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

Hidden Markov Models Markov Model (Finite State Machine with Probs) Modeling a sequence of

Graphical Models CS 6355: Structured Prediction 1 So far We discussed sequence labeling

Markov Models Kunsch, H.R., State Space and Hidden Markov Models . ETH- Zurich, Zurich;

Outline Sequential Data - Part 2 Greg Mori - CMPT 419/726 Hidden Markov Models - Most Likely

Recurrent Neural Models: Language Models, and Sequence Prediction and Generation CMSC 473/673

CSCE 970 Lecture 2: Markov Chains and Hidden Markov Models Stephen D. Scott 1 Introduction

Hidden Markov Models Pratik Lahiri Introduction A hidden Markov model (HMM) is a

Two-State Imprecise Markov Chains for Statistical Modelling of Two-State Non-Markovian Processes

HMM Review Lecture Outline 1. Markov models 2. Hidden Markov

A C Standard model has 1-1 correspondence between symbols and states, P(A | T) thus P ( x i

Hidden Markov Models Training Selecting model parameters What we know The terminology and

1 X 1 X 2 X 3 Ghostbusters HMM Chain Rule and HMMs E 1 E 2 E 3 P(X 1 ) = uniform 1/9 1/9

Hidden Markov Models Bhiksha Raj 10 Nov 2016 11755/18797 1 Prediction : a holy grail

Markov chains and Hidden Markov Models 9000 Markov chains and HMMs We will discuss: Markov

A Sequence-based Selection Hyper-heuristic Utilising a Hidden Markov Model Ahmed Kheiri Ed

Lecture 15: Decision Trees CS109A Introduction to Data Science Pavlos Protopapas, Kevin Rader and

Compositional Real-Time Scheduling Framework Insik Shin 1 , Insup Lee 1 1 University of

Average Cost Minimization Problems Nathalie T. Khalil Universit de Bretagne Occidentale, France

Constraint Reduction for Linear and Convex Optimization Meiyun He, Jin Jung, Paul Laiu, Sungwoo

How to Improve the Efficiency of Microfinance in Islamic Economic Perspective? Iraj Toutounchian

Swiss hydropower concession renewal: Where is the path toward sustainability leading us? A FOUR

Insurance Demand and the Mitigation of Default Risk Lukas Reichel, Hato Schmeiser and Florian

Orientation Night Purpose We Are Coaches What is Reno Devo Deep Thoughts Program