Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Sandhya Prabhakaran - A Bayesian Approach To Model Overlapping Objects Available As Distance Data

176 views

Published on

A Bayesian Approach To Model Overlapping Objects Available As Distance Data

Published in: Technology
  • Be the first to comment

  • Be the first to like this

Sandhya Prabhakaran - A Bayesian Approach To Model Overlapping Objects Available As Distance Data

  1. 1. A Bayesian Approach to Model Overlapping Objects Available as Distance Data Sandhya Prabhakaran1 and Julia E. Vogt2,3 Memorial Sloan Kettering Cancer Centre, NYC 1 University of Basel 2 Swiss Institute of Bioinformatics 3 MLconf, NYC 29th March 2019
  2. 2. Two religions in Machine Learning Frequentists (https://medium.com/datadriveninvestor/bayesian-vs-frequentist-for-dummies-58ce230c3796)
  3. 3. Two religions in Machine Learning Frequentists Bayesians (https://medium.com/datadriveninvestor/bayesian-vs-frequentist-for-dummies-58ce230c3796)
  4. 4. Two religions in Machine Learning ● A coin toss example: 10 heads in 10 tosses (= data given) ● Frequentists: ○ Probability is a Point estimate ○ What is the relative frequency of tails = no answer
  5. 5. Two religions in Machine Learning ● A coin toss example: 10 heads in 10 tosses (= data given) ● Frequentists: ○ Probability is a Point estimate ○ What is the relative frequency of tails = no answer ● Bayesians: ○ Probability is a distribution ○ What is the relative frequency of tails = 0.5
  6. 6. Two religions in Machine Learning ● A coin toss example: 10 heads in 10 tosses (= data given) ● Frequentists: ○ Probability is a Point estimate ○ What is the relative frequency of tails = no answer ● Bayesians: ○ Probability is a distribution ○ What is the relative frequency of tails = 0.5 ○ A Bayesian is one who, vaguely expecting a horse, and catching a glimpse of a donkey, strongly believes he has seen a mule. ○ More flexible: inference, thinking, planning and reasoning (downstream analyses)
  7. 7. Bayesian: Clustering
  8. 8. Bayesian: Clustering
  9. 9. Bayesian: Clustering of vectorial objects
  10. 10. Bayesian: Clustering of vectorial objects Clustering algorithm
  11. 11. Bayesian: Clustering of non-vectorial objects (Image courtesy: shutterstock)
  12. 12. Bayesian: Clustering of non-vectorial objects Mostly available as pairwise distance data
  13. 13. POCD: Probabilistic model for Overlap Clustering of Distance data
  14. 14. POCD: Overlap Clustering for distance data
  15. 15. POCD: Overlap Clustering for distance data
  16. 16. POCD: Overlap Clustering for distance data
  17. 17. POCD: Overlap Clustering for distance data
  18. 18. POCD: Overlap Clustering for distance data
  19. 19. POCD: Overlap Clustering for distance data
  20. 20. POCD: Overlap Clustering for distance data ● Bayesian clustering model ● Given pairwise D, we infer Z (the cluster assignment matrix)
  21. 21. POCD: Overlap Clustering for distance data Z ● Binary matrix ● Cluster assignment matrix ● Needs to be inferred
  22. 22. POCD: Overlap Clustering for distance data ● Bayesian clustering model ● Given pairwise D, we infer Z: p(Z|D,.) ∝ p(D|Z) p(Z) (posterior) (likelihood) (prior)
  23. 23. POCD: Overlap Clustering for distance data p(Z|D,.) ∝ p(D|Z) p(Z) (prior)(posterior) (likelihood)
  24. 24. POCD: Overlap Clustering for distance data Prior over Z: Indian Buffet process ● As k → infinity, we arrive at the IBP ● No need to fix the number of clusters p(Z|D,.) ∝ p(D|Z) p(Z) (prior)(posterior) (likelihood)
  25. 25. POCD: Overlap Clustering for distance data Invariant Likelihood: generalised Wishart ● Translation and rotation invariant p(Z|D,.) ∝ p(D|Z) p(Z) (prior)(posterior) (likelihood)
  26. 26. POCD: Overlap Clustering for distance data Inference using Metropolis Hastings ● MCMC algorithm ● Used in models deploying the IBP ● Asymptotically exact approximations of the posterior ● We need to infer Z and #clusters p(Z|D,.) ∝ p(D|Z) p(Z) (prior)(posterior) (likelihood)
  27. 27. POCD: Overlap Clustering for distance data Inference using Metropolis Hastings ● MCMC algorithm ● Used in models deploying the IBP ● Asymptotically exact approximations of the posterior ● We need to infer Z and #clusters p(Z|D,.) ∝ p(D|Z) p(Z) (prior)(posterior) (likelihood)
  28. 28. POCD: Overlap Clustering for distance data Clustering protein contact maps from HIV Protease inhibitors (PIs) ● Of the 26 FDA approved anti-HIV drugs: ○ 10 are PIs ● The PIs exhibit similar behaviour ○ Similar chemical structure ● Not readily available https://www.sciencedirect.com/science/article/pii/S0165614711001398
  29. 29. POCD: Overlap Clustering for distance data Clustering protein contact maps from HIV Protease inhibitors (PIs) ● Necessary to identify alternative PIs for therapy ○ What are the structural dissimilarities amongst PIs?
  30. 30. POCD: Overlap Clustering for distance data Clustering protein contact maps from HIV Protease inhibitors (PIs) ● Necessary to identify alternative PIs for therapy ○ What are the structural dissimilarities amongst PIs? ● Use Protein Contact Maps of each PI ○ Distances between all AA residue pairs for a protein ○ Row-wise vectorise the contact map ○ Compute the Normalised Information distance
  31. 31. POCD: Overlap Clustering for distance data Contact Maps of the Protease Inhibitors
  32. 32. POCD: Probabilistic model for Overlap Clustering of Distance data
  33. 33. Reading material ● A tutorial on Bayesian nonparametric models: http://gershmanlab.webfactional.com/pubs/GershmanBlei12.pdf ● Leo Breiman: ‘Statistical Modeling: The Two Cultures’: https://projecteuclid.org/download/pdf_1/euclid.ss/1009213726 ● An abstract of this work as Spotlight at the Bayesian Nonparametrics Workshop at NeurIPS 2018: https://drive.google.com/file/d/1ExVpeUomv8Z4mPMu5as_CbmrHjVY0IDV/view ● Tutorials on latest Deep learning papers: https://www.depthfirstlearning.com/ ( @DepthFirstLearn)
  34. 34. POCD: Overlap Clustering for distance data @sandhya212 Thank you

×