State sequence prediction in imprecise hidden Markov models Jasper - PowerPoint PPT Presentation

State sequence prediction in imprecise hidden Markov models Jasper De Bock & Gert de Cooman 27 July 2011

Jasper De Bock & Gert de Cooman

Research group SYSTeMS Jasper De Bock Gert de Cooman

Research group SYSTeMS Jasper De Bock Gert de Cooman Filip Hermans Erik Quaeghebeur Keivan Shariatmadar Arthur Van Camp

State sequence prediction in imprecise hidden Markov models

State sequence prediction in imprecise hidden Markov models The imprecise hidden Markov model

Imprecise hidden Markov model A sequence of hidden state variables X 2 X 3 X 1 O 2 O 1 O 3 S 1 (O 1 |X 1 ) S 2 (O 2 |X 2 ) S 3 (O 3 |X 3 ) A sequence of observable variables Jasper De Bock 8

Imprecise hidden Markov model Q 1 (X 1 ) Q 2 (X 2 |X 1 ) Q 2 (X 3 |X 2 ) A sequence of hidden state variables X 2 X 3 X 1 O 2 O 1 O 3 S 1 (O 1 |X 1 ) S 2 (O 2 |X 2 ) S 3 (O 3 |X 3 ) A sequence of observable variables Jasper De Bock 9

Imprecise hidden Markov model Q 1 (X 1 ) Q 2 (X 2 |X 1 ) Q 2 (X 3 |X 2 ) X 2 X 3 X 1 All local models are coherent lower previsions O 2 O 1 O 3 S 1 (O 1 |X 1 ) S 2 (O 2 |X 2 ) S 3 (O 3 |X 3 ) Jasper De Bock 10

Imprecise hidden Markov model Q 1 (X 1 ) Q 2 (X 2 |X 1 ) Q 2 (X 3 |X 2 ) X 2 X 3 X 1 O 2 O 1 O 3 S 1 (O 1 |X 1 ) S 2 (O 2 |X 2 ) S 3 (O 3 |X 3 ) Jasper De Bock 11

State sequence prediction in imprecise hidden Markov models Epistemic Irrelevance

Epistemic irrelevance X 2 X 3 X 1 O 1 O 2 O 3 Conditional on its mother variable , the non-parent non- descendants of any variable in the tree are epistemically irrelevant to this variable and its descendants Jasper De Bock 13

State sequence prediction in imprecise hidden Markov models Recursive construction of a joint model for the imprecise hidden Markov model

Recursive construction of a joint model

Recursive construction of a joint model • Marginal extension • Independent natural extension

State sequence prediction in imprecise hidden Markov models Conditioning the model on the observations

State sequence prediction in imprecise hidden Markov models Conditioning the model on the observations Generalised Bayes rule: An extension of the Bayes rule to imprecise probabilities

State sequence prediction in imprecise hidden Markov models Maximal state sequences

State sequence prediction in We predict the state sequence by calculating a set of optimal sequences imprecise hidden Notion of optimality: maximality Markov models Strict partial ordening: Maximal state sequences: Maximal state sequences

State sequence prediction in imprecise hidden Markov models EstiHMM: an efficient algorithm to determine the maximal state sequences in an imprecise hidden Markov model

EstiHMM: an efficient algorithm to determine the maximal sequences

EstiHMM: an efficient algorithm to determine the maximal sequences • Principle of optimality

EstiHMM: an efficient algorithm to determine the maximal sequences • Principle of optimality X 2 X 3 O 3 O 2

EstiHMM: an efficient algorithm to determine the maximal sequences • Principle of optimality X 1 X 2 X 3 O 3 O 1 O 2

EstiHMM: an efficient algorithm to determine the maximal sequences • Principle of optimality • Deriving an alternative Roptimality criterion

EstiHMM: an efficient algorithm to determine the maximal sequences • Principle of optimality • Deriving an alternative Roptimality criterion • A recursive approach

EstiHMM: an efficient algorithm to determine the maximal sequences • Principle of optimality • Deriving an alternative Roptimality criterion • A recursive approach Complexity

EstiHMM: an efficient algorithm to determine the maximal sequences • Principle of optimality • Deriving an alternative Roptimality criterion • A recursive approach Complexity • Theoretical analysis

EstiHMM: an efficient algorithm to determine the maximal sequences • Principle of optimality • Deriving an alternative Roptimality criterion • A recursive approach Complexity • Theoretical analysis • Linear in the number of Rmaximal sequences

EstiHMM: an efficient algorithm to determine the maximal sequences • Principle of optimality • Deriving an alternative Roptimality criterion • A recursive approach Complexity • Theoretical analysis • Linear in the number of Rmaximal sequences • Empirical confirmation

State sequence prediction in imprecise hidden Markov models A first experiment

A first experiment

A first experiment See you at the poster session!

State sequence prediction in imprecise hidden Markov models Jasper - PowerPoint PPT Presentation

State sequence prediction in imprecise hidden Markov models Jasper De Bock & Gert de Cooman 27 July 2011 Jasper De Bock & Gert de Cooman Jasper De Bock & Gert de Cooman Research group SYSTeMS Jasper De Bock Gert de Cooman Research

State sequence predic/on in imprecise hidden Markov models

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