In this paper, we study classification and regression error bounds for inhomogenous data that are independent but not necessarily identically distributed. First, we consider classification of data in the presence of non-stationary noise and establish ergodic type sufficient conditions that guarantee the achievability of the Bayes error bound, using universal rules. We then perform a similar analysis for $k$-nearest neighbour regression and obtain optimal error bounds for the same. Finally, we illustrate applications of our results in the context of wireless networks.

翻译：本文研究了独立但非同分布异构数据的分类与回归误差界。首先，我们考虑存在非平稳噪声时的数据分类问题，建立了保证贝叶斯误差界可达的遍历型充分条件，并采用通用决策规则。随后，我们对$k$-近邻回归进行了类似分析，获得了相应的最优误差界。最后，我们展示了研究结果在无线网络场景中的应用。