As methods for recording neural data advance rapidly in both volume and speed, neurophysiologists face increasing challenges in developing innovative techniques to assess and sort incoming spike signals (neuron firing rates) and inferring relationships between neural activities across different brain regions. We seek to create and utilize a method for extracting shared and independent latent features that accurately represent interpretable neural population dynamics across distinct brain regions.
The model we wish to construct builds on four main core components that serve as the foundation, allowing it to operate as we desire it to. These four components are: the Factor Analysis (FA) framework, the Auto-Encoding Variational Bayes (AEVB) framework, Probabilistic Canonical Correlation Analysis (pCCA), and Gaussian Processes (GPs). These components will be the key pieces used to build our two-step model pipeline that we will be inputting our data into: variational Latent Gaussian Process model (vLGP) and pCCA model. By using these core principles, our latent variable model will be able to extend the principles of factor analysis to extract latent representations within neural data to provide more interpretable firing rate dynamics than other current methods.
Model Hierarchy Pipeline
IBL Data➞vLGP➞pCCA
IBL Data
Using data collected by the International Brain Laboratory, we aim to analyze the latent behaviors of multiple regions of the brain in mice during standardized experiments. In these experiments, mice, with up to two probes recording 384 channels inserted into their brains, undergo a decision-making task where they are shown a stimulus of several different contrast strengths and is to move a wheel to center the stimulus on a screen. The IBL database contains large amounts of neural data (about 621,733 neurons) collected from 699 insertions of Neuropixel probes using 139 different mice over many experiment trials. These experiments give insight into regions and times in the brain that show sensitivity to stimulus, movement, reward, vision, and decision making.
Fig.1 - The mouse performing the standardized experiment. The mice have up to two Neuropixel probes recording 384 channels inserted into their brains while completing this task.Fig.2 - The experiment timeline from start to finish using a behavioral control system, a visual stimulus system, and audio signals for feedback tones.
We will be using spike train data that have been presorted into the groups that present themselves as the sources of the voltage changes. These clusters are sometimes hard to identify as a single neuron, a cluster of neurons, or perhaps a mixture of noise from neighboring sources, so labels have been assigned (1 being a good cluster, 0 being bad/unclear) to each cluster recorded in a session. The spike trains from good clusters will be the main focus of our work in finding representative latent variables.
Fig.3 - the sequence from capturing raw neural signals, performing high-pass filtering to refine the data, utilizing a clustering algorithm to analyze the signals, and finally sorting the spikes.
We seek to test firstMove, stimOn (and its contrast strength), and feedbackType. These represent the first movement of the mouse in each trial, the moment the stimulus appears on the screen, the strength of the contrast of the stimulus, and the reward/punishment the mouse receives after they make a decision, respectively.
Fig.4 - Peristimulus time histogram (PSTH) showing correct/incorrect and left/right firing rate averages over an entire session for a single cluster.Fig.5 - A bar graph showing correct/incorrect firing rate based on contrast strength averages over an entire session for a single cluster.
For each of these events, we performed a permutation test for each time interval and, using the False Discovery Rate to control our rate of Type I errors across trials, filtered for clusters with at least 5 statistically significant (alpha level = 0.005) time bins. Additionally, we tested each clusters correct/incorrect and left/right sensitivity by contrast strength levels. Through this exploration, we were able to select two of the most sensitive brain regions to pass through our model pipeline.
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Variational Latent Gaussian Process (vLGP) Model
The first model our data will be put through is a variational Latent Gaussian Process (vLGP) model, which is primarily used in neuroscience to decode neural data into a more interpretable lower-dimensional latent space governed by Gaussian Processes. The first model our data will be put through is a variational Latent Gaussian Process(vLGP) model, which is primarily used in neuroscience to decode neural data into a more interpretable lower-dimensional latent space governed by Gaussian Processes. vLGP assumes that the activity of a neuron at a particularly chosen time is drawn from the poisson distribution which in return causes the prior and posterior to be non-conjugate. Because of this, we would need to predict the posterior value of the latent process. To do so, we leverage variational inference to minimize the difference between the predicted posterior and the real posterior. Through variational inference, we maximize the ELBo which in turn minimizes the difference between the predicted and real posterior.
This model uses necessary imports from essential libraries such as NumPy, SciPy, Matplotlib, and the vLGP-specific library developed by Yuan Zhao and Il Memming Park to handle computations and visualizations.
Probabilistic Canonical Correlation Analysis (pCCA) Model
The next and final step of our pipeline involves a probabilistic Canonical Correlation Analysis (pCCA) model. The primary goal of pCCA is to find pairs of linear transformations that reveal correlation in the latent space between two separate sets of data. This assumes the two datasets have a shared latent space as well as their own individual latent spaces. In the field of neuroscience, pCCA is typically used to model latent variables that explain the variability between two or more modalities of data, which helps to understand complex neural dynamics.
After the IBL data is collected and cleaned, it is first put through the vLGP model to smoothen and move the data to a lower-dimensional latent space. Then, the vLGP model's output is used as the input to the pCCA model in order to conduct the analysis. With the pCCA step complete, this model can identify latent neural representations, explaining behaviors and neural dynamics across different regions of the brain.
Results
Our results from fitting the vLGP model with good clusters from the most dense region, (SCdg, where the highest quantity of clusters sensitive to the stimulus appearing were found), resulted in similar patterns for both left and right-positioned stimulus trials but slightly different positions. We can see that the pattern is similar across the first movement event in our second region SCiw. The shape is different in each region, but in both cases there is some uniqueness to the left and right trials where they encompass different ranges in the latent space. This could be a result of the fact that this is subsections of a larger brain region, poor spike variability, or perhaps the region lacks the capacity to differentiate left versus right as effectively as others.
Superior Colliculus Intermediate White Layer (SCIW): Contains fiber tracts that connect various layers within the superior colliculus and link it with other brain regions. While not directly processing sensory inputs, it facilitates the transmission of motor commands that underlie orienting responses and visually guided actions.
Fig.8 - SCIW latent variables plot Superior Colliculus Deep Grey Layer (SCDG): Involved in triggering complex motor responses, particularly those related to defensive or escape behaviors. Contributes to the coordination of multisensory inputs into appropriate motor outputs, such as rapid turning or withdrawal movements in response to threats
Fig.9 - SCDG latent variables plot
Conclusions
To assess the performance of our model, we decided to compute the Root Mean Squared Error (RMSE) and the R-squared coefficient. RMSE measures the average difference between predicted values and actual values. On the other hand, R-squared measures the proportion of variance explained by the latent variables in the PCCA model, or simply put, signifies how well the data fits the model.
Fig.10 - Root Mean Squared Error (RMSE) and R-squared
Our findings showcase strong, rapid improvements in performance when utilizing 1 to 3 latent variables, but diminishing returns in improvement when using more than 3 latent variables. This suggests stronger fitting to the model as more latent variables are employed with the biggest jump in performance when using 3 latent variables.
Our model offers potential for advancing our means of analysis on neural data by providing better representations that keep pace with the constantly evolving data collection methods.
