Probabilistic Plan Recognition from LowLevel Sensors

1
Probabilistic Plan Recognition from Low-Level
Sensors

• Qiang Yang, Hong Kong University of Science and
  Technology
• http//www.cs.ust.hk/qyang
• Joint Work with Jie Yin, Xiaoyong Chai and Dou
  Shen

2
Forbes Magazine 2003 Article ltltDigitally
Monitoring Momgtgt

• Eric Dishman is making a cup of tea-and his
  kitchen knows it
• (at Proactive Health Research lab in Hillsboro,
  OR)
• tiny sensors monitor the researcher's every move.
  
• Radio frequency identification tags and magnetic
  sensors discreetly affixed to
• mugs, a tea jar, and a kettle,
• plus switches that tell when cabinet doors are
  open or closed,
• track each tea-making step.
• A nearby computer makes sense of these signals
• if Dishman pauses for too long, video clips on a
  television prompt him with what to do next.
• Service
• High-tech systems to monitor and assist the
  elderly

(courtesy CMU)
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Context-Aware Computing A Solution

• A central theme in context-aware computing is to
  build predictive models of human behavior
• Where is the user? (location estimation)
• What is she doing now? (motion-pattern
  recognition)
• What is his ultimate goal? (goal/plan recognition)

• Applications
• Healthcare Assisted Cognition (Washington),
  Legacy Health (Oregon),
• Mobile commerce Wireless information services
• Tracking in sensor networks
• Logistics
• Etc.

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Application Domain A Wireless LAN
Time t (-80 -78 -62 -37)
Time t1 (-81 -77 -64 -41)
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Radio-Frequency Based Systems

• Mobile devices receive signals propagated from
  base stations
• Location estimation based on signal strength

Base Station 3
Base Station 1
Time t ( 69
58
75 )
Time t1 ( 67
60
73 )
Base Station 2
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Probabilistic Goal Recognition Architecture
Prob 2
Prob 4
Goals
Actions
Intermediate states
Prob 3
Prob 1
observations
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Static Radio Maps for Sensor Model Calibration

• Location-based sensor model relies on a static
  radio map to perform online localization
• a radio map is learned to estimate locations
• Inaccurate location estimation
• The signal-strength samples collected in the
  online phase may significantly deviate from those
  stored in the radio map.

• Sensor Model

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Problem 1 How to reduce the uncertainty in data
calibration?

• Problem signal data collected at one time period
  may significantly deviate from those collected at
  another time period
• Previous works
• Triangulation based no need to calibrate, but
  inaccurate Radar 00, Ni et al. 03
• Probabilistic based (the ML method) re-collect
  data at different time periods, but is labor
  intensive! Ladd et al. 02 Youssef et al.
  03
• Our solution
• Adaptive temporal radio maps

In Proceedings of the IEEE PERCOM 05
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RF-Based Systems

• Offline phase construct a sensor model
  Pr(ojli), Pr(li),where li ? L l1 , , ln
  , oj ? O o1 , , om .
• Online phase apply Bayes rule for estimation

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Our Solution Adaptive Radio Maps

• Key idea adapt the radio map based on reference
  points using a regression analysis

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Two-Phase Algorithm (1)

• During the offline phase (time period t0)
• At each location, we learn a predictive function
  fij for the jth AP
• fij indicates the relationship between
  signal-strength values received at reference
  points and the value received by the mobile
  client

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Two-Phase Algorithm (2)

• During the online phase (time period t)
• Based on the signal strength received at
  reference points, we compute the estimated
  signal-strength vector
  for each location using fij
• The signal strength received by the mobile client
  is referred to as
• Compute the Euclidean distance Di and output the
  location with minimum distance

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Critical Issue

• To learn the predictive function fij between the
  signal-strength values received by the mobile
  client and the reference points.
• Two algorithms via regression analysis
• A multiple-regression based algorithm
• A model-tree based algorithm

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Multiple Regression vs. Model Tree

• Multiple Regression a linear function
• Model Tree a nonlinear approximation function

15
Experimental Results

• Comparison of overall accuracy over different
  time periods

9 groups of one-hour data the data collected at
12am are used for training and other independent
groups for testing
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Experimental Results

• Comparison of accuracy within 1.5 meters over
  different time periods

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Problem 2 motion pattern segmentation to
discover actions

• Problem given a time series of signal vectors,
  find semantically meaningful segments
• Previous Work
• Human Labeled by hand, but labor intensive,
  error-prone Peursum et al. 04
• Dynamic programming pure syntactic to minimize
  fitting error but may not relate to semantics
  Keogh et al. 01
• Computer Vision LDS-based but unsupervised Li
  et al. 02
• Our Method
• Goal-oriented, LDS-based automatic algorithm

In Proceedings of the AAAI 05
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An Illustration Example

• The observation sequence is partitioned into 5
  segments and each represents a motion pattern

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From Signal Sequences to Actions
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Motion Pattern-based Sensor Model

• Defined as a linear dynamic system (LDS)
• Where is the hidden variable, and is the
  observed signal at time t.
• and are Independent Gaussian noise with
  covariance matrices Q and R.
• and are state transition matrix and
  observation matrix
• The parameters of an LDS is

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Motion Pattern-based Sensor Model

• For a specific goal, assume the transition
  probability among motion patterns satisfies a
  first-order Markov process
• The set of motion patterns and transition
  probability can be further used for high-level
  goal recognition

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Probabilistic Segmentation Model

• We partition an observation sequence Y into Ns
  segments
• Segment labels and
  segmentation points

M
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Goal-based Segmentation Algorithm (1)

• Given a sequence Y, the model parameters can be
  learned using a ML method
• By introducing S and H and applying the
  first-order Markov property

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Goal-based Segmentation Algorithm (2)

• Since S and H are hidden, an EM algorithm is used
  to solve the ML problem
• E-Step dynamic programming is used to find the
  optimal S and H given the current model
  parameters
• M-Step Model parameters are updated by fitting
  an LDS model to each segment. The transition
  matrix is updated by counting the labels of
  segments.

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Problem 3 How to recognize a users goals?

• Problem how to ensure that goal recognition
  framework is robust?
• Previous Work
• HMM and DBN based restricted to high-level
  inferences Albrecht et al. 98 Han Veloso 00
• Sensor-based DBN monolithic architecture but
  inflexible
• Nguyen et al.03 Bui 03 Liao et al.04
• Our Method
• A two-level recognition architecture

In Proceedings of the AAAI 04
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A Two-level Recognition Model

• Sensor-to-action level a DBN model
• Action-to-goal level an N-gram model

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N-gram Model

• Given an estimated action sequence, infer the
  most likely goal
• By applying the Bayes Rule,
• The compact form of action sequence

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N-gram Model

• Bigram model when n 2
• Assuming the transitions between actions are
  independent of action durations

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Experimental Results

• Comparison of average recognition accuracy vs.
  sampling interval (8 goals)

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Problem 4 How to recognize multiple goals?
Entrance2-to-Office
Stay-in-Office
Goto-Seminar1
Entrance1-Exit

• Objective
• Infer what he is doing
• recognize his ultimate goal

actions are notdirectly observable
Sensor-based
more than one goalis achieved
Multiple-goal
In Proceedings of the AAAI 05
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Sensor-Based Multiple-Goal Recognition

• Recognition based on sensory readings
• Multiple-goal in a single action sequence

Signal-goal
Multiple-goal
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Plan Recognition and Goal Recognition

• Two categories of approaches
• Consistency approaches
• Formal theory of plan recognition Kau87
• Scalable and adaptive goal recognition Les98
• Probabilistic approaches
• Hidden Markov models
• Bayesian Net and dynamic BN
• Limitations

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Framework of Sensor-Based Multiple-Goal
Recognition
Two-level multiple-goal recognition framework
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State Diagram

• (1) Instantiate (2) Evolve (3) Suspend (4)
  Terminate

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Model Instantiation

• Goal models are instantiated when the model set M
  is empty or all special-goal models are in state
  Sp
• A default-goal model M0 is instantiated if at
  least one special-goal model is created at time t
• Acc( M0 ) At and M0 is added into M
• Lt( M0 ) ?0Q0(At)
• A goal model Mk is instantiated if ?kQk(At)
  ??0Q0(At)
• Acc( Mk ) At and Mk is added into M
• Lt( Mk ) ?kQk(At)

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Environment Setting

• The environment is modeled as a space of 99
  locations, each representing a 1.5-meter grid
  cell.
• Sensor readings contain signal strength
  measurements from 8 base stations.
• Sensor model construction 100 signal samples at
  each location.
• 11 actions and 8 special goals are modeled.

99 locations 11 actions 8 goals
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Robot Strategy-Behavior Recognition Han99

• A Behavior Hidden Markov Model (BHMM) is defined
  as
• N s1 , s2 , s3 , s4 the state space
• M o1 , o2 , o3 the observation space
• A aij Pr ( St1sj Stsi ) the state
  transition matrix
• B bi(ok) Pr ( ok St si ) the
  observation probabilities
• ? ?i Pr ( S1 si ) the initial state
  distribution

lt N, M, A, B, ? gt
o1
o2
s2
s3
s1
o3
o3
o2, o3
o1
ball
o1
s4
Observations of Go-To-Ball
Behavior HMM
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Experiment Setting

• Actions and goals

• eight goals, 850 single-goal traces
• Multiple-goal traces are synthesized
• Segments of single-goal traces are pieced
  together to generate connective traces
  containing multiple goals.

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Comparison Targets Evaluation Criteria

• Three algorithms
• MG-Recognizer Cha05
• SG-Recognizer Yin04
• BHMM-Recognizer Han99
• Three criteria
• Recognition accuracy
• Inference efficiency
• Measured in terms of the number of models
  instantiated
• Scalability
• w.r.t. the number of goals modeled
• w.r.t. the number of goals contained in a single
  trace

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An Example

• Two goals are achieved in a single trace G1
  Print-in-Room2 and G2 Exit-through-Entran
  ce2

2
1
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Recognition Accuracy

• SG-Recognizer

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Accuracy and Efficiency

• Recognition accuracy
• Inference Efficiency

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Conclusions and Future Work

• We considered four linked open problems in plan
  recognition
• Adaptive sensor model to reduce calibration
• Motion pattern segmentation to discover actions
• Multiple Goal recognition from signals
• Future Work
• Solve goal clustering problem
• Integrate all four modules
• test algorithms on another, larger scale sensor
  data set