Applications of Active Learning in Sensor Network

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Applications of Active Learning in Sensor Network

• 11-785 Active Learning Seminar
• November 13, 2008

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Road Map

• Paper 1. Active Learning Driven Data Acquisition
  for Sensor Networks (Muttreja, Raghunathan, Ravi
  and Niraj, ISCC 2006)
• A sampling strategy for sensor networks based on
  predictive modeling technique.
• Paper 2. Cost-effective Outbreak Detection in
  Networks (Leskovec, Krause, Guestrin, Faloutsos,
  VanBriesen, Grance, KDD07)
• Optimal subset selection algorithm applied to
  sensor placement.

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Active Learning Driven Data Acquisition for
Sensor Network

• (Muttreja, Raghunathan, Ravi and Niraj, ISCC 2006)

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What is this paper about?

• Task Given a sensor network to monitor some
  physical phenomenon (temperature, air pressure,
  precipitate, etc), decide when to query which
  sensor.
• This problem is called data acquisition policy
  design.
• Approach Construct a probabilistic model over
  the network, and have it guide the sampling
  decision.

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Why is this relevant to Active Learning?

• Think of the untapped sensor nodes as a pool of
  possible data points one can get the true answer
  (label) of at some cost then the task here is an
  analogue of sampling policy in Active Learning
• In fact, many of the model driven approaches are
  studied from an active learning perspective
• Model-driven data acquisition in sensor network
  (Deshpande,Guestrin, et al 2004)
• Using probabilistic models for data management
  in acquisitional environments (Deshapande,
  Guestrin, Maddenn 2005)

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Sensor Network

• A wireless network consisting of spatially
  distributed autonomous devices using sensors to
  monitor physical or environmental conditions,
  such as temperature, sound, vibration, pressure,
  etc
• Severe energy constraint.
• Hence data acquisition policy is critical.

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Key assumption

• The data field is spatio-temporally correlated -
  i.e., measured at one sensor node is correlated
  to its neighbor node, or the measurements at near
  future/past.
• Certain level of distortion is acceptable - i.e.,
  users are often interested in only the
  approximation of the data field.

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Model-driven data collection

• Given those assumptions, how do you design data
  acquisition policy?
• Solution presented here is caled predictive
  modeling technique.
• In a nutshell maintain a model of the data
  field, have it decide which one to query at each
  cycle.

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Model-driven data collection

• Procedure
• Build a probabilistic model of the data field
  based on currently known readings.
• At each cycle T
• At each node, compute the predictive measurement
  and the confidence level.
• Sample a node if the confidence dips below some
  threshold
• Recalibrate the model with the new data
• Repeat the process till all node meet the
  threshold.
• Repeat 2 at all cycle

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Model-driven data collection

• Which model ?
• Some criterion
• As general as possible
• Output probabilistic estimate
• Incrementally trainable
• Provide efficient way to assess confidence of
  the candidate data point without actually
  measuring the reading at the point
• Gaussian Process (GP) is a popular choice
• http//www.gaussianprocess.org/

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Gaussian Process (GP) for sensor network modeling

• Gaussian Process is a nonparametric version of
  Gaussian distribution, extending multivariate
  Gaussian to infinite dimensionality.
• Sensor network felt natural as a Gaussian process
• Each node at each timeslot is a Gaussian r.v
• True measurement as a mean
• Distortion as variance.

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Gaussian Process for sensor network modeling

• If the the data field is a Gaussian Process
• Then, the collection of random variables y y1
  y2 yi (i.e., reading from the sensors) is a
  joint Gaussian distribution given a set of sensor
  location.
• Consider each node is indexed by xi ltnode,
  timegt tuple, and xi x1 x2 is any set of
  such nodes, then y is a mulitivairiate Gaussian
  r.v like this

C Covariance matrix set by Covariance Function
C(x, x ?) µ Mean Function
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Gaussian Process for sensor network modeling

• Given N training points, the model will make a
  inference on random variable y for a new node
  location (Derivation in tutorial from the
  website.)

CN is Covariance matrix of the training data
points, computed via Covariance Function C, k is
a covariance between the new node and all node in
the training
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Confident measurement

• Given GP,
• And one more leap of mind Maximizing confidence
  equivalent to minimizing variance.
• The task seems really simple
• The simplest greedy heuristic go compute
  variance at all the nodes, and chose the one with
  most variance to query next. (used often in
  reality)
• It may not be globally optimal.

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Problems with the model 1

• Greedy search may not be optimal.
• The author proposed a heuristic distribution of
  interest. Basically adding some weights to the
  sensor who historically recorded unpredictable
  change
• Define relative error and distribution of
  interest

Weight the confidence score with the interest
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Problems with the model 2

• Gaussian Process is not incrementally trainable
• Each time the data set change, Need to recompute
  and invert covariance matrix.
• Proposed solution Sparse approximation for GP
  Regression
• Idea Find the bases of that spanes the
  covariance matrix
• The paper does not provide detail on this
  technique.

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Problems with the model 2

• Express matrix in terms of the weights and the
  base vector (compact representation)
• Once bases are found, the computation is almost
  the same

CM is Covariance matrix of the basis vectors, W
is a vector of weights that is estimated during
the trainig. k is a covariance between the new
node and basis vectors
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Experiment

• Experiment on the simulated data.
• Two sets of experiments Centralized data
  aggregation and Clustered data aggregate
  (difference in terms of energy efficiency)
• Over 100 time unit, Models history length 5
• Two level of confidence threshold, ? 0.1 and
  0.2
• Used fixed Covariance Matrix

Note w1 and w2 were NOT learned during the
experiment but were tuned during the development
phase. Others suggest learning the Covariance
Parameters as well. See David MacKays tutorial
from http//www.gaussianprocess.org/
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Experiment

• Root mean square error averaged over all the
  cycles.
• Baseline method queries all nodes at each cycle
  (hence no error)
• The proposed model demonstrates the significant
  energy savings.

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Summary of the paper

• Gaussian Process is a nice framework to use for
  node selection in sensor network.
• Are there more principled way to search for
  optimal subset? (proposed solution looks a bit ad
  hoc)
• How to chose covariance matrix is not clear.
• How is the accuracy performance compared to
  competing framework?

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Summary of the paper

• Many details of the Gaussian Process are missing
  from this paper. See the following for more
  through discussion
• More through discussion on GP regression
• Gaussian process. Tutorial (MacKay, 1998)
• Sparse Approximation
• Gaussian process Iterative Sparse
  Approximation (Csato 2002)
• Sampling strategy using GP
• Model-driven data acquiring in sensor network
  (Deshpande,Guestrin, et al 2004)
• Using probabilistic models for data management
  in acquisitional environments (Deshapande,
  Guestrin, Maddenn 2005)