贝叶斯稀疏向量自回归切换模型及其在人类手势相位分割中的应用
Bayesian Sparse Vector Autoregressive Switching Models with Application to Human Gesture Phase Segmentation
AI总结：
本文提出一种稀疏VAR隐半马尔可夫模型，结合$l_1$-球投影先验和非局部先验，实现多元非平稳时间序列的变量选择与模型区分，并成功应用于人类手势相位分割。
摘要：
我们提出了一种稀疏向量自回归（VAR）隐半马尔可夫模型（HSMM），用于建模多元非平稳时间序列中的时间依赖和同期（如空间）依赖。HSMM的通用状态分布被嵌入到一个特殊的转移矩阵结构中，促进了高效的似然评估和任意的近似精度。为了促进VAR系数的稀疏性，我们部署了$l_1$-球投影先验，它将可微性与获得精确零的正概率相结合，在每个切换状态内实现变量选择。这也通过哈密顿蒙特卡洛（HMC）促进了后验估计。我们进一步在HSMM停留分布的参数上放置非局部先验，提高了贝叶斯模型选择区分数据是更受简单隐马尔可夫模型（HMM）还是更灵活的HSMM支持的能力。我们提出的方法通过基于传感器数据的人类手势相位分割应用进行了说明，其中我们成功识别并表征了静止和活跃手势的时期，以及与这些状态中每一个相关联的手势运动中涉及的动态模式。
英文摘要：
We propose a sparse vector autoregressive (VAR) hidden semi-Markov model (HSMM) for modeling temporal and contemporaneous (e.g. spatial) dependencies in multivariate nonstationary time series. The HSMM's generic state distribution is embedded in a special transition matrix structure, facilitating efficient likelihood evaluations and arbitrary approximation accuracy. To promote sparsity of the VAR coefficients, we deploy an $l_1$-ball projection prior, which combines differentiability with a positive probability of obtaining exact zeros, achieving variable selection within each switching state. This also facilitates posterior estimation via Hamiltonian Monte Carlo (HMC). We further place non-local priors on the parameters of the HSMM dwell distribution improving the ability of Bayesian model selection to distinguish whether the data is better supported by the simpler hidden Markov model (HMM), or the more flexible HSMM. Our proposed methodology is illustrated via an application to human gesture phase segmentation based on sensor data, where we successfully identify and characterize the periods of rest and active gesturing, as well as the dynamical patterns involved in the gesture movements associated with each of these states.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
