CS 470 Fall 2008
Exam 2 Review
Exam Logistics
- In the testing center from Nov 7-Nov 11. Available from
when
the testing center opens on Nov 7 until it closes on Nov 11.
- 3 hour timed.
- Closed book.
- One 8.5" by 11" sheet of notes allowed.
- Testing center calculator required.
- Mix of true/false, short answer, matching, and "solve the
following" problems.
Bayes Nets
- Distributions
- joint
- marginal
- conditional
- Bayes rule
- The chain rule
- product of conditional distributions
- conditional independence
- product of conditionals with parents
- Graphs for Bayes nets
- syntax
- semantics
- conditional probabilty tables
- Obtaining joint and marginal distributions from the graph and
tables
- The chain rule with conditional independence
- Canonical forms
- noisy OR
- noisy AND
- Markov processes -- 1st order, 2nd order, ...
Bayes Filter
- State space representations
- p(st | st-1)
- p(xt | xt-1)
- p(ot | st)
- p(zt | xt)
- equations for bel and \overline{bel} for both discrete and
continuous random variables
- interpretations for bel and \overline{bel}
- conditional independence assumptions
- Grid filter
- states
- implementation
- applications
The Kalman Filter
- Gaussians
- scalar and vector forms
- priors
- likelihoods
- posteriors
- Sequential estimates of the mean and variance
- Matrix form
- System model: x_{t+1} = Fx_t + eta_t
- Observation model: z_t = Hx_t + nu_t
- Sigma_0, mu_0
- P(x_{t+1} | x_t) ~ N(Fx_t,Sigma_x)
- P(z_t|x_t) ~ N(HX_t,Sigma_z)
- P(x_t|z_t) ~ N(mu_t, Sigma_t)
- Kalman filter equations: must be able
to interpret and manipulate
- mu_t
- Sigma_t
- K_t
- Balance between system and observation noise
- Applications
- Lessons from tutorial
- Limitations
- Tradeoffs between system model, observation sensors, and noise
covariance
Utility Theory
- CAS representation
- evidence=observation
- states, observations, and posterior probabilities
- Equation 16.1 in the book
- Axioms of "well behaved" preferences
- Constructing a utility function using the "Preferences among
lotteries" technique
- continuity
- lotteries
- algorithm
- Uniqueness: positive affine transformations
- Utility of money
- Expected utility
- computing expectations
- maximum expected utility
- arg max notation