People Forecasting Where people are going

1
People ForecastingWhere 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 users 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.

3
How O-D matrices are estimated? (Peeta et al.
2002)
4
Architecture
Learning Engine
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 model
dt
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
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Constraints in the model
If (distance(lt-1,gt-1)ltthreshold and Ft-10)
Then FtD If (distance(lt-1,gt-1)ltthreshold and
Ft-1gt0) Then FtFt-1-1 If(distance(lt-1,gt-1)gtthre
shold and Ft-1 0) Then Ft0 If(distance(lt-1,gt-
1)gtthreshold and Ft-1 gt 0) Then Ft0 If(Ft-1gt0
and Ft0) gt is given by P(gtgt-1) If(Ft-10 and
Ft0) gt is same as gt-1 If(Ft-1gt0 and Ftgt0) gt
is same as gt-1 If(Ft-10 and Ftgt0) gt is given
by P(gtgt-1)
gt
gt-1
Ft-1
Ft
lt-1
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Example Queries

• Where the person will be 10 minutes from now?
• P(lTd1t,w1t,y1t) where Tt10 minutes
• What is the persons next goal?
• P(gTd1t,w1t,y1t)

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Example of Goals
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Example of Route
Grocery store
Route Seen Route Predicted
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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.

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Inference in Hybrid Dynamic Mixed Networks (HDMN)

• Filtering problem
• The Belief state at time t given evidence until
  time t P(Xte1t)
• 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!

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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.

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Steps in IJGP-S(i)

• Create a Join graph in a sequential manner.
• Extends a method by Murphy 02 that creates
  junction-tree in a sequential manner.
• Perform message passing in slice t and its
  interfaces with slice t-1 and t1
• Complexity O(exp(i)) where i is maximum number
  of variables in a clique of a join-graph.

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Rao-Blackwellised Particle Filtering (RBPF)

• Divide the current state-space into Rt and Xt
  where
• Rt Rao-Blackwellised (RB) variables
• Xt Marginal Variables.
• For i1 to N do
• Sample Rt(i) and compute marginals on Xt(i) given
  Rt(i),Rt-1(i),Xt-1(i) and observation yt using an
  exact inference algorithm.
• W-cutset (Bidyuk and Dechter 04)
• An elegant way to select the RB variables.

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Extending RBPF to Hybrid Dynamic Mixed Networks

• Naïve Extension
• Sample from the distribution given by the
  Bayesian Network and reject all samples which are
  not solutions to the constraint portion.
• However, If the distribution generates
  non-solutions to the constraint portion with a
  high probability, most samples will be rejected.

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Extending RBPF to Hybrid Dynamic Mixed Networks

• Use IJGP for Hybrid Mixed Networks (Gogate and
  Dechter 05, UAI) to generate an importance
  function.
• Sample from this importance function
• All other steps are same as in Doucet et al.2002
• The resulting algorithm IJGP-RBPF
• Complexity O(MAX(exp(i),exp(w)))
• i is the i-bound of the join-graph
• w is the treewidth of the RB-variables also
  called the w-cutset.

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Experimental ResultsData 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.

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Experimental ResultsModels 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)

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Various Activity models
dt
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
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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)

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Predicting Goals (MODEL-1)

• Compute P(gte1t) and compare it with the actual
  goal.
• Accuracy percentage of goals predicted
  correctly.
• N number of particles
• Column learning algorithm
• Row inference algorithm

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Predicting Goals (Model-2)

• Compute P(gte1t) and compare it with the actual
  goal.
• Accuracy percentage of goals predicted
  correctly.
• N number of particles
• Column learning algorithm
• Row inference algorithm

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Predicting Goals (Model-3)

• Compute P(gte1t) and compare it with the actual
  goal.
• Accuracy percentage of goals predicted
  correctly.
• N number of particles
• Column learning algorithm
• Row inference algorithm

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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.

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

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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.