Spectral learning of Bernoulli linear dynamical systems models for decision-making
Authors: Iris R Stone, Yotam Sagiv, Il Memming Park, Jonathan W. Pillow
TMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Here we develop a spectral learning method for fast, efficient fitting of probit-Bernoulli latent linear dynamical system (LDS) models. Our approach extends traditional subspace identification methods to the Bernoulli setting via a transformation of the first and second sample moments. This results in a robust, fixed-cost estimator that avoids the hazards of local optima and the long computation time of iterative fitting procedures like the expectation-maximization (EM) algorithm. In regimes where data is limited or assumptions about the statistical structure of the data are not met, we demonstrate that the spectral estimate provides a good initialization for Laplace-EM fitting. Finally, we show that the estimator provides substantial benefits to real world settings by analyzing data from mice performing a sensory decision-making task. |
| Researcher Affiliation | Academia | Iris Stone EMAIL Princeton Neuroscience Institute Princeton University Yotam Sagiv EMAIL Princeton Neuroscience Institute Princeton University Il Memming Park EMAIL Champalimaud Foundation Jonathan Pillow EMAIL Princeton Neuroscience Institute Princeton University |
| Pseudocode | Yes | To summarize, the steps of best LDS are: 1. Compute the moments of y 2. Convert those moments to moments of z as defined in Equation 4 (a) Compute µ and Σzz by solving the system in Equation 5 (b) Use µ and Σzz to compute Σuz by solving the system in Equation 6 3. Cholesky decompose Σ = RRT 4. Take R as the input to the standard N4SID algorithm to recover the system matrices |
| Open Source Code | Yes | Code availability Code for general use applications of best LDS analyses developed in this study, including all applications to simulated and real data presented in the manuscript, are available on Git Hub at https://github.com/irisstone/best LDS/. |
| Open Datasets | Yes | Data availability The data that support the findings of this study are publicly available on figshare at https://figshare.com/articles/dataset/best LDS_associated_data/23750670. |
| Dataset Splits | Yes | To further assess best LDS performance on the real data, we use five-fold cross-validation to compare its performance to three other models |
| Hardware Specification | No | All computations were performed on an internal CPU cluster. |
| Software Dependencies | No | Implemented using the Python ssm package, licensed under the MIT license |
| Experiment Setup | Yes | For the q p regime, we say that EM has converged when the avg. | | in the gain matrix on successive steps is within a tolerance (tol = 0.15); for p < q we found that comparing the log-evidence on successive steps to be more reliable (tol = 10, in bits/sample). |