Probabilistic Reasoning Over Time

1
Probabilistic Reasoning Over Time

• CSE P573
• Autumn 2004

2
questions

• What is the Markov assumption?
• What is difference between filtering and
  smoothing?
• Is finding the most likely sequence of states the
  same as finding the sequence of most likely
  states? What algorithm do you use?

3
questions

• Is a Kalman filter appropriate for discrete or
  for continuous variables?
• What kinds of distributions does it handle?

4
questions

• What is the main advantage of an using an HMM
  (hidden Markov model) over using a DBN (Dynamic
  Bayesian Network)?
• What is the main advantage of using a DBN over an
  HMM?

5
questions

• What is a "particle" as used in particle
  filtering algorithms?
• Go on to Ch 15 slides
• Go on to Robotics slides

6
Track the Robot
7
Particle Filtering Core Idea

• Initialize particles S randomly with weight 1
• For each observation yt
• For each particle s? S
• Choose a sample s according to
  P(XtsXt-1s)
• s s
• w(s) P(YtytXts) w(s)

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Particle Filtering Resampling

• After every K-th observation is processed
• Randomly select (with replacement) a new set of
  particles S according to the distribution
  w(s) s ? S
• S S
• For all s ? S w(s)1

Resampling KILLS unlikely particles Resampling
DUPLICATES likely particles
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Particle Filtering Computing the Belief State

• Compute P(Xtx y1, , yt) as
• Sum( w(s) s ? S value(s)x ) /
• Sum( w(s) s ? S )

10
Shakey

• Shakey Video