The Complexity of Forecast Testing
研究预测检验的计算复杂性,展示了一种线性时间检验和自然分布,使得不了解未来的预测者若想通过检验,必须能解决计算困难问题,从而说明计算高效的预测者无法总是欺骗检验。
Consider a weather forecaster predicting a probability of rain for the next day. We consider tests that, given a finite sequence of forecast predictions and outcomes, will either pass or fail the forecaster. Sandroni showed that any test which passes a forecaster who knows the distribution of nature can also be probabilistically passed by a forecaster with no knowledge of future events. We look at the computational complexity of such forecasters and exhibit a linear-time test and distribution of nature such that any forecaster without knowledge of the future who can fool the test must be able to solve computationally difficult problems. Thus, unlike Sandroni's work, a computationally efficient forecaster cannot always fool this test independently of nature.