Extracting Low-Dimensional Latent Structure from Time Series in the Presence of Delays.
Extracting Low-Dimensional Latent Structure from Time Series in the Presence of Delays.
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在存在延迟的情况下从时间序列中提取低维潜在结构。
DOI：
10.1162/neco_a_00759
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发表时间：
2015-09
影响因子：
2.9
通讯作者：
Yu BM
中科院分区：
文献类型：
--
作者：
Lakshmanan KC;Sadtler PT;Tyler-Kabara EC;Batista AP;Yu BM
有噪声的高维时间序列观测值通常可以由一组低维潜在变量来描述。提取这些潜在变量的常用方法通常假设潜在变量和观察变量之间的瞬时关系。在许多物理系统中，潜在变量的变化表现为时间延迟后观测变量的变化。不考虑这些延迟的技术可以恢复比系统中存在的更多数量的潜在变量，从而使潜在表示更难以解释。在这项工作中，我们引入了一种新颖的概率技术，即时滞高斯过程因子分析（TD-GPFA），该技术在每对潜在变量和观测变量之间存在不同时间延迟的情况下执行降维。我们演示了如何使用高斯过程对每个潜在变量的演化进行建模，使我们能够在连续域上轻松地学习这些延迟。此外，我们还展示了 TD-GPFA 如何将时间平滑和降维结合到一个通用的概率框架中。我们提出了期望/条件最大化（ECME）算法来学习模型参数。我们的模拟表明，当存在时间延迟时，TD-GPFA 能够正确识别这些延迟并恢复潜在空间。然后，我们将 TD-GPFA 应用于猕猴运动皮层在执行伸手任务期间同时记录的数十个神经元的活动。 TD-GPFA 能够使用比 GPFA 更简洁的潜在空间更好地描述神经活动，GPFA 是一种已用于解释运动皮层数据的方法，但不考虑时间延迟。更广泛地说，TD-GPFA 可以通过考虑系统中的物理延迟来帮助揭示高维时间序列数据背后的机制。
Noisy, high-dimensional time series observations can often be described by a set of low-dimensional latent variables. Commonly-used methods to extract these latent variables typically assume instantaneous relationships between the latent and observed variables. In many physical systems, changes in the latent variables manifest as changes in the observed variables after time delays. Techniques that do not account for these delays can recover a larger number of latent variables than are present in the system, thereby making the latent representation more difficult to interpret. In this work, we introduce a novel probabilistic technique, time-delay Gaussian-process factor analysis (TD-GPFA), that performs dimensionality reduction in the presence of a different time delay between each pair of latent and observed variables. We demonstrate how using a Gaussian process to model the evolution of each latent variable allows us to tractably learn these delays over a continuous domain. Additionally, we show how TD-GPFA combines temporal smoothing and dimensionality reduction into a common probabilistic framework. We present an Expectation/Conditional Maximization Either (ECME) algorithm to learn the model parameters. Our simulations demonstrate that when time delays are present, TD-GPFA is able to correctly identify these delays and recover the latent space. We then applied TD-GPFA to the activity of tens of neurons recorded simultaneously in the macaque motor cortex during a reaching task. TD-GPFA is able to better describe the neural activity using a more parsimonious latent space than GPFA, which is a method that has been used to interpret motor cortex data, but does not account for time delays. More broadly, TD-GPFA can help to unravel the mechanisms underlying high-dimensional time series data by taking into account physical delays in the system.