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Probabilistic IntervalValued Computation: Toward a Practical Surrogate for Statistics Inside (2008)
| Content Provider | CiteSeerX |
|---|---|
| Author | Singhee, Amith Fang, Claire F. Ma, James D. Rutenbar, Rob A. |
| Abstract | Abstract 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 sim-correlated 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 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 in-bounds, we minimize the probability ofnumerical "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: lib-ued 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 ofoperators 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. Ide-goal is to understand where we might use these as a surrogate for ex- arithmetcan 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, thisces and.graphdelayalgorithmsdmonstratetheutilityofth is not intrinsically a statistical model, but rather, a model of the un-approach, and the remaining challenges. |
| File Format | |
| Journal | CAD Tools”, IEEE Trans. on CAD of Integrated Circuits and Systems |
| Language | English |
| Publisher Date | 2008-01-01 |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
