Analyzing Sequential Data about Gene Regulation

Making 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 information

STATS 306B: Unsupervised Learning Spring Lecture 13 May 12

STATS 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 information

The coxvc_1-1-1 package

The 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 information

Deep 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 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 information

Machine learning - HT Maximum Likelihood

Machine 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 information

Ph.D. course: Regression models. Regression models. Explanatory variables. Example 1.1: Body mass index and vitamin D status

Ph.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 information

Power and Sample Size Calculations with the Additive Hazards Model

Power 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 information

Lecture 12. Multivariate Survival Data Statistics Survival Analysis. Presented March 8, 2016

Lecture 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 information

Machine Learning 2nd Edition

Machine 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 information

Multivariable Fractional Polynomials

Multivariable 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 information

CIMAT Taller de Modelos de Capture y Recaptura Known Fate Survival Analysis

CIMAT 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 information

Multimodal context analysis and prediction

Multimodal 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 information

Discriminative Direction for Kernel Classifiers

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

More information

The 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 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 information

Speech and Language Processing. Chapter 9 of SLP Automatic Speech Recognition (II)

Speech 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 information

What s an HMM? Extraction with Finite State Machines e.g. Hidden Markov Models (HMMs) Hidden Markov Models (HMMs) for Information Extraction

What 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 information

Package CoxRidge. February 27, 2015

Package 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 information

Lecture 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 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 information

Extensions of Cox Model for Non-Proportional Hazards Purpose

Extensions 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