Many time series can be modeled as a sequence of segments representing high-level discrete states, such as running and walking in a human activity application. Flexible models should describe the system state and observations in stationary "pure-state" periods as well as transition periods between adjacent segments, such as a gradual slowdown between running and walking. However, most prior work assumes instantaneous transitions between pure discrete states. We propose a dynamical Wasserstein barycentric (DWB) model that estimates the system state over time as well as the data-generating distributions of pure states in an unsupervised manner. Our model assumes each pure state generates data from a multivariate normal distribution, and characterizes transitions between states via displacement-interpolation specified by the Wasserstein barycenter. The system state is represented by a barycentric weight vector which evolves over time via a random walk on the simplex. Parameter learning leverages the natural Riemannian geometry of Gaussian distributions under the Wasserstein distance, which leads to improved convergence speeds. Experiments on several human activity datasets show that our proposed DWB model accurately learns the generating distribution of pure states while improving state estimation for transition periods compared to the commonly used linear interpolation mixture models.
翻译:许多时间序列可以作为代表高度离散状态的区段序列进行模拟,例如运行和在人类活动应用中行走。灵活模型应当描述系统状态和在固定的“质状态”期间以及相邻段间过渡期的系统观察,例如运行和行走之间的逐渐减速。然而,大多数先前的工作假设了纯离散状态之间的瞬间转换。我们提议了一个动态瓦西斯坦野蛮中心(DWB)模型,该模型以不受监督的方式对系统长期状况以及纯状态的生成数据分布进行估算。我们的模型假设每个纯状态生成多变正常分布的数据,并描述通过瓦塞斯坦大气中枢规定的离位-内插度期间的系统状态和观察。这个系统状态代表着一种固态的重量矢量矢量,随着时间的演变,通过在简单x上随机行走动而演变。Parameter学习利用瓦塞斯坦距离下高斯分布的自然里曼地理测量,从而改进了趋同速度。在几个人类活动模型上进行的实验表明,通过瓦塞斯坦大气中位的模型将改进了我们使用的纯度分布模型,同时将不断学习。