独立噪声观测大规模聚集的普适性
Universal Behavior in Large-scale Aggregation of Independent Noisy Observations
摘要：
噪声观测的聚合涉及观测质量和聚合质量之间的困难权衡，观测质量可以通过增加观测的数量来增加，聚合质量如果观测的数量太大则会降低。我们澄清这种行为的一个典型的系统中，任意大量的观察超过系统容量可以聚合使用有损数据压缩。我们证明了集体误差和系统容量之间存在比例关系，并表明大规模有损聚合可以优于无损聚合的观察噪声的临界水平以上。进一步，我们证明了当系统容量趋于无穷大时，通过考虑系统容量的渐近行为，可以得到与系统容量无关的标度和噪声临界值的普遍结果.
英文摘要：
Aggregation of noisy observations involves a difficult tradeoff between observation quality, which can be increased by increasing the number of observations, and aggregation quality which decreases if the number of observations is too large. We clarify this behavior for a protypical system in which arbitrarily large numbers of observations exceeding the system capacity can be aggregated using lossy data compression. We show the existence of a scaling relation between the collective error and the system capacity, and show that large scale lossy aggregation can outperform lossless aggregation above a critical level of observation noise. Further, we show that universal results for scaling and critical value of noise which are independent of system capacity can be obtained by considering asymptotic behavior when the system capacity increases toward infinity.
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