Bayesian Inference in High-Dimensional Time-Serieswith the Orthogonal Stochastic Linear Mixing Model
基于正交随机线性混合模型的高维时间序列贝叶斯推断AI 解读 ↓
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基于正交随机线性混合模型的高维时间序列贝叶斯推断
- 研究问题
- 面对长时间记录的高维多输出序列，如何保留随输入变化的复杂输出依赖，同时降低随机线性混合模型的推断计算负担？
- 方法与思路
- 作者在随机线性混合模型的混合系数间施加正交约束，提出 OSLMM，并为原模型与新模型提供马尔可夫链蒙特卡洛推断程序。
- 材料陈述的贡献
- 摘要称，多个真实应用中 OSLMM 的可扩展性和预测误差优于比较方法，其潜在函数还支持神经群体对听觉刺激响应的紧凑可视化。
- 阅读关注点
- 应核对正交约束对表达能力的影响、计算复杂度与采样收敛、预测比较的设置，以及潜在函数可视化是否具有稳定解释。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审及期刊接收未经核实；摘要未给出复杂度或预测误差数值，不能据此判断普遍优越性。
原文摘要
Many modern time-series datasets contain large numbers of output response variables sampled for prolonged periods of time. For example, in neuroscience, the activities of 100s-1000's of neurons are recorded during behaviors and in response to sensory stimuli. Multi-output Gaussian process models leverage the nonparametric nature of Gaussian processes to capture structure across multiple outputs. However, this class of models typically assumes that the correlations between the output response variables are invariant in the input space. Stochastic linear mixing models (SLMM) assume the mixture coefficients depend on input, making them more flexible and effective to capture complex output dependence. However, currently, the inference for SLMMs is intractable for large datasets, making them inapplicable to several modern time-series problems. In this paper, we propose a new regression framework, the orthogonal stochastic linear mixing model (OSLMM) that introduces an orthogonal constraint amongst the mixing coefficients. This constraint reduces the computational burden of inference while retaining the capability to handle complex output dependence. We provide Markov chain Monte Carlo inference procedures for both SLMM and OSLMM and demonstrate superior model scalability and reduced prediction error of OSLMM compared with state-of-the-art methods on several real-world applications. In neurophysiology recordings, we use the inferred latent functions for compact visualization of population responses to auditory stimuli, and demonstrate superior results compared to a competing method (GPFA). Together, these results demonstrate that OSLMM will be useful for the analysis of diverse, large-scale time-series datasets.