将可解释的稀疏回归嵌入神经网络，解析细胞成像中的时序动态。
Embedding interpretable $\ell_1$-regression into neural networks for uncovering temporal structure in cell imaging
- 用带ℓ₁正则的向量自回归模型嵌入卷积自编码器，实现时序结构建模。
- 在双光子钙成像数据上，成功提取出稀疏自回归动态，关键因子可定位。
- 适合关注生物信号可解释性、需定位驱动区域的研究者使用。
尽管人工神经网络在无监督学习非稀疏结构方面表现优异，但经典统计回归技术通过ℓ₁正则化提供更强的可解释性，尤其适用于识别驱动观测动态的关键因素。本文研究如何最优结合两类方法，以两光子钙成像数据为例，目标是从中提取稀疏自回归动态。提出将向量自回归（VAR）模型作为可解释回归技术嵌入卷积自编码器中，实现维度压缩以支持可处理的时序建模。通过跳跃连接独立处理非稀疏静态空间信息，选择性将稀疏结构输入ℓ₁正则化的VAR。利用分段线性解路径的可微性实现ℓ₁参数估计。对比了未适配VAR模型的自编码器方法。嵌入的统计模型还支持对同一观测单元的时序序列进行比较检验。贡献图可视化驱动学习动态的空间区域。
原文摘要 · Abstract (English)
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.
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