论文标题
与融合套索的图表中的差异估计
Variance estimation in graphs with the fused lasso
论文作者
论文摘要
我们研究一般图形结构问题中的方差估计问题。首先，我们为均质的情况开发了一个线性时间估计器，可以始终如一地估计一般图中的方差。我们表明，当平均信号与规范缩放的总变化时，我们的估计器可达到链和2D网格图的最小速率。此外，我们在瞬间条件下的一般图中的融合Lasso估计器的平均平方误差性能以及误差的尾巴行为上的绑定。这些上限使我们能够概括更广泛的分布类别，例如亚指数，在融合套索上的许多现有结果，这些结果仅在误认为是下高斯随机变量的情况下才知道。利用我们的上限，我们研究了一个简单的总变异正则估计器，用于估计异性范围的方差信号。我们还提供了下限，表明我们的异质方差估计器达到了最小值的速率，用于估计网格图中有界变化的信号和$ k $ neart的邻域图，并且估计值对于在任何连接图中估算方差估算方差一致。
We study the problem of variance estimation in general graph-structured problems. First, we develop a linear time estimator for the homoscedastic case that can consistently estimate the variance in general graphs. We show that our estimator attains minimax rates for the chain and 2D grid graphs when the mean signal has total variation with canonical scaling. Furthermore, we provide general upper bounds on the mean squared error performance of the fused lasso estimator in general graphs under a moment condition and a bound on the tail behavior of the errors. These upper bounds allow us to generalize for broader classes of distributions, such as sub-exponential, many existing results on the fused lasso that are only known to hold with the assumption that errors are sub-Gaussian random variables. Exploiting our upper bounds, we then study a simple total variation regularization estimator for estimating the signal of variances in the heteroscedastic case. We also provide lower bounds showing that our heteroscedastic variance estimator attains minimax rates for estimating signals of bounded variation in grid graphs, and $K$-nearest neighbor graphs, and the estimator is consistent for estimating the variances in any connected graph.
