Sequentially detecting multiple changepoints in a data stream is a challenging task. Difficulties relate to both computational and statistical aspects, and in the latter, specifying control parameters is a particular problem. Choosing control parameters typically relies on unrealistic assumptions, such as the distributions generating the data, and their parameters, being known. This is implausible in the streaming paradigm, where several changepoints will exist. Further, current literature is mostly concerned with streams of continuous-valued observations, and focuses on detecting a single changepoint. There is a dearth of literature dedicated to detecting multiple changepoints in transition matrices, which arise from a sequence of discrete states. This paper makes the following contributions: a complete framework is developed for adaptively and sequentially estimating a Markov transition matrix in the streaming data setting. A change detection method is then developed, using a novel moment matching technique, which can effectively monitor for multiple changepoints in a transition matrix. This adaptive detection and estimation procedure for transition matrices, referred to as ADEPT-M, is compared to several change detectors on synthetic data streams, and is implemented on two real-world data streams – one consisting of over nine million HTTP web requests, and the other being a well-studied electricity market data set.

顺序检测数据流中的多个变更点是一项艰巨的任务。困难涉及计算和统计方面，在后者中，指定控制参数是一个特殊的问题。选择控制参数通常依赖于不切实际的假设，例如已知生成数据的分布及其参数。这在流式范式中是难以置信的，在流式范式中将存在多个更改点。此外，当前的文献主要涉及连续值观测的数据流，并着重于检测单个变化点。缺乏用于检测过渡矩阵中多个变化点的文献，这是由一系列离散状态引起的。本文做出了以下贡献：开发了一个完整的框架，用于自适应地和顺序地估计流数据设置中的马尔可夫转移矩阵。然后使用一种新颖的矩匹配技术开发了一种变化检测方法，该方法可以有效地监视过渡矩阵中的多个变化点。该过渡矩阵的自适应检测和估计程序称为ADEPT-M，与合成数据流上的多个变化检测器进行了比较，并在两个实际数据流上实现–一个包含超过900万个HTTP Web请求，以及另一个是经过深入研究的电力市场数据集。