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Our goal is to recover time-delayed latent causal variables and identify their relations from measured temporal data. Estimating causally-related latent variables from observations is particularly challenging as the latent variables are not uniquely recoverable in the most general case. In this work, we consider both a nonparametric, nonstationary setting and a parametric setting for the latent processes and propose two provable conditions under which temporally causal latent processes can be identified from their nonlinear mixtures. We propose LEAP, a theoretically-grounded architecture that extends Variational Autoencoders (VAEs) by enforcing our conditions through proper constraints in causal process prior. Experimental results on various data sets demonstrate that temporally causal latent processes are reliably identified from observed variables under different dependency structures and that our approach considerably outperforms baselines that do not leverage history or nonstationarity information. This is one of the first works that successfully recover time-delayed latent processes from nonlinear mixtures without using sparsity or minimality assumptions.

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Several Drosophila receptor-linked protein tyrosine phosphatases (R-PTPs) are selectively expressed on axons of the developing embryonic central nervous system. The extracellular domains of these axonal R-PTPs are homologous to neural adhesion molecules. Thus, R-PTPs may directly couple cell recognition to signal transduction via control of tyrosine phosphorylation. To examine the function of these molecules during nervous system development, we wished to generate mutations in R-PTP genes. It was unclear whether a mutation in a single R-PTP gene would confer lethality, however, because the similarities in sequence and expression pattern between the axonal R-PTPs suggest that they may have partially redundant functions. To circumvent this problem, we developed a directed mutagenesis strategy based on local transposition of P elements, and used this approach to isolate a null mutation in the DPTP99A gene. This strategy, which we describe in detail here, should be applicable to any Drosophila gene within a lettered division of an appropriately marked P element. Flies lacking DPTP99A expression are viable and fertile, and we have been unable to detect any alterations in the embryonic nervous system of DPTP99A embryos using a variety of antibody markers.