Learning and Learning and Inferring Inferring

Transportation Transportation RoutinesRoutines

By: By: Lin Liao, Dieter Fox and Henry KautzLin Liao, Dieter Fox and Henry Kautz

Best Paper award AAAI’04Best Paper award AAAI’04

AIM of the paperAIM of the paper• Describe a system that creates a

probabilistic model of a user’s daily movements through the community using unsupervised learning from raw GPS data.

What this probabilistic What this probabilistic model can do?model can do?

• Infer locations of usual goal like home or work place.

• Infer mode of transportation• Predict future movements (short and long-

term)• Infer flawed behavior or broken routine• Robustly track and predict behavior even

in the presence of total loss of GPS signal.

Describing the modelDescribing the model• Hierarchical activity model of a

user from a data collected from a wearable GPS.

• Represented by a Dynamic Bayesian network

• Inference performed by Rao-Blackwellised particle filtering

xk-1

zk-1 zk

xk

mk-1 mk Transportation mode m

x=<l,v,c>Location, velocity and car

GPS reading z

tk-1tk

ftk

gk Goal g

Trip segment t

fgk

gk-1

fmk

τk-1τk

Θk-1Θk

Goal switching fg

Trip switching ft

Mode switching fm

Location and Transportation Location and Transportation modesmodes

• Xk = <lk,vk,ck> gives location, velocity of the person and location of person’s car– Location lk is estimated on a graph structure

representing a street map using the parameter θk.

• zk is generated by person carrying GPS data.

• mk can be {Bus,Foot,Car,Building}• τ models the decision a person makes

when moving over a vertex in the graph, for example, to turn right on a signal.

Trip segmentsTrip segments• tk is defined by:

– Start location tsk– End location tek and– Mode of transportation tmk

• Switching nodes– Handle transfer between modes and

trip segments.

GoalsGoals• A goal represents the current target

location of the person.• E.g. Home, grocery store, locations of

friends• Assumption: Goal of a person can

only change when the person reaches the end of a trip segment level.

InferenceInference• Inference: estimate current state

distribution given all past readings• Particle filtering

– Evolve approximation to state distribution using samples (particles)

– Supports multi-modal distributions– Supports discrete variables (e.g.: mode)

• Rao-Blackwellisation– Particles include distributions over variables,

not just single samples– Improved accuracy with fewer particles

(hopefully)

Types of InferenceTypes of Inference1. Goal and trip segment estimation2. GPS based tracking on street maps

– Estimate a person’s location by a graph-structure S = (V,E)

– Aim: Find the posterior probability by Rao-Blackwellised particle filtering.

Prior by Kalman-filtering

LearningLearning• Structural learning

– Searches for significant locations, e.g. user goals and mode transfer locations

• Parameter learning– Estimate transition probabilities– Transitions between blocks– Transitions between modes

Structural learningStructural learning• Finding goals

– Locations where a person spends extended period of time

• Finding mode transfer locations– Estimate mode transition probabilities

for each street– E.g. bus stops and parking lots are those

locations where the mode transition probabilities exceed a certain threshold

Detection of abnormal Detection of abnormal behaviorbehavior

• If person always repeats usual activities, activity tracking can be done with a small number of particles.

• In reality, people often do novel activities or commit some errors

• Solution: Use two trackers simultaneously and compute Bayes factors between the two models.

Experimental resultsExperimental results• 60 days of GPS data from one person

using wearable GPS.• First 30 days for learning and the

rest for empirical comparison

Activity model learningActivity model learning

Infering Trip SegmentsInfering Trip Segments

Empirical comparison to flat Empirical comparison to flat modelmodel

Comparison to 2MM modelComparison to 2MM model

Model Start 25% 50% 75%

2MM 0.69 0.69 0.69 0.69

Hierarchical model 0.66 0.75 0.82 0.98

Detection of user errorsDetection of user errors

Detection of user errorsDetection of user errors

SummarySummary• Paper introduces Hierarchical markov model that

can learn and infer user’s daily movements.• Model uses multiple levels of abstractions: lowest

level GPS, highest level transportation modes and goals.

• Rao-Blackwellised particle filtering used for inference

• Learning significant locations was done in an unsupervised manner using the EM algorithm.

• Novelty detection or abnormal behavior by model detection.