bayesian nonparametric models for data exploration
play

Bayesian Nonparametric Models for Data Exploration Melanie F. - PowerPoint PPT Presentation

Sep 26, 2023 •632 likes •1.82k views

Bayesian Nonparametric Models for Data Exploration Melanie F. Pradier Friday 15 th September, 2017 Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Outline 1 Introduction 2 Bayesian

  1. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Contributions Goal: build useful BNP models for specific data exploration tasks. Atom-dependent DP mixture model Poisson factor analysis (PFA) models • estimates density in stratified data → flexible feature models for count data • suitable for fairness requirements • link to mixture of experts 1 Hierarchical PFA: • deals with stratified data Case-control IBP feature model 2 Three-parameter Restricted PFA: • infers latent features in • imposes structured sparsity in heterogeneous structured data latent space • suitable to separate global and 3 Dynamic PFA: group-specific effects • allows for time-varying • combined with statistical testing activation of latent factors Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 6/50

  2. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Contributions Goal: build useful BNP models for specific data exploration tasks. Atom-dependent DP mixture model Poisson factor analysis (PFA) models • estimates density in stratified data → flexible feature models for count data • suitable for fairness requirements • link to mixture of experts 1 Hierarchical PFA: • Application: marathon • deals with stratified data 2 Three-parameter Restricted PFA: Case-control IBP feature model • imposes structured sparsity in • infers latent features in latent space heterogeneous structured data 3 Dynamic PFA: • suitable to separate global and • allows for time-varying group-specific effects activation of latent factors • combined with statistical testing • Application: international trade • Application: clinical trial Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 6/50

  3. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Outline 1 Introduction 2 Bayesian nonparametrics 3 ADDP mixture model for marathon model 4 C-IBP feature model for clinical trials 5 PFA models for international trade 6 Conclusions Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 7/50

  4. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Bayesian nonparametrics (BNPs) • Bayesian framework for model selection • Nonparametric: number of parameters grows with the amount of data: • Prior over infinite-dimensional parameter space • Only a finite subset of parameters is used for any finite dataset Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 8/50

  5. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Bayesian nonparametrics (BNPs) • Bayesian framework for model selection • Nonparametric: number of parameters grows with the amount of data: • Prior over infinite-dimensional parameter space • Only a finite subset of parameters is used for any finite dataset • Rely on stochastic processes: • Dirichlet process • Beta process • Gaussian process • · · · Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 8/50

  6. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Dirichlet process (DP) G ∼ DP( α, H ) ∞ � G = π k δ φ k k =1 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 9/50

  7. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Dirichlet process (DP) G ∼ DP( α, H ) ∞ � G = π k δ φ k k =1 • central block for infinite mixture models Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 9/50

  8. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Dirichlet process (DP) G ∼ DP( α, H ) Stick-breaking representation (Ishwaran et.al, 2001) For k = 1 , · · · , ∞ k − 1 � v k ∼ Beta( α, 1) , π k = v k (1 − v ℓ ) ℓ =1 1 π 1 k = 1 π 2 k = 2 ∞ π 3 � G = π k δ φ k k = 3 . . . k =1 π ∼ GEM( α ) • central block for infinite mixture models Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 9/50

  9. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Dirichlet process (DP) Stick-breaking representation G ∼ DP( α, H ) (Ishwaran et.al, 2001) For k = 1 , · · · , ∞ k − 1 � v k ∼ Beta( α, 1) , π k = v k (1 − v ℓ ) ℓ =1 1 π 1 k = 1 π 2 k = 2 π 3 ∞ k = 3 � G = π k δ φ k . . . π ∼ GEM( α ) k =1 For k = 1 , · · · , ∞ • central block for infinite mixture models φ k ∼ H Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 9/50

  10. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Indian buffet process (IBP) • central block for infinite latent feature models Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 10/50

  11. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Indian buffet process (IBP) • central block for infinite latent feature models • hierarchy of a Beta process (BP) with multiple Bernoulli processes (BeP) ∞ � G = π k δ φ k ∼ BP( c, α, H ) k =1 1 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 10/50

  12. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Indian buffet process (IBP) • central block for infinite latent feature models • hierarchy of a Beta process (BP) with multiple Bernoulli processes (BeP) ∞ � G = π k δ φ k ∼ BP( c, α, H ) k =1 1 For n = 1 , · · · , ∞ ∞ � ζ n = z nk δ φ k ∼ BeP( G ) k =1 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 10/50

  13. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Indian buffet process (IBP) • central block for infinite latent feature models • hierarchy of a Beta process (BP) with multiple Bernoulli processes (BeP) ∞ � G = π k δ φ k ∼ BP( c, α, H ) k =1 1 For n = 1 , · · · , ∞ ∞ � ζ n = z nk δ φ k ∼ BeP( G ) k =1 Z ∼ IBP( α ) Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 10/50

  14. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Outline 1 Introduction 2 Bayesian nonparametrics 3 ADDP mixture model for marathon model 4 C-IBP feature model for clinical trials 5 PFA models for international trade 6 Conclusions Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 11/50

  15. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation 1 What is the impact of age and gender on runners performance? 2 Can we compare different runners in a fair manner? • entry requirements • rewards Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 12/50

  16. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation 1 What is the impact of age and gender on runners performance? 2 Can we compare different runners in a fair manner? • entry requirements • rewards Our Approach • dependent density estimation model • delivers scientific knowledge in sport sciences • constitutes a fair age-gender grading system • relies on dependent Dirichlet process Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 12/50

  17. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Dependent Dirichlet process (DDP) (MacEachern,2000) J : number of groups ∞ � G j = π jk δ φ jk k =1 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 13/50

  18. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Dependent Dirichlet process (DDP) (MacEachern,2000) J : number of groups ∞ � G j = π jk δ φ jk k =1 • hierarchical DP (Teh et.al, 2005) ∞ � G j = π jk δ φ k k =1 hierarchical DP single-p DDP • single-p DDP (MacEachern, 2000) G 0 ∼ DP ( α, H) G 0 ∼ DP ( α, H) ∞ � G j = π k δ φ jk G j ∼ DP ( γ, G 0 ) G j = T j [ G 0 ] k =1 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 13/50

  19. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Atom-dependent DP mixture model Generative model x i ≡ marathon finishing time for runner i π | α ∼ GEM( α ) c i | π ∼ Cat( π ) µ 0 , σ 2 � � µ k ∼ N 0 σ 2 x ∼ IG ( a, b ) x i | µ c i , σ 2 � � x i | other vars ∼ N x Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 14/50

  20. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Atom-dependent DP mixture model Generative model x ji ≡ marathon finishing time for runner i in age group j π | α ∼ GEM( α ) c ji | π ∼ Cat( π ) µ 0 , σ 2 � � µ k ∼ N 0 σ 2 x ∼ IG ( a, b ) θ ∼ N ( 0 , Σ θ ) x ji | µ c ji + θ j , σ 2 x ji | other vars ∼ N � � x � � − ( ℓ − q ) 2 ( Σ θ ) ℓq = σ 2 θ exp + κδ ( ℓ − q ) 2 ν 2 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 14/50

  21. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Atom-dependent DP mixture model Generative model x ji ≡ marathon finishing time for runner i in age group j g ji ≡ gender π | α ∼ GEM( α ) c ji | π ∼ Cat( π ) µ 0 , σ 2 µ k ∼ N � � 0 σ 2 x ∼ IG ( a, b ) θ ∼ N ( 0 , Σ θ ) 0 , σ 2 � � δ ∼N ω ω ∼N ( 0 , Σ ω ) x ji | µ c ji + θ j + ✶ [ g ji = 1]( δ + ω j ) , σ 2 � � x ji | other vars ∼ N x � − ( ℓ − q ) 2 � ( Σ θ ) ℓq = σ 2 θ exp + κδ ( ℓ − q ) 2 ν 2 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 15/50

  22. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions • MCMC approach Results • conditional conjugacy Impact of age • block Gibbs sampler • 1 / 4 M runners 0 . 8 Histogram pdf by ADDP 0 . 6 Indiv. clusters 0 . 4 0 . 2 0 2 4 6 8 Finishing time (hours) Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 16/50

  23. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions • MCMC approach Results • conditional conjugacy Impact of age • block Gibbs sampler 5 • 1 / 4 M runners New York City Boston 0 . 8 London Finishing time (hours) Histogram WMA 4 pdf by ADDP 0 . 6 Indiv. clusters 0 . 4 3 0 . 2 0 2 4 6 8 2 20 30 40 50 60 70 Finishing time (hours) Age Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 16/50

  24. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions • MCMC approach Results • conditional conjugacy Impact of age • block Gibbs sampler 5 • 1 / 4 M runners µ 1 + θ j µ 2 + θ j 0 . 8 New York City Finishing time (hours) Histogram Boston 4 pdf by ADDP London 0 . 6 Indiv. clusters WMA 0 . 4 3 0 . 2 0 2 4 6 8 2 20 30 40 50 60 70 Finishing time (hours) Age Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 16/50

  25. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Results Impact of gender 34 δ + ω j (mins) 32 30 28 26 10 20 30 40 50 60 70 age (years) Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 17/50

  26. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Results Impact of gender 34 δ + ω j (mins) 32 30 28 26 10 20 30 40 50 60 70 age (years) 12 Other Results 11 Cluster 0 (7.2%, T=3.80h) • Speed-dependent cluster means Cluster 1 (24.4%, T=3.93h) 10 Cluster 1 − (14.9%, T=4.03h) Speed (km/h) Elevation (m) Cluster 1 − − (3.6%, T=4.16h) • Link to mixture of experts 9 100 Cluster 2A (13.4%, T=4.17h) Cluster 2A − (11.3%, T=4.27h) 80 Cluster 2A − − (3.2%, T=4.43h) • Analysis of running patterns 8 60 Cluster 2B (1.1%, T=4.32h) Cluster 2B − (1.6%, T=4.47h) 40 • Prediction of finishing time 7 Cluster 3 (3.4%, T=4.56h) Cluster 3 − (4.4%, T=4.59h) 20 Cluster 3 −− (1.4%, T=4.88h) 6 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40 42.2 40 42.2 km Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 17/50

  27. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Outline 1 Introduction 2 Bayesian nonparametrics 3 ADDP mixture model for marathon model 4 C-IBP feature model for clinical trials 5 PFA models for international trade 6 Conclusions Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 18/50

  28. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: biomarker discovery in clinical trials Def: ”any variable that can be used as an indicator of a particular disease state”. Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 19/50

  29. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: biomarker discovery in clinical trials Def: ”any variable that can be used as an indicator of a particular disease state”. We want to discover: Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 19/50

  30. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: biomarker discovery in clinical trials Def: ”any variable that can be used as an indicator of a particular disease state”. We want to discover: 1 Indicators of disease progression: prognostic biomarkers Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 19/50

  31. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: biomarker discovery in clinical trials Def: ”any variable that can be used as an indicator of a particular disease state”. We want to discover: 1 Indicators of disease progression: prognostic biomarkers 2 Indicators of (positive) drug response: predictive biomarkers Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 19/50

  32. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: biomarker discovery in clinical trials Def: ”any variable that can be used as an indicator of a particular disease state”. 0 1 We want to discover: 1 Indicators of disease progression: prognostic biomarkers 2 Indicators of (positive) drug response: predictive biomarkers Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 19/50

  33. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions General latent feature model (GLFM) (Valera et.al, 2017) Latent feature model for heterogeneous datasets σ 2 B d = 1 . . . D B • d φ d α Z Y • d X Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 20/50

  34. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions General latent feature model (GLFM) (Valera et.al, 2017) • Link functions T d depend on type of Latent feature model for data for each dimension d heterogeneous datasets x nd = T d ( y nd ; φ d ) σ 2 B N ( Z n • B • d , σ 2 y nd | Z , B ∼ y ) N (0 , σ 2 d = 1 . . . D B kd ∼ B ) B • d ∼ Z IBP( α ) φ d α Z Y • d X Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 20/50

  35. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions General latent feature model (GLFM) (Valera et.al, 2017) • Link functions T d depend on type of Latent feature model for data for each dimension d heterogeneous datasets x nd = T d ( y nd ; φ d ) σ 2 B N ( Z n • B • d , σ 2 y nd | Z , B ∼ y ) N (0 , σ 2 d = 1 . . . D B kd ∼ B ) B • d ∼ Z IBP( α ) φ d Our contribution to GLFM project α Z Y • d X • Open-source python code • Simulations for data exploration https://github.com/ivaleraM/GLFM Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 20/50

  36. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Our contribution: Case-control IBP (C-IBP) R n : drug indicator por patient n σ 2 B x nd = T d ( y nd ; φ d ) d = 1 . . . D y nd | Z , W , B , C , R ∼ N ( Z n • B • d + ✶ [ R n = 1] W n • C • d , σ 2 B • d y ) R B kd ∼ N (0 , σ 2 B ) φ d Z ∼ IBP ( α ) C kd ∼ N (0 , σ 2 C ) α Y • d Z X W ∼ IBP ( α ) • Inference : MCMC approach with α W C • d accelerated Gibbs sampling • Biomarker discovery : statistical multiple hypothesis testing σ 2 C Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 21/50

  37. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Results: subpopulations GPC3 Antibody Treatment against Liver Cancer (J. Hepatology. 2016 Apr, Abou-Alfa et.al.) • 180 patients: 60 took a placebo, 120 took the drug • PFS: Progression Free Survival Sub-population Drug Identifier Size (number Median PFS of patients) Mean PFS (months) (months) F1 F2 F3 1. 0 0 0 0 33.37 3.06 1.65 2. 0 0 1 0 4.07 2.29 2.24 3. 0 1 0 0 17.84 2.72 1.81 4. 0 1 1 0 4.72 7.05 7.18 5. 1 0 0 0 51.52 3.22 2.55 6. 1 0 0 1 16.77 4.17 3.65 7. 1 0 1 0 8.38 1.74 1.33 8. 1 0 1 1 2.07 2.69 2.65 9. 1 1 0 0 29.88 3.36 2.03 10. 1 1 0 1 4.90 4.44 4.34 11. 1 1 1 0 4.53 6.31 5.31 12. 1 1 1 1 1.94 10.04 10.01 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 22/50

  38. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Results: subpopulations GPC3 Antibody Treatment against Liver Cancer (J. Hepatology. 2016 Apr, Abou-Alfa et.al.) • 180 patients: 60 took a placebo, 120 took the drug • PFS: Progression Free Survival Sub-population Drug Identifier Size (number Median PFS of patients) Mean PFS (months) (months) F1 F2 F3 1. 0 0 0 0 33.37 3.06 1.65 2. 0 0 1 0 4.07 2.29 2.24 3. 0 1 0 0 17.84 2.72 1.81 4. 0 1 1 0 4.72 7.05 7.18 5. 1 0 0 0 51.52 3.22 2.55 6. 1 0 0 1 16.77 4.17 3.65 7. 1 0 1 0 8.38 1.74 1.33 8. 1 0 1 1 2.07 2.69 2.65 9. 1 1 0 0 29.88 3.36 2.03 10. 1 1 0 1 4.90 4.44 4.34 11. 1 1 1 0 4.53 6.31 5.31 12. 1 1 1 1 1.94 10.04 10.01 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 22/50

  39. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Results: subpopulations GPC3 Antibody Treatment against Liver Cancer (J. Hepatology. 2016 Apr, Abou-Alfa et.al.) • 180 patients: 60 took a placebo, 120 took the drug • PFS: Progression Free Survival Sub-population Drug Identifier Size (number Median PFS of patients) Mean PFS (months) (months) F1 F2 F3 1. 0 0 0 0 33.37 3.06 1.65 2. 0 0 1 0 4.07 2.29 2.24 3. 0 1 0 0 17.84 2.72 1.81 4. 0 1 1 0 4.72 7.05 7.18 5. 1 0 0 0 51.52 3.22 2.55 6. 1 0 0 1 16.77 4.17 3.65 7. 1 0 1 0 8.38 1.74 1.33 8. 1 0 1 1 2.07 2.69 2.65 9. 1 1 0 0 29.88 3.36 2.03 10. 1 1 0 1 4.90 4.44 4.34 11. 1 1 1 0 4.53 6.31 5.31 12. 1 1 1 1 1.94 10.04 10.01 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 22/50

  40. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Results: subpopulations GPC3 Antibody Treatment against Liver Cancer (J. Hepatology. 2016 Apr, Abou-Alfa et.al.) • 180 patients: 60 took a placebo, 120 took the drug • PFS: Progression Free Survival Sub-population Drug Identifier Size (number Median PFS of patients) Mean PFS (months) (months) 15 F1 F2 F3 1. 0 0 0 0 33.37 3.06 1.65 PFS (months) 2. 0 0 1 0 4.07 2.29 2.24 10 3. 0 1 0 0 17.84 2.72 1.81 4. 0 1 1 0 4.72 7.05 7.18 5. 1 0 0 0 51.52 3.22 2.55 6. 1 0 0 1 16.77 4.17 3.65 5 7. 1 0 1 0 8.38 1.74 1.33 8. 1 0 1 1 2.07 2.69 2.65 9. 1 1 0 0 29.88 3.36 2.03 10. 1 1 0 1 4.90 4.44 4.34 0 11. 1 1 1 0 4.53 6.31 5.31 12. 1 1 1 1 1.94 10.04 10.01 1 2 3 4 5 6 7 8 9 1 0 2 1 1 1 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 22/50

  41. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Results: biomarker discovery Treatment-specific feature F3 2 0 ∆ d − 2 − 4 e t t I D h P T P e 6 3 6 3 a c r e c r e t m 7 6 5 B 3 4 8 8 K 6 + t - t K 6 6 N P F F 5 7 7 6 L h h M o o y h 6 h g g r 1 D 1 D m i l i l 0 1 4 D D D D 1 5 4 6 5 0 9 T g g F A R o t m b t b C N 6 g g N D D S S A u D D o m e 1 D D D 1 D P 1 / 6 / B A C C a o a C C C C 1 E E D i i o A C c o r M i D i / 0 / 1 e e u i r u i D r r K s C C P r c v c e C C / 8 C D b b C M M W H r t t T V C 4 3 0 1 S t e e r C 4 D N P P S o e C 6 6 1 3 C n 6 6 N P P C D m 6 6 3 3 c r C 5 1 1 C P 1 1 o C - 1 4 s C 6 D D C 3 C 6 D P C i D P D c C d 3 P C P 1 H D 5 C C C s 6 C K C D C D D G P G A 5 m / H N P G / A C s s C D 3 3 i G s / d D D C 6 s 3 C 5 D C D C C Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 23/50

  42. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Outline 1 Introduction 2 Bayesian nonparametrics 3 ADDP mixture model for marathon model 4 C-IBP feature model for clinical trials 5 PFA models for international trade 6 Conclusions Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 24/50

  43. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: wealth of nations What makes some countries wealthier than others? Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 25/50

  44. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: wealth of nations What makes some countries wealthier than others? Classical view • Division of labor (A. Smith, 1776; Ricardo, 1817) Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 25/50

  45. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: wealth of nations What makes some countries wealthier than others? Classical view • Division of labor (A. Smith, 1776; Ricardo, 1817) • Specialization leads to economic efficiency Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 25/50

  46. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: wealth of nations What makes some countries wealthier than others? Classical view • Division of labor (A. Smith, 1776; Ricardo, 1817) • Specialization leads to economic efficiency • Export portfolios Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 25/50

  47. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: wealth of nations What makes some countries wealthier than others? Classical view • Division of labor (A. Smith, 1776; Ricardo, 1817) • Specialization leads to economic efficiency • Export portfolios → block-structure Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 25/50

  48. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: wealth of nations The reality: 0 Countries 40 80 120 0 200 400 600 Products E nd / � p E nd RCA nd = � n E nd / � n,d E nd � if RCA nd ≥ 1 1 , x nd = 0 , otherwise Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 26/50

  49. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: wealth of nations The reality: Properties: 0 Countries 40 80 120 0 200 400 600 Products E nd / � p E nd RCA nd = � n E nd / � n,d E nd � if RCA nd ≥ 1 1 , x nd = 0 , otherwise Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 26/50

  50. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: wealth of nations The reality: Properties: 0 Countries 1 Triangularity 40 80 120 0 200 400 600 Products E nd / � p E nd RCA nd = � n E nd / � n,d E nd � if RCA nd ≥ 1 1 , x nd = 0 , otherwise Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 26/50

  51. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: wealth of nations The reality: Properties: 0 Countries 1 Triangularity 40 2 D ≫ N 80 120 0 200 400 600 Products E nd / � p E nd RCA nd = � n E nd / � n,d E nd � if RCA nd ≥ 1 1 , x nd = 0 , otherwise Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 26/50

  52. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Motivation: wealth of nations The reality: Properties: 0 Countries 1 Triangularity 40 2 D ≫ N 80 120 Our Approach 0 200 400 600 Products 1 Develop an infinite Poisson factor analysis model . . . E nd / � p E nd RCA nd = • flexible prior � n E nd / � n,d E nd • feature sparsity � if RCA nd ≥ 1 1 , x nd = 2 Design a time-varying 0 , otherwise extension Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 26/50

  53. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Bernoulli process Poisson factor analysis (BeP-PFA) Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 27/50

  54. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Bernoulli process Poisson factor analysis (BeP-PFA) Generative Model � � x nd ∼ Poisson Z n • B • d α B , µ B � � B kd ∼ Gamma α B Z ∼ IBP( α ) Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 27/50

  55. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Limitation of the IBP • Number of ones per row J n ∝ Poisson( α ) • Number of non-empty features K ∝ Poisson( α � N 1 j ) j =1 • Mass parameter α couples both J n and K α = 1 α = 10 0 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 50 0 5 0 10 20 30 40 nz = 97 nz = 339 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 28/50

  56. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Beyond the standard IBP Three-parameter IBP (Teh et.al, 2007) • More flexible distribution for feature weights Z n • ∼ BeP( µ ) (5.1) µ ∼ SBP(1 , α, H, c, σ ) (5.2) � α Γ(1 + c )Γ( n + c + σ − 1) � ∼ p ( J new ) Poisson Γ( n + c )Γ( c + σ ) Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 29/50

  57. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Beyond the standard IBP Three-parameter IBP (Teh et.al, 2007) • More flexible distribution for feature weights Z n • ∼ BeP( µ ) (5.1) µ ∼ SBP(1 , α, H, c, σ ) (5.2) � α Γ(1 + c )Γ( n + c + σ − 1) � ∼ p ( J new ) Poisson Γ( n + c )Γ( c + σ ) Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 29/50

  58. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Beyond the standard IBP Restricted IBP Three-parameter IBP (Doshi-Velez et.al, 2015) (Teh et.al, 2007) • Arbitrary prior f over J n • More flexible distribution for feature weights Z n • ∼ R - BeP( µ, f ) (5.3) µ ∼ BP(1 , α, H ) (5.4) Z n • ∼ BeP( µ ) (5.1) µ ∼ SBP(1 , α, H, c, σ ) (5.2) � α Γ(1 + c )Γ( n + c + σ − 1) � ∼ p ( J new ) Poisson Γ( n + c )Γ( c + σ ) Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 29/50

  59. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Beyond the standard IBP Restricted IBP Three-parameter IBP (Doshi-Velez et.al, 2015) (Teh et.al, 2007) • Arbitrary prior f over J n • More flexible distribution for feature weights Z n • ∼ R - BeP( µ, f ) (5.3) µ ∼ BP(1 , α, H ) (5.4) Z n • ∼ BeP( µ ) (5.1) µ ∼ SBP(1 , α, H, c, σ ) (5.2) � α Γ(1 + c )Γ( n + c + σ − 1) � • Combination of both ∼ p ( J new ) Poisson Γ( n + c )Γ( c + σ ) • Flexible prior Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 29/50

  60. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Our contributions α = 1 α = 10 0 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 50 0 5 0 10 20 30 40 nz = 97 nz = 339 3RBeP-PFA for static scenario � � x nd ∼ Poisson Z n • B • d α B , µ B � � B kd ∼ Gamma α B ∼ 3R - IBP( α, c, σ, f ) Z • Inference : aux. vars + dynamic programming (Doshi-Velez et.al, 2015) Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 30/50

  61. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Our contributions α = 1 α = 10 0 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 50 0 5 0 10 20 30 40 nz = 97 nz = 339 dBeP-PFA for dynamic scenario 3RBeP-PFA for static scenario x ( t ) Z ( t ) � � ∼ Poisson n • B • d � � x nd ∼ Poisson Z n • B • d nd α B , µ B � � α B , µ B � � B kd ∼ Gamma B kd ∼ Gamma α B α B Z ( • ) ∼ 3R - IBP( α, c, σ, f ) ∼ mIBP( α, γ, δ ) Z n • • Inference : forward-filtering • Inference : aux. vars + dynamic backward-sampling (Gael et.al, 2009) programming (Doshi-Velez et.al, 2015) Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 30/50

  62. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Results in static scenario Quantitative analysis: accuracy Vs interpretability Metric PMF NNMF BeP-PFA sBeP-PFA 3RBeP-PFA Log Perplexity 1 . 68 ± 0 . 01 1 . 61 ± 0 . 01 1 . 59 ± 0 . 04 3 . 26 ± 0 . 17 1 . 62 ± 0 . 01 Coherence − 264 . 60 ± 4 . 74 − 263 . 27 ± 7 . 45 − 149 . 36 ± 7 . 56 − 178 . 44 ± 4 . 50 − 140 . 51 ± 2 . 73 (a) 2010 SITC database ( N = 126 , D = 744 ) Metric PMF NNMF BeP-PFA sBeP-PFA 3RBeP-PFA Log Perplexity 1 . 48 ± 0 . 01 1 . 47 ± 0 . 01 1 . 58 ± 0 . 01 2 . 56 ± 0 . 12 1 . 57 ± 0 . 02 Coherence − 264 . 73 ± 3 . 11 − 264 . 67 ± 6 . 22 − 148 . 91 ± 10 . 57 − 168 . 39 ± 13 . 16 − 134 . 51 ± 4 . 43 (b) 2010 HS database ( N = 123 , D = 4890 ) • PMF: Probabilistic matrix factorization (Mnih et.al, 2008) • NNMF: Non-negative matrix factorization (Schmidt et.al, 2009) • BeP-PFA: Bernoulli process Poisson factor analysis • sBeP-PFA: sparse Bernoulli process Poisson factor analysis • 3RBeP-PFA: Three-parameter Restricted Bernoulli process Poisson factor analysis Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 31/50

  63. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Results in static scenario Capturing input sparsity structure 400 400 Inferred Inferred 0 400 0 400 Empirical Empirical (a) Baseline (b) BeP-PFA 400 400 Inferred Inferred 0 400 0 400 Empirical Empirical (c) sBeP-PFA (d) 3RBeP-PFA Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 32/50

  64. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Results in static scenario Interpretability Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 33/50

  65. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Temporal Dynamics Indonesia 1 F4 Capabilities F5 F0 Bias F9 F1 Agriculture 0 . 5 F2 F2 Clothing I F15 F3 Farming F4 Clothing II 0 F5 Electronics I 1965 1975 1985 1995 2005 F6 Processed Materials F7 Electronics II Egypt F8 Materials I F9 Machinery I 1 F10 Materials II F4 F11 Automobile F11 F12 Chemicals I 0 . 5 F1 F13 Chemicals II F2 F14 Machinery II F15 Miscellaneous 0 1965 1975 1985 1995 2005 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 34/50

  66. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Temporal Dynamics Indonesia 1 F4 Capabilities F5 F0 Bias F9 F1 Agriculture 0 . 5 F2 F2 Clothing I F15 F3 Farming F4 Clothing II 0 F5 Electronics I 1965 1975 1985 1995 2005 F6 Processed Materials F7 Electronics II Egypt F8 Materials I F9 Machinery I 1 F10 Materials II F4 F11 Automobile F11 F12 Chemicals I 0 . 5 F1 F13 Chemicals II F2 F14 Machinery II F15 Miscellaneous 0 1965 1975 1985 1995 2005 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 34/50

  67. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Temporal Dynamics Indonesia 1 F4 Capabilities F5 F0 Bias F9 F1 Agriculture 0 . 5 F2 F2 Clothing I F15 F3 Farming F4 Clothing II 0 F5 Electronics I 1965 1975 1985 1995 2005 F6 Processed Materials F7 Electronics II Egypt F8 Materials I F9 Machinery I 1 F10 Materials II F4 F11 Automobile F11 F12 Chemicals I 0 . 5 F1 F13 Chemicals II F2 F14 Machinery II F15 Miscellaneous 0 1965 1975 1985 1995 2005 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 34/50

  68. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Model extension: Dynamic PFA Indonesia 1 F1 F4 F7 Model extension 0 . 5 F10 F13 x ( t ) Z ( t ) � � ∼ Poisson n • B • d nd 0 α B , µ B � � 1965 1975 1985 1995 2005 B kd ∼ Gamma α B Egypt Z ( • ) ∼ mIBP( α, γ, δ ) n • 1 F3 mIBP: markov Indian buffet process F5 0 . 5 (Gael et.al, 2009) F7 F10 0 1965 1975 1985 1995 2005 Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 35/50

  69. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Outline 1 Introduction 2 Bayesian nonparametrics 3 ADDP mixture model for marathon model 4 C-IBP feature model for clinical trials 5 PFA models for international trade 6 Conclusions Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 36/50

  70. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Conclusions BNPs • useful BNP models for specific data exploration tasks • Fair density estimation model • Structured general latent feature model (global and group-specific factors) • Flexible Poisson factor analysis models in static/dynamic scenarios Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 37/50

  71. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Conclusions BNPs • useful BNP models for specific data exploration tasks • Fair density estimation model • Structured general latent feature model (global and group-specific factors) • Flexible Poisson factor analysis models in static/dynamic scenarios Sports science • age-gender curves • fair grading system • running patterns over time Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 37/50

  72. Intro BNPs ADDP for Marathon Modeling C-IBP for Clinical Trial PFAs for International Trade Conclusions Conclusions BNPs • useful BNP models for specific data exploration tasks • Fair density estimation model • Structured general latent feature model (global and group-specific factors) • Flexible Poisson factor analysis models in static/dynamic scenarios Cancer research Sports science • subpopulation • age-gender curves learning • fair grading system • biomarker discovery • running patterns • clinico-genetic over time associations Melanie F. Pradier (UC3M) Bayesian Nonparametric Models for Data Exploration 2017-09-15 37/50

Recommend

Nonparametric Bayesian Models for Sparse Matrices and Covariances Zoubin Ghahramani Department

Nonparametric Bayesian Models for Sparse Matrices and Covariances Zoubin Ghahramani Department

Nonparametric Bayesian Models for Sparse Matrices and Covariances Zoubin Ghahramani Department of Engineering University of Cambridge, UK zoubin@eng.cam.ac.uk http://learning.eng.cam.ac.uk/zoubin/ Bayes 250 Edinburgh 2011 Bayesian Machine

402 views • 36 slides
Bayesian nonparametric inference for diffusion models with discrete sampling Delft University of

Bayesian nonparametric inference for diffusion models with discrete sampling Delft University of

Bayesian nonparametric inference for diffusion models with discrete sampling Delft University of Technology Jakob S ohl joint work with Richard Nickl Van Dantzig Seminar, Leiden, 26 October 2016 Jakob S ohl (TU Delft) Bayesian

514 views • 29 slides
On a Class of Nonparametric Bayesian Autoregressive Models Maria Anna Di Lucca 1 , Alessandra

On a Class of Nonparametric Bayesian Autoregressive Models Maria Anna Di Lucca 1 , Alessandra

On a Class of Nonparametric Bayesian Autoregressive Models Maria Anna Di Lucca 1 , Alessandra Guglielmi 2 , uller 3 , Fernando A. Quintana 4 Peter M Karolinska Institutet 1 Politecnico di Milano 2 University of Texas, Austin 3 olica de Chile 4

1.02k views • 89 slides
Dirichlet Processes and Nonparametric Bayesian Modelling Volker Tresp 1 Motivation Infinite

Dirichlet Processes and Nonparametric Bayesian Modelling Volker Tresp 1 Motivation Infinite

Dirichlet Processes and Nonparametric Bayesian Modelling Volker Tresp 1 Motivation Infinite models have recently gained a lot of attention in Bayesian machine learning They offer great flexibility and, in many applications, allow a more

1.84k views • 144 slides
Outline Motivation and challenge Dirichlet Process and Infinite Mixture Formulation

Outline Motivation and challenge Dirichlet Process and Infinite Mixture Formulation

Nonparametric Bayesian M Nonparametric Bayesian Models odels --Learning and Reasoning in Open Possible Worlds -- Learning and Reasoning in Open Possible Worlds Eric Xing epxing@cs.cmu.edu Machine Learning Dept./Language Technology

783 views • 40 slides
Bayesian nonparametric models for bipartite graphs Fran cois Caron Department of Statistics,

Bayesian nonparametric models for bipartite graphs Fran cois Caron Department of Statistics,

Bayesian nonparametric models for bipartite graphs Fran cois Caron Department of Statistics, Oxford Statistics Colloquium, Harvard University November 11, 2013 F. Caron 1 / 27 Bipartite networks Readers/Customers A 1 A 2 B 1 B 2 B 3 B 4

745 views • 51 slides
Synergies in learning syllables and words or Adaptor grammars: a class of nonparametric Bayesian

Synergies in learning syllables and words or Adaptor grammars: a class of nonparametric Bayesian

Synergies in learning syllables and words or Adaptor grammars: a class of nonparametric Bayesian models Mark Johnson Brown University Joint work with Sharon Goldwater and Tom Griffiths NECPHON, November, 2008 1 / 26 Research goals Most

470 views • 26 slides
Nonparametric analysis of CMB Nonparametric analysis of CMB power spectrum data and consistency

Nonparametric analysis of CMB Nonparametric analysis of CMB power spectrum data and consistency

Nonparametric analysis of CMB Nonparametric analysis of CMB power spectrum data and consistency power spectrum data and consistency test of cosmological models test of cosmological models Amir Aghamousa Asia Pacific Center for Theoretical

254 views • 22 slides
Toward Reliable Bayesian Nonparametric Learning Erik Sudderth Brown University Department of

Toward Reliable Bayesian Nonparametric Learning Erik Sudderth Brown University Department of

Toward Reliable Bayesian Nonparametric Learning Erik Sudderth Brown University Department of Computer Science Donglai Wei & Michael Bryant (HDP topics) Joint work with Michael Hughes & Emily Fox (BP-HMM) Documents & Topic Models

649 views • 61 slides
Unsupervised Music Understanding based on Nonparametric Bayesian Models Kazuyoshi Yoshii Masataka

Unsupervised Music Understanding based on Nonparametric Bayesian Models Kazuyoshi Yoshii Masataka

Unsupervised Music Understanding based on Nonparametric Bayesian Models Kazuyoshi Yoshii Masataka Goto AIST, Japan Why can we recognize music as music? Is this because we are taught music theory? Definitely No! Why Unsupervised Understanding?

393 views • 22 slides
Unsupervised Coreference Resolution in a Nonparametric Bayesian Model Aria Haghighi and Dan Klein

Unsupervised Coreference Resolution in a Nonparametric Bayesian Model Aria Haghighi and Dan Klein

Unsupervised Coreference Resolution in a Nonparametric Bayesian Model Aria Haghighi and Dan Klein Presented by Brandon Norick Overview Introduction Preliminaries Coreference Resolution Models Experiments Conclusion

656 views • 37 slides
Bayesian and Non-Bayesian Analysis of Soccer Data using Bivariate Poisson Regression Models

Bayesian and Non-Bayesian Analysis of Soccer Data using Bivariate Poisson Regression Models

Bivariate Poisson models for soccer April 2003 Bayesian and Non-Bayesian Analysis of Soccer Data using Bivariate Poisson Regression Models Dimitris Karlis John Ntzoufras Department of Statistics Dept. of Business Administration

909 views • 39 slides
Nonparametric Estimation in Panel Data Models with Heterogeneity and TimeVaryingness Jiti Gao

Nonparametric Estimation in Panel Data Models with Heterogeneity and TimeVaryingness Jiti Gao

Nonparametric Estimation in Panel Data Models with Heterogeneity and TimeVaryingness Jiti Gao , Fei Liu , Yanrong Yang Monash University Australian National University Dec 12, 2019 An Econometric Problem Panel Data

1.37k views • 66 slides
Parametric vs Nonparametric Models Parametric models assume some finite set of parameters .

Parametric vs Nonparametric Models Parametric models assume some finite set of parameters .

Parametric vs Nonparametric Models Parametric models assume some finite set of parameters . Given the parameters, future predictions, x , are independent of the observed data, D : P ( x | , D ) = P ( x | ) therefore capture

679 views • 5 slides
A Fast New Bayesian Approach to High-Dimensional Nonparametric Regression Without MCMC Ray Bai

A Fast New Bayesian Approach to High-Dimensional Nonparametric Regression Without MCMC Ray Bai

A Fast New Bayesian Approach to High-Dimensional Nonparametric Regression Without MCMC Ray Bai Department of Biostatistics, Epidemiology, and Informatics, University of Pennsylvania Joint work with Gemma E. Moran (co-first author), Joseph

775 views • 55 slides
Introduction to Big Data and Machine Learning Nonparametric methods Dr. Mihail October 1, 2019

Introduction to Big Data and Machine Learning Nonparametric methods Dr. Mihail October 1, 2019

Introduction to Big Data and Machine Learning Nonparametric methods Dr. Mihail October 1, 2019 (Dr. Mihail) Intro Big Data October 1, 2019 1 / 20 Nonparametric Idea So far we focused on models (probabilistic or deterministic) that are

1.23k views • 20 slides
Introduction to Nonparametric Bayesian Modeling and Gaussian Process Regression Piyush Rai Dept.

Introduction to Nonparametric Bayesian Modeling and Gaussian Process Regression Piyush Rai Dept.

Introduction to Nonparametric Bayesian Modeling and Gaussian Process Regression Piyush Rai Dept. of CSE, IIT Kanpur (Mini-course: lecture 3) Nov 07, 2015 Piyush Rai (IIT Kanpur) Nonparametric Bayesian Modeling and Gaussian Process Regression

1.03k views • 54 slides
Nonparametric Bayesian Storyline Detection from Microtexts Vinodh Krishnan and Jacob Eisenstein

Nonparametric Bayesian Storyline Detection from Microtexts Vinodh Krishnan and Jacob Eisenstein

Nonparametric Bayesian Storyline Detection from Microtexts Vinodh Krishnan and Jacob Eisenstein Georgia Institute of Technology Clustering microtexts into storylines Strong start for Barcelona Dog tuxedo bought with county credit card Messi

665 views • 33 slides
Unsupervised Coreference Resolution in a Nonparametric Bayesian Model Aria Haghighi and Dan

Unsupervised Coreference Resolution in a Nonparametric Bayesian Model Aria Haghighi and Dan

Unsupervised Coreference Resolution in a Nonparametric Bayesian Model Aria Haghighi and Dan Klein Computer Science Division University of California Berkeley Coreference Resolution The Weir Group , whose headquarters is in the U.S , is a

1.75k views • 143 slides
Comparison of Bayesian Network Meta-Analysis Models for Survival Data Purvi Prajapati James

Comparison of Bayesian Network Meta-Analysis Models for Survival Data Purvi Prajapati James

Comparison of Bayesian Network Meta-Analysis Models for Survival Data Purvi Prajapati James Stamey John Seaman May 22, 2019 1 Table of Contents 1. Introduction 2. Bayesian Network Meta-Analysis Models for Survival Data 3. Simulation Study

501 views • 37 slides
h ( n ) w ( n ) x ( n ) Linear nonparametric vs. parametric models Many researchers use

h ( n ) w ( n ) x ( n ) Linear nonparametric vs. parametric models Many researchers use

Linear Signal Models Overview Introduction Introduction h ( n ) w ( n ) x ( n ) Linear nonparametric vs. parametric models Many researchers use signal models to analyze stationary Equivalent representations univariate time series

507 views • 5 slides
Poster #20 Bayesian Nonparametric Federated Learning of Neural Networks Mikhail Yurochkin Mayank

Poster #20 Bayesian Nonparametric Federated Learning of Neural Networks Mikhail Yurochkin Mayank

IBM Research, MIT-IBM Watson AI Lab PFNM , Poster #20 ICML 2019 Poster #20 Bayesian Nonparametric Federated Learning of Neural Networks Mikhail Yurochkin Mayank Agarwal, Soumya Ghosh, Kristjan Greenewald, Nghia Hoang, Yasaman Khazaeni IBM

120 views • 9 slides
A Nonparametric Bayesian Basket Trial Slide 4 Design Report (decision) Peter M uller , UT

A Nonparametric Bayesian Basket Trial Slide 4 Design Report (decision) Peter M uller , UT

recursive splits @ Mdn( x j s ), s = 1 , 2 , 3 Slide 1 A Nonparametric Bayesian Basket Trial Slide 4 Design Report (decision) Peter M uller , UT Austin www.math.utexas.edu/users/pmueller/oncostat.pdf subset-specific mean outome p ( y i

417 views • 3 slides
Nonparametric Bayesian Word Sense Induction Xuchen Yao 1 and Benjamin Van Durme 1,2 1 Department of

Nonparametric Bayesian Word Sense Induction Xuchen Yao 1 and Benjamin Van Durme 1,2 1 Department of

Nonparametric Bayesian Word Sense Induction Xuchen Yao 1 and Benjamin Van Durme 1,2 1 Department of Computer Science 2 Human Language Technology Center of Excellence Johns Hopkins University TextGraphs-6 June 23 2011 1 / 14 Word Sense Induction

665 views • 21 slides

More recommend