1. People Forecasting Where people are going?
Vibhav Gogate-Computer Science
Rina Dechter-Computer Science
Other Collaborators:
Bozhena Bidyuk-Computer Science
James Marca-Transportation Science
Craig Rindt-Transportation Science
University of California, Irvine, CA 92967

2. Motivation
Origin/Destination (O-D) matrix
A necessary input to most microscopic simulation models in transportation literature.
Old method (Peeta et al. 2002) uses paper and pencil surveys to generate O-D matrices
Can IT help?
Our proposed “Activity Model” learns and predicts a user’s origins/destinations and routes using his GPS log.
Our hope is that even if a small sample of population agrees to share their GPS data, we can compute the aggregate O-D matrix for a large area like a city.
So for people who do not know what transportation simulation models are, they are a way to achieve by simulation what you cannot do due to limitations of IT or lack of data. They are of 2 types: Microscopic simulation models, macroscopic simulation models.

3. How O-D matrices are estimated? (Peeta et al. 2002)

4. Architecture Learning Engine Probabilistic Model GIS Database
O-D matrix for a region
Probabilistic Model
GIS
Database
Inference Engine

5. Probabilistic model: Hybrid Dynamic Mixed Networks
Extends Hybrid Dynamic Bayesian Networks (Lerner 2002) to include Discrete constraints
Able to model all of the following:
Discrete, Continuous Gaussian variables
Markov processes
Deterministic (constraint networks)+probabilistic information (Bayesian Networks)

6. Building the activity modeldt wt
dt-1
wt-1
D: Time-of-day (discrete)
W: Day of week (discrete)
Goal: collection of locations where the person spends significant amount of time. (discrete)
F: Counter to control goal switching.
Route: A hidden variable that just predicts what path the person takes (discrete)
Location: A pair (e,d) e is the edge on which the person is and d is the distance of the person from one of the end-points of the edge (continuous)
Velocity: Continuous
GPS reading: (lat,lon,spd,utc).
gt-1 gt
Ft-1 Ft
rt-1 rt
vt-1 vt
lt-1 lt
yt-1 yt

7. Constraints in the model
If (distance(lt-1,gt-1)<=threshold and Ft-1=0) Then Ft=D
If (distance(lt-1,gt-1)<=threshold and Ft-1>0) Then Ft=Ft-1-1
If(distance(lt-1,gt-1)>threshold and Ft-1 = 0) Then Ft=0
If(distance(lt-1,gt-1)>threshold and Ft-1 > 0) Then Ft=0
If(Ft-1>0 and Ft=0) gt is given by P(gt|gt-1)
If(Ft-1=0 and Ft=0) gt is same as gt-1
If(Ft-1>0 and Ft>0) gt is same as gt-1
If(Ft-1=0 and Ft>0) gt is given by P(gt|gt-1) gt
gt-1
Ft-1 Ft
lt-1

8. Example Queries Where the person will be 10 minutes from now?
P(lT|d1:t,w1:t,y1:t) where T=t+10 minutes
What is the person’s next goal?
P(gT|d1:t,w1:t,y1:t)

9. Example of Goals
This is one result of our experiment. In this experiment, a graduate student carries this GPS for three months. We get the GPS log. We put it into our system without any labeling. After a few hours, the system output such a picture, this picture tells us where the common goals are for the person. We then label them manually to make it clear (e.g. Home, church etc).

10. Example of Route Route Seen Route Predicted Grocery store
Once a probabilistic model is learnt, we can use our system to predict what route the person is more likely to take and what is his current goal. For example, the route on the left was seen in the form of GPS reading by our model and the route on the right was predicted by our model. As we can see our model predicted that the person was likely to go to a grocery store.
Grocery store
Route Seen
Route Predicted

11. Contributions
A new modeling framework of “Hybrid Dynamic Mixed Networks”
A “Hybrid Dynamic Mixed Network model” for transportation routines
Predict origin/destinations and routes taken by an individual.
Novel inference algorithms for reasoning in Hybrid Dynamic Mixed Networks
An Expectation propagation based algorithm
A new algorithm that combines Particle Filtering and Generalized Belief Propagation in a systematic way.

12. Inference in Hybrid Dynamic Mixed Networks (HDMN)
Filtering problem:
The Belief state at time t given evidence until time t : P(Xt|e1:t)
Complexity of exact inference: NP-hard
Exponential in treewidth
Discrete Dynamic Mixed Networks
Treewidth = number of variables in each time slice
Hybrid Dynamic Mixed Networks
Treewidth = O(T) where T is the number of time-slices.
Approximation is a must in most cases!

13. Approximate Inference
Two popular approximate inference algorithms for Dynamic Networks
Generalized Belief Propagation (Heskes et al. ’02)
Rao-Blackwellised Particle Filtering (Doucet et al. ’02)
Our contribution: Extend these two algorithms to allow discrete constraints
Iterative Join Graph Propagation-Sequential (IJGP-S)
A new Rao-Blackwellised Particle Filtering (RBPF) algorithm called IJGP-RBPF.
Use output of IJGP to compute an importance function
Parameterized by two complexity parameters of “i” and “w” which provides us with a range of algorithms to choose from.

14. Experimental Results: Data Collection
GPS data was collected by one of the authors for a period of 6 months.
Latitude and longitude pairs
3 months data was used for training and 3 months for testing.
Data divided into segments
A segment is a series of GPS readings such that two consecutive readings are less than 15 minutes apart.

15. Experimental Results: Models and algorithms
Test if adding new variables improves prediction accuracy.
Model-1: Model as described before
Model-2: Remove variables dt and wt
Model-3: Remove variables dt, wt,ft,rt,gt from each time slice.
Algorithms:
IJGP-RBPF(1,2), IJGP-RBPF(2,1), IJGP-S(1) and IJGP-S(2)

16. Various Activity modelsdt wt
dt-1
wt-1
gt-1 gt
Model-1
Ft-1 Ft
rt-1 rt
Model-2
vt-1 vt
Model-3
lt-1 lt
yt-1 yt

17. Learning the models from data
EM algorithm used for learning the models
Takes about 3 to 5 days to learn data that is distributed over 3 months.
Since EM uses inference as a sub-step, we have 4 EM algorithms corresponding to the 4 algorithms used for inference
IJGP-RBPF(1,2), IJGP-RBPF(2,1), IJGP-S(1) and IJGP-S(2)

18. Predicting Goals (MODEL-1)
Compute P(gt|e1:t) and compare it with the actual goal.
Accuracy = percentage of goals predicted correctly.
N = number of particles
Column: learning algorithm
Row: inference algorithm

19. Predicting Goals (Model-2)
Compute P(gt|e1:t) and compare it with the actual goal.
Accuracy = percentage of goals predicted correctly.
N = number of particles
Column: learning algorithm
Row: inference algorithm

20. Predicting Goals (Model-3)
Compute P(gt|e1:t) and compare it with the actual goal.
Accuracy = percentage of goals predicted correctly.
N = number of particles
Column: learning algorithm
Row: inference algorithm

21. Predicting Routes
Compare the path of the person predicted by the model with the actual path.
False positives (FP)---Precision
count the number of roads that were not taken by the person but were in the predicted path.
False Negatives (FN)---Recall
count the number of roads that were taken by the person but were not in the predicted path.

22. False Positives and False Negatives for Route prediction
Model-1 shows the highest route prediction accuracy, given by low false positives and false negatives.

23. Future Work: O-D estimation through Simulation
Randomly generate regions and a population
Land-use structures through Microsoft Map-point
Assume an activity model per individual
Simulation gives an aggregate O-D matrix (called actual O-D)
Take a random sample of the population and use their GPS data
Our proposed System would predict an O-D matrix (predicted O-D)
Success: Distance between predicted and accurate O-D matrix.

24. Challenges Scalable algorithms
Our algorithms take about 3-5 days/individual!
Does the proposed simulation represent real-world?
A model for data aggregation
Inference and Learning for other continuous frameworks
Poisson distribution.
Discrete children of continuous parents.