Probabilistic interval-valued computation: toward a practical surrogate for statistics inside CAD tools
A. Singhee, C.R. Fang, J.D. Ma, R.A. Rutenbar
2006
Proceedings - Design Automation Conference
2nd-order cone program [3] . Connections between time-domain cir-Interval methods offer a general, fine-grain strategy for modeling cuit moments and moments ofprobability distributions enable a simcorrelated range uncertainties in numerical algorithms. We present a ilarly attractive variational analysis for linear circuits [4] . new, improved interval algebra that extends the classical affine form Unfortunately, not every variational problem we seek to solve has a to a more rigorous statistical
more »
... foundation. Range uncertainties now tractable analytical form. What then? Monte Carlo analysis remains take the form of confidence intervals. In place ofpessimistic interval the gold standard for "arbitrary" problems -accurate, but often inbounds, we minimize the probability of numerical "escape"; this can tractably slow. Are there other, general options? tighten interval bounds by lOX, while yielding 10-1OX speedups Another altemative, with a surprisingly long history, is interval-va/over Monte Carlo. The formulation relies on three critical ideas: libued analysis [5] . The key idea is to replace individual real values, erating the affine model from the assumption of symmetric intervals; such as x 3, with finite ranges on the real line, such as x[l1,4], and a unifying optimization formulation; and a concrete probabilistic construct a suitable algebra of operators that supports interval-valued model. We refer to these as probabilistic intervals, for brevity. Our arithmetic and basic nonlinear functions such as exp(o and logo. Idegoal is to understand where we might use these as a surrogate for exarithmetcan basconlinalnumerichasgexp(h) and laceIt pensive, explicit statistical computations. Results from sparse matri-ally we can take a conventional numerical algorithm, and replace it ces and graph delay algorithms demonstrate the utility of the operator by operator with an interval-valued version. Of course, this ces and.graph delay algorithmsdmonstratetheutilityofth is not intrinsically a statistical model, but rather, a model of the unapproach, and the remaining challenges. certainty in the extent of these ranges. One must transform the distri-Categories and Subject Descriptors bution statistics of the problem into some suitable set of range B.7.2 [Integrated Circuits]: Design Aids uncertainties, with some concomitant loss of fidelity. See [7] for an General Terms early application in the domain of interconnect modeling. Algorithms, Design, Statistics The problem with these "classical" intervals is that, without any explicit mechanisms to track essential correlations among interval op-Keywords erands, range estimation errors explode during complex calculations.
doi:10.1109/dac.2006.229201
fatcat:urwrnn3645cjxmvsh25l7yydfq