Topic: Probabilistic latent variable models
1. Latent variable models in neuroscience
1.1 Principle component analysis (PCA)
sensitive to trial-to-trial noise, so it needs a large amount of trials. Linear Assumption between the latent variables and the observations of nerual activity. ### 1.2 Gassuain process factor analysis - Developed by Byron Yu, et al. commonly used to analyze single trial data. It allows information sharing across time, which can help denoise single trial latent trajectories. Linear Assumption between the latent variables and the observations of nerual activity. ### 1.3 Gausian process latent variable models (LVMs) Allow to fit non-linear observations data. ### 1.4 PfLDS Rely on the rise of deep learning. Comine a linear dynamical system with like Kalman Filter, with a readout that is basically a deep network, which can learn by fitting it to a large quantity of neural data. linear dynamical system with a nonlinear readout. ### 1.5 LFADS nonlinear dynamical system with a linear readout.
前三个 non-parametric methods, 后两个dynamical system (parametric) methods
brige this gap: GPFADS (Gaussian Process Factor Analysis with Dynmaical Systems)
2. Where do we begin? Bayesian Inference!
jpg.
Primer on Gaussian Processes
GP1.png Clearly the answer depends on prior beliefs. 比如如果知道noise很大，那么可能就是一条横线。
GP4 用covariance来表示smoothness。
