Probabilistic Graphical Models: Applications in Biomedicine

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2 Probabilistic Graphical Models: Applications in Biomedicine L. Enrique Sucar, INAOE Puebla, México May 2012

3 What do you see? What we see depends on our previous knowledge (model) of the world and the information (data) form the images Bayesian framework

4 Outline Endoscopy assistant Predicting HIV mutations User adaptation for rehabilitation

5 Bayesian Models combine our previous knowledge (priors) with the evidence (likelihood) P ( H E) P ( H ) P (E H ) relations among the variables in a domain independence

6 Probabilistic Graphical Models X = X 1, X 2,, X N P(X 1, X 2,, X N )

7 Probabilistic Graphical Models It is generally much more compact (space) It is generally much more efficient (time) It is easier to understand and communicate It is easier to build (from experts) or learn (from data)

8 Probabilistic Graphical Models G(V,E), Y i f(y i ), X P(X 1, X 2,, XN) n i 1 f(y i)

9 Probabilistic Graphical Models Inference: Learning: Z X Y

10 Probabilistic Graphical Models Directed vs. Undirected Static vs. Dynamic Probability vs. Decision

11 Probabilistic Graphical Models

12 Probabilistic Graphical Models C H S t S t+1 S t+2 S t+3 E E E E E

13 Probabilistic Graphical Models 1 A D 2 3 B C U 4 5 D

14 Types of PGMs Bayesian classifiers Bayesian networks Hidden Markov models Dynamic Bayesian networks Temporal Bayesian networks Markov Random Fields Influence diagramas Markov decision processes

15 Bayesian Networks Node: Propositional variable. Arcs: Probabilistic dependencies

16 An example of a Bayesian Network Wine Drunk Thirsty Headache Represents (in a compact way) the joint probability distribution: P(W,D,T,H) = P(W) P(D W) P(T D) P(H D)

17 Structure

18 Parameters Root nodes Other nodes

19 Parameters for the example P(T D) P(D W) Thirsty Drunk Wine Headache P(W) P(H D)

20 Inference C H Given certain evidence, E, estimate the posterior probaililty of the other variables, H, C E

21 Inference Variable elimination Message passing (Pearl s algorithm) Junction Tree Stochastic simulation

22 Learning Wine P(W) Drunk P(D W) Thirsty P(T D) Headache P(H D)

23 Structure Learning Independence tests Search and score

24 Structural Improvement combine expert knowledge and data Node elimination Node combination Node insertion

25 Structural improvement Z Z X Y Z Z W X XY X Y

26 Endoscopy semi-automatic system that can assist an endoscopist recognize the objects in endoscopy images lumen diverticula Bayesian network that combines the information and arrives to final decisions

27 Colon Image

28 Low level features dark region

29 Low level features shape from shading (pq histogram)

30 Model Construction

31 BN for endoscopy (partial)

32 Semi-automatic Endoscope

33 Endoscope navigation system: example 1

34 Endoscope navigation system: example 2

35 Temporal Nodes Bayesian Networks (TNBN) An alternative to Dynamic Bayesian Networks to model dynamic processes with uncertainty Temporal information is within the nodes in the model, which represent the time of occurrance of certain events The links represent temporal-causal relation Adequate for applications in which there are few state changes in the temporal range

36 Example

37 37

38 1. Initial discretization of the temporal variables 2. Standard BN structural learning 3. Refines the intervals for each TN 38

39 HIV fastest evolving organisms dynamics of the appearance chain of mutations temporal occurrence of specific mutations in HIV that may lead to drug resistance

40 drug-associated mutational pathways in the protease gene, revealing the co-occurrence of mutations and its temporal relationships predict the most likely evolution of the virus prevents the appearance of mutations, effectively increasing HIV control

41 Alma Ríos-Flores (INAOE) 41

42 Patient Initial Treatment List of Mutations Weeks P1 LPV, FPV, RTV L63P, L10I, V77I, I62V P2 NFV, RTV, SQV L10I V77I

43 Model 1: Assessment of TNBN to capture known relations. Uncovering more common mutational networks 43

44 Known relationships are appropiately captured DRV isolation: New drug is hardly ever given as a first treatment Link between SQV and L10I Role of RTV is often used in conjunction with other drugd (boosting) 44

45

46 The model was able to capture some mutational pathways already known (obtained by clinical experimentation).

47 Markov decision processes (MDPs) planning under uncertainty

48 MDP A finite set of states, S A finite set of actions, A A transition model, P (s s, a) A reward function for each state-action, r (s, a)

49 POMDP An observation probability distribution, P(O S) An initial probability distribution, P(S)

50 A POMDP as a Dynamic Decision Network D t-1 D t D t+1 D t+2 U S t S t+1 S t+2 S t+3 E E E E

51 Basic solution techniques Dynamic programming techniques reinforcement learning

52 Factored MDPs The state is decomposed in a set of factors or state variable: X = {x1, x2, x3, x4, x5} x1 x2 x3 X x1 x2 x3 So the transition function is represented as a two-stage DBN per action x4 x4 x5 x5 t t+1

53 Gesture Therapy low-cost technology that allows stroke patients to practice intensive movement training at home without the need of an always present therapist

54 Gesture Therapy Simulated environment Monocular tracker Gripper Trunk compensation detection Adaptation to the patient Visual/Sensor tracking Shared memory Torque Game Engine (C/C++) Data Archival Communication Adaptation Tools (C++ Java) scripts GAMES

55 Adptation to the patient The system estimates the patient state based on observing its performance in the game (speed, control) and decides the game difficulty accordingly according to the policy dictated by the Actions POMDP difficulty difficulty Perform ance Perform ance Obs: duration Obs: coordina tion Obs: duration Obs: coordina tion

56 Evaluation

57 Prototype of the system at the INNN rehabilitation unit

58 Policy adaptation model could be wrong best policy could depend on the patient improves an initial policy based on the therapist feedback

59 Initial results

60 Conclusions Bayesian approach Graphical models

61 Conclusions set of techniques which can be applied to solve complex problems in biomedicine interesting challenges that require novel developments in representation, inference and learning

62 References L. E. Sucar, D.F. Gillies, D. A. Gillies, Objective probabilities in expert systems, Artificial Intelligence, L. E. Sucar, D. F. Gillies, Probabilistic reasoning in high-level vision, Image and Vision Computing, L. E. Sucar, R. Luis, R. Leder, J. Hernández, I. Sánchez, GESTURE THERAPY: A Vision-Based System for Upper Extremity Stroke Rehabilitation, IEEE EMBC, 2010 P. Hernández, F. Orihuela, A. Rios, J. González, L.E. Sucar, Unveiling HIV mutational networks associated to pharmacological selective pressure: a temporal Bayesian approach, AIME, 2011.

63 Acknowedgements Collaborators Sponsors

64 Thanks! Questions? ccc.inaoep.mx/esucar

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