Application of Bagged Copula-GP: Confirming Neural Dependency on Pupil Dilation
Authors: Maximilian Walden
TMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Here, we validated usage of Copula-GP together with Gaussian Process Factor Analysis (GPFA) to investigate the information interaction between neuronal processes within the visual cortex of live mice and pupil dilation. We additionally extended Copula-GP with a bagging framework, allowing for the aggregation of model estimations and allowing for more accurate estimation accuracy and representation of dependency shape. We validated our bagging algorithm on simulated data sampled from known distributions, and utilized bagged Copula-GP with GPFA on said neuronal data to find results in agreement with baseline Copula-GP but with more stability. |
| Researcher Affiliation | Academia | Maximilian Walden EMAIL University of Edinburgh |
| Pseudocode | Yes | Algorithm 1 Implemented bivariate mixture copula bagging algorithm. Here, mixture copulas consist of mixed copula variants variants, their corresponding dependency parameter values Θ (for each of the m inputs), and their corresponding mixing parameters mix. We assume weights have been defined over all m input points. |
| Open Source Code | Yes | The code repository for work shown can be found at: https://github.com/mwalden00/HonProj. |
| Open Datasets | Yes | The main data set we wished to explore is the Visual Coding: Neuropixels dataset, a publicly available dataset containing spike-signals recorded from the visual cortex of live mice at single neuron spatial resolution utilizing novel Neuropixel probes, a high-fidelity and -resolution brain probe developed in 2021 (Steinmetz et al., 2021). Due to the volume of in vivo data recorded, as well as the quality metrics included in the data, it is an invaluable tool for analysis of underlying processes within the visual cortex. All technical claims surrounding the data in question is sourced from the technical white paper (see D). For more information surrounding data production and specificities not covered in the body of this paper, i.e specifics on how probes were used and how visual stimuli were produced, one should see the technical white paper. The technical white-paper for the dataset is also available at: https://brainmapportal-live-4cc80a57cd6e400d854-f7fdcae.divio-media.net/filer_public/80/75/8075a100-ca64-429a-b39a-569121b612b2/neuropixels_visual_coding_-_white_paper_v10.pdf. |
| Dataset Splits | Yes | To generate the data, we drew 10000 samples from the true copula, splitting samples and their corresponding parameterizations into train and test sets (80:20 split). Validation tests 1 and 2 utilized parameterization on a normally distributed variable x N(0.5, 0.2), restricted to the interval [0, 1]. Validation test 3 utilized a parameterization in a time-based variable t scaling linearly from 0 to 1. Copula training and model selection utilized train set samples, with accuracy validation utilizing metrics described on test set samples. All validations utilized the heuristic algorithm for individual estimator model selection, and for bagged estimations 4 estimators underwent individual training and model selection routines. We include random seed, module version, and hardware information for test reproducability purposes in the appendix (see G). |
| Hardware Specification | Yes | Experiments were ran on a machine utilizing 128 GB of system memory, an Intel Xeon Gold 6142 processor, an NVidia 2080, and an NVidia 2080Ti. Plots were made on a laptop with 8 GB of system memory and an Apple M2 processor. |
| Software Dependencies | Yes | The python version utilized for all computations and plots made was 3.10.6; Elephant 1.0.0 and Copula-GP 0.0.5 were utilized for computations, and Matplotlib 3.6.1 and Seaborn 0.10.0 were utilized for plot production. |
| Experiment Setup | Yes | For all validation tests in this section, the task was to accurately replicate the true copula s parametric entropy and dependency shape, parameterized on some variable x. For validation, the weighted aggregation methods utilized were 1. Copulas weighted point-wise dynamically by BIC / AIC on input, 2. Copulas weighted statically by BIC / AIC on input, and 3. naive average of copulas. In addition, we also examine copula entropy point-wise root mean squared error (RMSE) of baseline and bagging methods. GPFA was fit on 100 consecutive spike trains during Drifting Gratings stimulus presentations, each of which have a uniform temporal length of 2s followed by a 1s interval during which no stimulus is presented. We fit the model for the entirety of the dataset with the dimensionality of the elbow of the log-likelihood plot (figure 9), reducing the original dimensionality of 178 down to a latent dimensionality of 13. After GPFA application, little interim processing is needed: we removed drift and concatenated trials as per the process described in section F.2 to produce semi-continuous data and mapped onto the domain (0, 1) via additional interim steps described in section F.2. We utilized Copula-GP to estimate C-vines over the concatenation of GPFA-treated trials, possessing 12 layers (78 copulas total) with parameterization in normalized pupil dilation (as per steps described in D), testing both baseline unbagged and bagged Copula-GP. For baseline, Copula-GP was fit over the full semi-continuous data of 80 trials. For bagged Copula-GP, 4 individual models were fit over 4 semi-continuous subsets of 20 trials each. For model ensembling, we utilized the BIC dynamically-weighted aggregation method. |