Fig 1.
Schematic diagram of the Orthogonal Stochastic Linear Mixing Model (OSLMM).
(A) illustrates data generated by the model with a three-dimensional latent processes. Note that is a positive diagonal matrix with log([S1/2(t)]qq) = hq(t). (B) illustration of the graphical model of OSLMM.
Fig 2.
Training OSLMM on neural data scales well with the number of latent functions.
The running time per iteration with different number of latent functions for the Stochastic Linear Mixing Model (SLMM), the Orthogonal Stochatic Linear Mixing Model (OSLMM), and the Stochastic Gaussian Process Regression Network (SGPRN).
Fig 3.
OSLMM provides superior recovery performance on noisy observations of the Lorenz system.
The difference of root mean square error (ΔRMSE) of latent trajectories reconstructed from GPFA and OSLMM in three different scenarios. (A) Three data generation processes with different time scales and data size N = 200. (B) Three medium time-scale data generating processes in terms of various number of time steps, N = 100, 200, 500. (C) Three data generating processes in terms of different levels of noise on the subspace specified by the standard deviation of noise σ. Data are presented as mean and standard deviation. *: 0.01 < p ≤ 0.05, **: 0.001 < p ≤ 0.01, Wilcoxon signed-rank test.
Fig 4.
OSLMM latent spaces provide superior prediction performance for neural recordings from auditory cortex.
(A) Schematic location of μECoG grid on rat brain over auditory cortex. (B) Photomicrograph of the 128-channel micro-electrocorticography array on the rat auditory cortex. The blue circle refers to one of 128 channels. (C) Heat-map of z-scored high-gamma responses from the electrode circled with blue in (B) for each frequency-attenuation pair of the presented pure-tone pip stimulus. Dashed black line demarcates the best-frequency of this electrode. (D) Functional boxplot of the z-scored activity across electrodes for a single stimuli; black lines refer to the median and light/dark grey shaded regions refer to non-outlying and central 50% regions. The stimulus takes frequency 7627 Hz and attenuation -10 dB and it starts from 0 ms and ends at 50 ms, which would affect some of electrodes in terms of Z-score displayed in this panel. (E) Prediction error on the stimuli-wise analysis for four stimuli. (F) Prediction error on the global analysis across all stimuli; each point is an electrode (p = 1.16 × 10−38, Wilcoxon signed-rank test, N = 128 channels). Panel B is reproduced from [28].
Fig 5.
OSLMM latent spaces extracted from auditory cortex population activity are structured by external stimuli.
(A, C) Trial-averaged latent neural trajectories for all attenuations with a fixed frequency 7627 Hz for OSLMM and GFPA respectively; (B, D) Trial-averaged latent neural trajectories for all frequencies with a fixed attenuation (−10dB) for OSLMM and GPFA respectively. (E) Stimulus attenuation vs. the amplitude of the latent trajectory. (F) Stimulus frequency vs. the angle of latent trajectory. Lines in (E,F) are a moving average.
Fig 6.
OSLMM’s latent spaces extracted from motor cortex are predictive of behavior.
(A) (top) Schematic location of motor cortex recordings on non-human primate brain; (middle) schematic of maze reaching task; (bottom) raster plot of extracted neural spike data from monkeys’ motor cortex (each tick mark corresponds to detected spike time). (B) The average speed profiles for 108 conditions. Each profile is colored according to the average reach angle. (C)Functional boxplots of the smoothed spike rates for each condition where black lines refer to the median curve and light/dark grey shaded areas refer to non-outlying region and 50% central region. It displays the general the spike rates pattern across all conditions. Panel A is reproduced from [10, 34].
Fig 7.
OSLMM latent spaces extracted from motor cortex population activity are structured by kinematics.
(A,B) Trial-averaged latent trajectories for all reach conditions colored by reach angle for OSLMM (A) and GPFA (B). (C,D) Scatter plot of cosine distance between reach angles vs. the distance between latent trajectories for OSLMM (C) and GPFA (D). Each point is colored (gray-scale) according to the speed (at 350ms) of the reach. (E,F) Trial-averaged latent trajectories but for all reach conditions colored (grey scale) by the speed at 350ms for OSLMM (E) and GPFA (F). (G,H) Scatter plot of difference in speeds vs. the rate of change of latent trajectories for OSLMM (G) and GPFA (H). Each point is colored according to the average angle of the reach.
Fig 8.
OSLMM latent spaces of motor cortex dynamics are structured by reach angle.
(A, C) First three jPCA dimensions from the OSLMM extracted latent space; (B, D)First three jPCA dimensions from the GPFA extracted latent space. We encoded reach angle as color in (A,B) and reach speed into grey scale in (C, D).