论文标题
通过迭代修剪学习纠缠的单样本分布
Learning Entangled Single-Sample Distributions via Iterative Trimming
论文作者
论文摘要
在纠缠单样本分布的设置中，目标是估算一个分布家族共享的一些常见参数，给定每个分布中的一个\ emph {single}样本。我们研究一般条件下的平均估计和线性回归，并基于迭代修剪样品并在修剪样品集中重新估计参数，分析一种简单且计算上有效的方法。我们表明，对数迭代中的方法输出了一个估计值，该估计仅取决于$ \lceilαn\ rceil $的噪声水平 - 最高的数据点，其中$α$是常数，而$ n $是样本大小。这意味着它可以忍受恒定的高噪声点。这些是该方法在我们的一般条件下的第一个这样的结果。这也证明了迭代修剪在实践中的广泛应用和经验成功。关于合成数据的实验，我们的理论结果得到了补充。
In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of distributions, given one \emph{single} sample from each distribution. We study mean estimation and linear regression under general conditions, and analyze a simple and computationally efficient method based on iteratively trimming samples and re-estimating the parameter on the trimmed sample set. We show that the method in logarithmic iterations outputs an estimation whose error only depends on the noise level of the $\lceil αn \rceil$-th noisiest data point where $α$ is a constant and $n$ is the sample size. This means it can tolerate a constant fraction of high-noise points. These are the first such results for the method under our general conditions. It also justifies the wide application and empirical success of iterative trimming in practice. Our theoretical results are complemented by experiments on synthetic data.
