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Probabilistic Decomposed Linear Dynamical Systems for Robust Discovery of Latent Neural Dynamics
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Proposes probabilistic decomposed linear dynamical systems (p-dLDS), a variational-EM method with time-informed sparse priors and a time-varying offset term that makes decomposed latent dynamics inference more robust to noise and nonlinearity.
Problem
Latent variable estimation in decomposed linear dynamical systems (dLDS) is sensitive to dynamical noise and cannot represent systems with multiple fixed points, leading to inconsistent and unstable latent inferences on neural signals.
Approach
Replaces dLDS's noise-sensitive point-estimate BPDN-DF inference with a variational EM procedure that marginalizes over latent uncertainty using time-informed hierarchical sparsity priors (coefficients smoothed via previous estimates), and adds a time-varying offset decomposition x_t = l_t + b_t (b_t estimated by moving average) to handle multiple fixed points while avoiding trivial degenerate sol
Key results
- On NASCAR with random speeds, p-dLDS reached dynamics MSE 0.033 (x1e-3) and 100-step R^2 0.450 vs. 0.184 for SLDS and dLDS diverging.
- On Lorenz, p-dLDS achieved 100-step R^2 of 0.418 while SLDS and rSLDS were negative (-3.47, -11.54).
- On the reaching task, p-dLDS reached 42.31% top-1 and 70.51% top-3 reach-direction accuracy vs. 38.46% and 57.69% for SLDS.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use probabilistic inference instead of dLDS point-estimate inference | dLDS on NASCAR · NASCAR | Dynamics MSE: 123.19 -> 0.033 | Helped |
| Use probabilistic inference instead of dLDS point-estimate inference | dLDS on NASCAR · NASCAR | 100-step R²: -> 0.450 | Helped |
| Use p-dLDS, including the time-varying offset, instead of dLDS | dLDS on Lorenz · Lorenz | Dynamics MSE: 1.123 -> 0.141 | Helped |
| Use p-dLDS, including the time-varying offset, instead of dLDS | dLDS on Lorenz · Lorenz | Switch MSE: 0.1529 -> 0.0137 | Helped |
| Use p-dLDS, including the time-varying offset, instead of dLDS | dLDS on Lorenz · Lorenz | 100-step R²: -> 0.418 | Helped |
| Use p-dLDS instead of SLDS | SLDS on Reaching · Reaching | Top-1 accuracy: 38.46 -> 42.31 | Helped |
| Use p-dLDS instead of SLDS | SLDS on Reaching · Reaching | Top-3 accuracy: 57.69 -> 70.51 | Helped |
| Use p-dLDS instead of SLDS | SLDS on Reaching · Reaching | State MSE: 0.5289 -> 0.4061 | Helped |
| Use p-dLDS instead of SLDS | SLDS on Reaching · Reaching | Dynamics MSE: 0.3942 -> 0.0567 | Helped |
Surprising findings
- Analytically, adding an unconstrained time-varying offset to the dLDS dynamics makes the F_t estimation degenerate (F_t = 0 minimizes the objective with a single transition), motivating the decomposition.
- Baseline dLDS diverged (100-step R^2 undefined/-infinity) on NASCAR and Lorenz.
Limitations
- Coefficient transition model is primarily motivated by smoothness and lacks a mechanism for generating future unseen coefficients.
- Clinical evaluation is a preliminary analysis on a single subject.
- Emission model is Gaussian; extension to Poisson spiking likelihoods is left for future work.
Experimental setup
Datasets: NASCAR (synthetic, random speeds) Lorenz (synthetic, random ramping) simulated motor cortex reaching LFP (WSLFP-based) clinical SCC LFP recordings from a TRD patient
Benchmarks: NASCAR Lorenz simulated monkey reaching task clinical SCC LFP
Metrics: dynamics MSE switch MSE 100-step R^2 state MSE top-1 accuracy top-3 accuracy
Baselines: SLDS rSLDS dLDS
Builds on: decomposed linear dynamical systems SBL-DF BPDN-DF switching linear dynamical systems
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