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One-hot Generalized Linear Model for Switching Brain State Discovery
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Proposes one-hot HMM-GLM (OHG), a state-switching GLM whose per-state connection types are soft one-hot variables tied by a learnable Gumbel-Softmax prior, separating connectivity from strength to recover anatomically plausible interactions in neural spike data.
Problem
Existing HMM-GLMs infer time-varying functional interactions between neurons without constraints from the anatomical connectome, making the inferred interactions biologically implausible and hard to interpret.
Approach
Decompose each state's GLM weight into a discrete soft one-hot connection type (inhibitory/none/excitatory) and a positive strength; place a learnable Gumbel-Softmax prior over connection types shared across states, while strengths vary freely per state. A Gaussian-prior variant (GHG) is also proposed.
Key results
- On the simulated data, OHG achieved the best test LL (14.64), state accuracy (92.75%), weight error (10.99), and connection accuracy (73.90%) versus GLM, HG, GHG and L1 variants.
- On the PFC-6 dataset, OHG had the highest test log-likelihood for all S in {2,3,4,5} (e.g., -35.77 at 4 states vs. -37.22 for HG and -37.12 for GHG).
- On barrel cortex data, OHG had the highest test log-likelihood; a chi-squared test rejected the null of no state-contact relation in 73% of sessions for OHG and GHG vs 54% for HG.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use one-hot connection and strength decomposition with a shared connection prior instead of Gaussian HMM-GLM with L1 | HMM-GLM on the synthetic dataset · Synthetic dataset | connection accuracy: 41.08 -> 73.90 | Helped |
| Use one-hot connection and strength decomposition with a shared connection prior instead of Gaussian HMM-GLM with L1 | HMM-GLM on the synthetic dataset · Synthetic dataset | LL: 9.77 -> 14.64 | Helped |
| Use one-hot connection and strength decomposition with a shared connection prior instead of Gaussian HMM-GLM with L1 | HMM-GLM on the synthetic dataset · Synthetic dataset | weight error: 14.16 -> 10.99 | Helped |
| Use one-hot connection and strength decomposition with a shared connection prior instead of HMM Bern | HMM-GLM on the synthetic dataset · Synthetic dataset | state accuracy: 87.95 -> 92.75 | Helped |
| Use one-hot connection and strength decomposition with a shared connection prior instead of HMM Bern | HMM-GLM on the synthetic dataset · Synthetic dataset | connection prior accuracy: 40.70 -> 80.60 | Helped |
| Add an L1 penalty to HG (ablation) | HG on the synthetic dataset · Synthetic dataset | LL: -5.49 -> 9.14 | Helped |
| Add an L1 penalty to GHG (ablation) | GHG on the synthetic dataset · Synthetic dataset | weight error: 21.54 -> 14.16 | Helped |
| Add an L1 penalty to GHG (ablation) | GHG on the synthetic dataset · Synthetic dataset | connection accuracy: 42.53 -> 41.08 | Hurt |
| Use OHG instead of HMM Bern | HMM-GLM on the PFC-6 test set · PFC-6 test set, 2 states | LL: -36.89 -> -35.92 | Helped |
| Use OHG instead of HMM Bern | HMM-GLM on the PFC-6 test set · PFC-6 test set, 5 states | LL: -36.38 -> -35.71 | Helped |
| Add an L1 penalty to HG (ablation) | HG on the PFC-6 dataset · PFC-6 test set | LL | Helped |
| Add an L1 penalty to GHG (ablation) | GHG on the PFC-6 dataset · PFC-6 test set | connection discrimination | No clear effect |
Surprising findings
- Adding an L1 penalty to HG and GHG did not help discriminate weak from absent connections, whereas the one-hot decomposition did.
- Across the barrel cortex dataset, GHG showed fast-switching states (<0.1 s) while OHG produced stable states over 1 s.
Limitations
- Connection accuracy is sensitive to the thresholding technique used for non-OHG baselines, so comparisons depend on the chosen conversion (Eq. for connection from weights).
- Performance gains on real data are modest in some comparisons, and state interpretability for barrel cortex with S>2 is unclear (rarely occupied states).
- Simulated data uses categorical rather than Gumbel-Softmax sampling, introducing a mismatch with the model's generative process.
Experimental setup
Datasets: simulated 5-state 20-neuron spike data PFC-6 (CRCNS) prefrontal cortex recordings barrel cortex whisking recordings (27 sessions, 5 mice)
Benchmarks: simulated 5-state 20-neuron synthetic dataset PFC-6 dataset barrel cortex dataset
Metrics: test log-likelihood state accuracy weight error connection accuracy connection prior accuracy chi-squared test on state-contact association
Baselines: GLM HMM Corr HMM Bern HG HG-L1 GHG-L1
Builds on: HMM-GLM Gumbel-Softmax Baum-Welch algorithm
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