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Probabilistic Interval-Valued Computation: Toward a Practical Surrogate for Statistics Inside CAD Tools

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4 Author(s)
Singhee, A. ; IBM T J. Watson Res. Center, Yorktown Heights, NY ; Fang, C.F. ; Ma, J.D. ; Rutenbar, R.A.

Interval methods offer a general fine-grain strategy for modeling correlated range uncertainties in numerical algorithms. We present a new improved interval algebra that extends the classical affine form to a more rigorous statistical foundation. Range uncertainties now take the form of confidence intervals. In place of pessimistic interval bounds, we minimize the probability of numerical "escape"; this can tighten interval bounds by an order of magnitude while yielding 10-100 times speedups over Monte Carlo. The formulation relies on the following three critical ideas: liberating the affine model from the assumption of symmetric intervals; a unifying optimization formulation; and a concrete probabilistic model. We refer to these as probabilistic intervals for brevity. Our goal is to understand where we might use these as a surrogate for expensive explicit statistical computations. Results from sparse matrices and graph delay algorithms demonstrate the utility of the approach and the remaining challenges.

Published in:

Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on  (Volume:27 ,  Issue: 12 )

Date of Publication:

Dec. 2008

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