We study algorithms for online change-point detection (OCPD), where samples
that are potentially heavy-tailed, are presented one at a time and a change in
the underlying mean must be detected as early as possible. We present an
algorithm based on clipped Stochastic Gradient Descent (SGD), that works even
if we only assume that the second moment of the data generating process is
bounded. We derive guarantees on worst-case, finite-sample false-positive rate
(FPR) over the family of all distributions with bounded second moment. Thus,
our method is the first OCPD algorithm that guarantees finite-sample FPR, even
if the data is high dimensional and the underlying distributions are
heavy-tailed. The technical contribution of our paper is to show that
clipped-SGD can estimate the mean of a random vector and simultaneously provide
confidence bounds at all confidence values. We combine this robust estimate
with a union bound argument and construct a sequential change-point algorithm
with finite-sample FPR guarantees. We show empirically that our algorithm works
well in a variety of situations, whether the underlying data are heavy-tailed,
light-tailed, high dimensional or discrete. No other algorithm achieves bounded
FPR theoretically or empirically, over all settings we study simultaneously.

本文研究了在线变点检测算法，提出了基于剪切随机梯度下降的算法，可以在只假设数据生成过程的第二矩有界的情况下工作，并使用联合边界论证形成具有有限样本假阳性率保证的顺序变点算法，可在各种情况下成功检测到概率密度分布的变化。

在线重尾变点检测

Online Heavy-tailed Change-point detection

We consider the problem of detecting abrupt changes in the distribution of a
multi-dimensional time series, with limited computing power and memory. In this
paper, we propose a new, simple method for model-free online change-point
detection that relies only on fast and light recursive statistics, inspired by
the classical Exponential Weighted Moving Average algorithm (EWMA). The
proposed idea is to compute two EWMA statistics on the stream of data with
different forgetting factors, and to compare them. By doing so, we show that we
implicitly compare recent samples with older ones, without the need to
explicitly store them. Additionally, we leverage Random Features (RFs) to
efficiently use the Maximum Mean Discrepancy as a distance between
distributions, furthermore exploiting recent optical hardware to compute
high-dimensional RFs in near constant time. We show that our method is
significantly faster than usual non-parametric methods for a given accuracy.

本文提出了一种基于 Exponential Weighted Moving Average，使用随机特征进行 Maximum Mean Discrepancy 距离度量、实现高效率非参数在线变点检测的方法。