Variational Gaussian Process State-Space Models
Authors: Roger Frigola, Yutian Chen, Carl Edward Rasmussen
NeurIPS 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 6 Experiments The goal of this section is to showcase the ability of variational GP-SSMs to perform approximate Bayesian learning of nonlinear dynamical systems. In particular, we want to demonstrate: 1) the ability to learn the inherent nonlinear dynamics of a system, 2) the application in cases where the latent states have higher dimensionality than the observations, and 3) the use of non-Gaussian likelihoods. 6.1 1D Nonlinear System We apply our variational learning procedure presented above to the one-dimensional nonlinear system described by p(xt+1|xt) = N(f(xt), 1) and p(yt|xt) = N(xt, 1) where the transition function is xt + 1 if x < 4 and 4xt + 21 if x 4. ... In Table 1, we compare our method (Variational GP-SSM) against the PMCMC sampling procedure from [8] taking 100 samples and 10 burn in samples. |
| Researcher Affiliation | Academia | Roger Frigola, Yutian Chen and Carl E. Rasmussen Department of Engineering University of Cambridge {rf342,yc373,cer54}@cam.ac.uk |
| Pseudocode | Yes | Algorithm 1 Variational learning of GP-SSMs with particle smoothing. Batch mode (i.e. non-SVI) is the particular case where the mini-batch is the whole dataset. Require: Observations y1:T . Initial values for θ, η1 and η2. Schedules for ρ and λ. i = 1. yτ:τ SAMPLEMINIBATCH(y1:T ) {xτ:τ }L l=1 GETSAMPLESOPTIMALQX(yτ:τ , θ, η1, η2) sample from eq. (12) θL GETTHETAGRADIENT({xτ:τ }L l=1, θ) supp. material η 1, η 2 GETOPTIMALQU({xτ:τ }L l=1, θ) eq. (11) or (14) η1 η1 + ρi(η 1 η1) η2 η2 + ρi(η 2 η2) θ θ + λi θL i i + 1 until ELBO convergence |
| Open Source Code | No | The paper does not provide any explicit statements about open-sourcing its code or links to a code repository. |
| Open Datasets | Yes | We use data in neuron cluster 1 (the most active) from experiment ec013.717 in [14]. [14] K. Mizuseki, A. Sirota, E. Pastalkova, K. Diba, and G. Buzski. Multiple single unit recordings from different rat hippocampal and entorhinal regions while the animals were performing multiple behavioral tasks. CRCNS.org. http://dx.doi.org/10.6080/K09G5JRZ, 2013. |
| Dataset Splits | No | The paper mentions training and test set sizes (e.g., T=500 for training, 105 data points for test), but it does not specify explicit training/validation/test dataset splits or validation procedures. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., CPU, GPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions various algorithms and models (e.g., Gaussian processes, sequential Monte Carlo) but does not provide specific version numbers for any software, libraries, or frameworks used in the experiments. |
| Experiment Setup | Yes | To solve the expectations with respect to the approximate smoothing distribution q(x) we use a bootstrap particle fixed-lag smoother with 1000 particles and a lag of 10. Smoothing is done with a fixed-lag particle smoother and training until convergence takes approximately 50 iterations of Algorithm 1. We use a Poisson likelihood relating the spike counts to the second latent state yt|xt Poisson(exp(αx(2) t + β)). |