LECTURE SET 6 PROBABILISTIC BEHAVIOUR RECOGNITION ECVision Summer - - PowerPoint PPT Presentation

School of Informatics, University of Edinburgh

LECTURE SET 6 PROBABILISTIC BEHAVIOUR RECOGNITION

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 1

School of Informatics, University of Edinburgh

PROBABILISTIC BEHAVIOUR RECOGNITION SUPPOSE AT FRAME i:

• HAVE A FRAME DESCRIPTION

fi

• FRAME IS IN STATE si OF A SET OF

STATES S = {λ1, . . . , λS}

• NO DETERMINISTIC MAP OF

fi to si.

• IE. STATE si HIDDEN.
• WE KNOW p(si |

fi) < 1 FOR ALL si ∈ S.

• si∈S p(si |

fi) = 1. WHAT TO DO NOW?

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 2

School of Informatics, University of Edinburgh

BROWSE CONTEXT MODEL

M1 B M2

HERE: S = {M1, M2, B} ASSUME WE CAN COMPUTE: p(M1 | f), p(M1 | f), p(B | f)

• EG. BAYES RULE:

p(S | f) = p( f | S)p(S)/p( f)

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 3

School of Informatics, University of Edinburgh

MARKOV ASSUMPTION FUTURE STATE IDENTITY DEPENDS ONLY ON THE PRESENT STATE (EG. CURRENT FRAME) AND NOT ON THE EXACT DETAILS OF THE PAST IMPLICIT IN GRAPH MODEL

M1 B M2

M2 DEPENDS ON B, NOT M1

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 4

School of Informatics, University of Edinburgh

BENEFITS OF MARKOV MODEL MORE EFFICIENT EVALUATION (INCREMENTAL) REDUCES NUMBER OF MODEL PARAMETERS REDUCES TRAINING DATA NEEDED

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 5

School of Informatics, University of Edinburgh

EXTENDED STATE DIAGRAM ASSUME STATE CAN REMAIN SAME IN EACH VIDEO FRAME, SO NEED EXTENDED GRAPH:

* * *

M1 B M2

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 6

School of Informatics, University of Edinburgh

KNOWLEDGE OF TRANSITIONS ASSUME PROBABILITY OF TRANSITION FROM STATE λi TO EACH STATE λj AT EACH TIME FRAME: p(λi → λj) ALSO WANT PERSISTENCE IN A STATE FOR A WHILE: p(λi → λi)

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 7

School of Informatics, University of Edinburgh

KNOWLEDGE OF TRANSITIONS II THEREFORE THE PRIOR PROBABILITY OF STAYING IN STATE λi FOR EXACTLY τ FRAMES IS p(λi → λi)τ(1 − p(λi → λi))

τ P

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 8

School of Informatics, University of Edinburgh

NEW BROWSE MODEL PARAMETERS

* * *

M1 B M2

NEED: p(M1 → B), p(B → B), p(B → M2), p(M2 → M2), p(M2 → B)

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 9

School of Informatics, University of Edinburgh

HIDDEN MARKOV MODEL (HMM) COMBINES ALL OF ABOVE

• STATE TRANSITION PROBABILITIES:

p(λi → λj)

• STATE PROBABILITIES A FUNCTION

OF OBSERVATIONS: p(si | fi)

• CURRENT STATE DEPENDS ONLY ON

PREVIOUS STATE

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 10

School of Informatics, University of Edinburgh

SEQUENCE LABELLING GIVEN A SEQUENCE OF FRAMES 1 : T OBSERVED FEATURES f1:T = { f1, . . . fT} DESIRE STATE LABELLING OF SEQUENCE s1:T = {s1, . . . sT} WITH THE LARGEST PROBABILITY p(s1:T | f1:T) MOST LIKELY SET OF LABELS FOR THE FRAMES

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 11

School of Informatics, University of Edinburgh

FINDING SEQUENCE LABELLING p(s1:T | f1:T) =

  T

• t=1

p(st | ft)

    T−1

• t=1

p(st → st+1)

 

REFORMULATE p(s1:T | f1:T) AS p(s1:T−1 | f1:T−1)p(sT | fT)p(sT−1 → sT) INCREMENTAL FORM

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 12

School of Informatics, University of Edinburgh

EFFICIENT SOLUTION DYNAMIC PROGRAMMING KEEPS ONLY BEST LABELLINGS AT EACH TIME t REMOVES INFERIOR LABELLINGS COMPLEXITY O(| S |2 T)

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 13

School of Informatics, University of Edinburgh

TRANSITION DISTRIBUTION PROBLEM IF FRAME TIME NEARLY SAME AS TIME IN EACH LABEL CLASS, THEN HMM MODEL REASONABLE IF FRAME RATE FASTER:

τ P

EG: GAMMA DISTRIBUTION

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 14

School of Informatics, University of Edinburgh

POTENTIAL SOLUTION HSMM - HIDDEN SEMI-MARKOV MODEL EXPLICIT DURATION HMM USES DISTRIBUTION OF TIME SPENT IN EACH STATE CLASS: PROBABILITY THAT THE NUMBER OF CONSECUTIVE STATES THE SAME EFFECTIVELY SPLITS SEQUENCE INTO SEGMENTS LABELLED WITH THE STATE

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 15

School of Informatics, University of Edinburgh

OPEN RESEARCH PROBLEM STANDARD HSMM ALGORITHM HAS COMPLEXITY O(| S |2 T 2) COMBINATORIAL EXPLOSION AS SEQUENCES GET LONGER WE ARE INVESTIGATING AN INCREMENTAL ALGORITHM WITH COMPLEXITY O(| S |2 T) RESULTS SOON

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 16

School of Informatics, University of Edinburgh

SUMMARY

• PROBABILITIES SHOULD COPE

BETTER WITH PROPERTY NOISE AND AMBIGUITY

• HMM CAN MODEL STATE TRANSITION

STRUCTURE

• HSMM CAN MODEL DIFFERENT

DURATIONS IN A GIVEN STATE

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 17

School of Informatics, University of Edinburgh

Lecture Problem HOW WOULD YOU ESTIMATE THE GAMMA DISTRIBUTION FOR THE BROWSE CONTEXT? SKETCH A REASONABLE BROWSE SITUATION DISTRIBUTION.

ECVision Summer School: 6 - Probabilistic Behaviour Understanding Fisher slide 18