Linear Time GPs for Inferring Latent Trajectories from Neural Spike Trains
Linear Time GPs for Inferring Latent Trajectories from Neural Spike Trains
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DOI：
10.48550/arxiv.2306.01802
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发表时间：
2023-06
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影响因子：
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通讯作者：
Matthew Dowling;Yuan Zhao;Il Memming Park
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作者：
Matthew Dowling;Yuan Zhao;Il Memming Park
潜高斯过程（GP）模型在神经科学中被广泛用于从序列观测中揭示隐藏的状态演化，主要是在神经活动记录中。虽然潜在的GP模型在理论上提供了一个原则性和强大的解决方案，但非共轭设置中的棘手后验需要近似推理方案，这可能缺乏可扩展性。在这项工作中，我们提出了cvHM，一个通用的推理框架，潜在的GP模型利用Hida-Mat\'ern内核和共轭计算变分推理（CVI）。使用cvHM，我们能够对任意可能性执行具有线性时间复杂度的潜在神经轨迹的变分推理。使用Hida-Mat\'ern GP对静态内核进行重新参数化有助于我们将通过动力系统对先验假设进行编码的潜变量模型与通过GP对轨迹假设进行编码的潜变量模型联系起来。与以前的工作相比，我们使用双向信息过滤，导致一个更简洁的实现。此外，我们采用Whittle近似似然来实现高效的超参数学习。
Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in theory, the intractable posterior in non-conjugate settings necessitates approximate inference schemes, which may lack scalability. In this work, we propose cvHM, a general inference framework for latent GP models leveraging Hida-Mat\'ern kernels and conjugate computation variational inference (CVI). With cvHM, we are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods. The reparameterization of stationary kernels using Hida-Mat\'ern GPs helps us connect the latent variable models that encode prior assumptions through dynamical systems to those that encode trajectory assumptions through GPs. In contrast to previous work, we use bidirectional information filtering, leading to a more concise implementation. Furthermore, we employ the Whittle approximate likelihood to achieve highly efficient hyperparameter learning.