Embedding interpretable $\ell_1$-regression into neural networks for uncovering temporal structure in cell imaging

TL;DR

This paper introduces a novel neural network architecture that embeds an interpretable $1$-regularized VAR model into an autoencoder to uncover sparse temporal structures in cell imaging data, enhancing interpretability and analysis.

Contribution

It proposes integrating a $1$-regularized VAR model into a convolutional autoencoder for interpretable, sparse temporal modeling in neural networks, enabling statistical testing and visualization.

Findings

Effective extraction of sparse autoregressive dynamics from calcium imaging data.

Enhanced interpretability through contribution maps and statistical testing.

Differentiable $1$-estimation within the neural network framework.

Abstract

While artificial neural networks excel in unsupervised learning of non-sparse structure, classical statistical regression techniques offer better interpretability, in particular when sparseness is enforced by $\ell_1$ regularization, enabling identification of which factors drive observed dynamics. We investigate how these two types of approaches can be optimally combined, exemplarily considering two-photon calcium imaging data where sparse autoregressive dynamics are to be extracted. We propose embedding a vector autoregressive (VAR) model as an interpretable regression technique into a convolutional autoencoder, which provides dimension reduction for tractable temporal modeling. A skip connection separately addresses non-sparse static spatial information, selectively channeling sparse structure into the $\ell_1$-regularized VAR. $\ell_1$-estimation of regression parameters is enabled by differentiating through the piecewise linear solution path. This is contrasted with approaches where the autoencoder does not adapt to the VAR model. Having an embedded statistical model also enables a testing approach for comparing temporal sequences from the same observational unit. Additionally, contribution maps visualize which spatial regions drive the learned dynamics.