1. Neural Decoding: Model and Algorithm for Evidence Accumulator Inference Thomas Desautels University College London Gatsby Computational Neuroscience Group Whitaker Enrichment Seminar, Budapest, 30 April 2015

2. Some (Engineering) Motivation: BrainGate (Hochberg et al., Nature, 2012) 30/4/15Thomas Desautels, Gatsby Unit2

3. Motivation Areas of the brain have task-related neuronal activity. o E.g.: hand location-related activity in motor and premotor areas. Patients with paralyzing conditions (SCI, ALS, etc.) could be aided by an interface which extracts information from the brain. o Brain – Computer Interface (BCI) Can test hypotheses about functions of specific brain areas 30/4/15Thomas Desautels, Gatsby Unit3

4. Neural Decoding A variety of signals have been examined: o penetrating electrodes, EEG, ECoG How can we make sense of these signals? Goal: Extract meaningful information from neural recordings 30/4/15Thomas Desautels, Gatsby Unit4

5. Neural Decoding II Procedure (Bayesian): o Create generative mathematical model of the neural activity Expressive enough to capture the important features of the data Links observed activity to latent variables (intent) we want to decode o Create a learning algorithm which can fit the model to an individual patient’s data Computational efficiency in learning (parameters) and inference (online / single trial trajectory estimation) Variants of Kalman filtering have often been applied in BCI (e.g., Hochberg 2012, Shenoy, Carmena) o This works best with many channels / neurons What if we don’t have enough data for that? 30/4/15Thomas Desautels, Gatsby Unit5

6. Structure If you have less data, you may be able to use a more structured model In my problem, we know a lot about: o the task the being performed, and o how this problem should be solved Other problems may also fall into this low-data, known-structure regime 30/4/15Thomas Desautels, Gatsby Unit6

7. Poisson Clicks: Evidence Accumulation From Brunton et al., Science, 2013 (C. Brody, Princeton) 30/4/15Thomas Desautels, Gatsby Unit7

8. Model Correctly solve task: evidence accumulator a(t) o a(t c + ) = a(t c - ) + s c, where s c = +1 for right, -1 for left Animal’s performance is suboptimal o Model the suboptimalities in a(t) and its inputs 30/4/15Thomas Desautels, Gatsby Unit8 Brunton et al., 2013

9. Goals Have recordings from PPC, FOF: o Neural spiking data y[t] Estimate the trial-by- trial trajectories a(t) of the evidence Learn the model parameters GP, GLM which describe each animal’s neural data 30/4/15Thomas Desautels, Gatsby Unit9

10. Algorithm 30/4/15Thomas Desautels, Gatsby Unit10

11. Results: Trajectory Estimates Given good parameters, get reasonable decoded trajectories 30/4/15Thomas Desautels, Gatsby Unit11

12. Results: Learned Parameters Estimating GP is much harder, and the subject of ongoing verification efforts 30/4/15Thomas Desautels, Gatsby Unit12

13. Ongoing Work Continue to verify the performance of the algorithm o Parameter identification: Compare with other methods o Expand set of latents to include common noise processes Examine alternative algorithms o Variations on the existing Laplace EM algorithm o Variational EM o Expectation Propagation (EP) 30/4/15Thomas Desautels, Gatsby Unit13

14. Dynamics 30/4/15Thomas Desautels, Gatsby Unit14

15. Observation Model 30/4/15Thomas Desautels, Gatsby Unit15