Making HCC Probabilistic (safely)

1
Making HCC Probabilistic (safely)
Jonathan Moody CMU Aug. 16, 2001
2
Outline

• What is HCC?
• Modeling in HCC with Randomness
• Semantics of Probabilistic Choice
• Related Work
• Conclusions

3
What is HCC?

• Hybrid Concurrent Constraint
• Hybrid modeling continuous change
• Concurrent declarative, no ordering of
  operations
• Constraint logical inference on (in)equalities
• Example

4
What is HCC?
5
What is HCC?

• HCC constraint processing occurs in phases.

time
Trace
Point
Interval
6
Outline

• What is HCC?
• Modeling in HCC with Randomness
• Semantics of Probabilistic Choice
• Related Work
• Conclusions

7
Randomness in HCC

• HCC has a Foreign Function Interface (FFI)
• Calls to a random number generator can be made.
• x gaussian(mean, sigma)
• But the meaning of some programs is not so clear.

8
(No Transcript)
9
Modeling with Randomness

• What would we like to model?
• Component failures
• Uncertain initial conditions
• Time dependent noise
• x' F(x) noise(t)
• Two mechanisms formulated to represent these uses
  of randomness in a model.

10
Modeling with Randomness

• Random Choices
• choose ltvargt from ltexprgt
• choose b from coinflip(pFail)
• choose x0 from random(low, high)
• Random Processes
• class BrownianProcess ... defined in HCC it
  chooses a new random value periodically.
• noise new BrownianProcess(deltaT)
• m x'' F(x) - (b x') noise.val()

11
Outline

• What is HCC?
• Modeling in HCC with Randomness
• Semantics of Probabilistic Choice
• Related Work
• Conclusions

12
Probabilistic Choice

• Meaning and Implementation
• choose ltvargt from ltexprgt
• Intention is that ltexprgt will contain a call to a
  non-deterministic function.
• After evaluation, behaves like ltvargt ltvaluegt.
• Strategy Use existing FFI, but protect these
  expressions from unnecessary re-evaluation.
• The question When to evaluate?

13
Probabilistic Choice

• By "when", I mean "at what step in HCC's
  constraint propagation process".
• As early as possible? no.
• HCC has no current estimate for variable.
• Any time? no.
• Value could depend on order of statements.
• As late as possible? no.
• The evaluation might trigger more inference.

14
Probabilistic Choice

• When the variables in the expression are fully
  determined.
• for intervals a,b this means a b
• other data types are either unknown or fully
  determined.
• Once variables are fully determined, their
  estimated values cannot change without triggering
  a conflict (which can be detected and dealt with).

15
Outline

• What is HCC?
• Modeling in HCC with Randomness
• Semantics of Probabilistic Choice
• Related Work
• Conclusions

16
Related Work (PCC)

• "choose" inspired by proposal for Probabilistic
  CC by Vineet Gupta, et al.
• Different operational semantics based on
  evaluating a call to an external random number
  generator.
• Accommodates continuous distributions without
  resorting to computing limit of recursive
  choices.
• Other distributions (uniform, gaussian, etc.) can
  be plugged in easily.

17
Related Work (SDE)

• Stochastic Differential Equations
• Analytical and numerical methods for solving
  SDE's are available.
• Ideally, HCC's numerical integrator should be
  made aware of stochastic terms.
• Modeling noise processes with an HCC object
  sidesteps implementation difficulties.

18
Related Work (FLP)

• Functional Logic Programming
• Simple syntactic unification is inadequate to
  unify
• 2 X 4
• FLP adds reasoning about equality between
  functional expressions.
• Residuation (analogous to our strategy)
• Narrowing (unfortunately not applicable)

19
Outline

• What is HCC?
• Modeling in HCC with Randomness
• Semantics of Probabilistic Choice
• Related Work
• Conclusions

20
Conclusions

• Goals achieved
• HCC supports random choice and processes.
• Other related improvements to HCC...
• Performance limitations
• There is overhead associated with modeling random
  processes inside of HCC.

21
Acknowledgements
Benoit Hudson Adam Sweet Anupa Bajwa (mentor)
22
C lt-gt HCC Coupling

• Why work on the C lt-gt HCC interface?
• True that HCC is used primarily for simulation.
  Output is a trace file of model values over time.
• But if it is ever to be used for control (or
  diagnosis), a better interface must be defined.

23
C lt-gt HCC Coupling

• A tighter integration and more uniform interface.
• HCC_tell, HCC_ask, HCC_eval
• Primary achievement
• HCC_ask enables stopping at any conditional point
  in the simulation, whereupon the C program
  resumes execution.

24
C lt-gt HCC Coupling