Probabilistic Interval-Valued Computation: Toward a Practical Surrogate for Statistics Inside CAD Tools
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 x 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.
statistics algorithms arithmetic design automation error analysis interval arithmetic simulation variational methods