未来预测误差的单调条件复杂性界
Monotone Conditional Complexity Bounds on Future Prediction Errors
摘要：
当在线预测任何（可计算的）随机序列时，我们限制了未来的损失。所罗门诺夫通过m的算法复杂度限制了他的通用预测器M与真实分布m的总偏差。在这里，我们假设我们在时间t>1并且已经观察到x=x_1. x_t。我们将未来的预测性能绑定在x_{t+1} x_{t+2}上.通过给定x的m的算法复杂度的新变体，加上x的随机性不足的复杂度。新的复杂性在其条件下是单调的，在这个意义上，这个复杂性只能减少，如果条件延长。我们还简要讨论了潜在的概括贝叶斯模型类和分类问题。
英文摘要：
We bound the future loss when predicting any (computably) stochastic sequence online. Solomonoff finitely bounded the total deviation of his universal predictor M from the true distribution m by the algorithmic complexity of m. Here we assume we are at a time t>1 and already observed x=x_1...x_t. We bound the future prediction performance on x_{t+1}x_{t+2}... by a new variant of algorithmic complexity of m given x, plus the complexity of the randomness deficiency of x. The new complexity is monotone in its condition in the sense that this complexity can only decrease if the condition is prolonged. We also briefly discuss potential generalizations to Bayesian model classes and to classification problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
