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1. Proximal mediation analysis

   https://doi.org/10.1093/biomet/asad015  

   Dukes, Oliver; Shpitser, Ilya; Tchetgen Tchetgen, Eric J (March 2023, Biometrika)

   Summary A common concern when trying to draw causal inferences from observational data is that the measured covariates are insufficiently rich to account for all sources of confounding. In practice, many of the covariates may only be proxies of the latent confounding mechanism. Recent work has shown that in certain settings where the standard no-unmeasured-confounding assumption fails, proxy variables can be leveraged to identify causal effects. Results currently exist for the total causal effect of an intervention, but little consideration has been given to learning about the direct or indirect pathways of the effect through a mediator variable. In this work, we describe three separate proximal identification results for natural direct and indirect effects in the presence of unmeasured confounding. We then develop a semiparametric framework for inference on natural direct and indirect effects, which leads us to locally efficient, multiply robust estimators. 

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2. Resolvent and Proximal Compositions

   https://doi.org/10.1007/s11228-023-00678-z  

   Combettes, Patrick L. (September 2023, Set-Valued and Variational Analysis)
3. Maximally highly proximal flows

   https://doi.org/10.1017/etds.2020.40  

   ZUCKER, ANDY (May 2020, Ergodic Theory and Dynamical Systems)

   For G a Polish group, we consider G-flows which either contain a comeager orbit or have all orbits meager. We single out a class of flows, the maximally highly proximal (MHP) flows, for which this analysis is particularly nice. In the former case, we provide a complete structure theorem for flows containing comeager orbits, generalizing theorems of Melleray, Nguyen Van Thé, and Tsankov and of Ben Yaacov, Melleray, and Tsankov. In the latter, we show that any minimal MHP flow with all orbits meager has a metrizable factor with all orbits meager, thus ‘reflecting’ complicated dynamical behavior to metrizable flows. We then apply this to obtain a structure theorem for Polish groups whose universal minimal flow is distal. 

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4. Plant promoter-proximal pausing?

   https://doi.org/10.1038/s41477-021-00970-6  

   Morffy, Nicholas; Strader, Lucia C. (July 2021, Nature Plants)
5. Proximal Mapping for Deep Regularization

   Li, Mao; Ma, Yingyi; Zhang, Xinhua (January 2020, Advances in neural information processing systems)

   null (Ed.)

   Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most regularizers are specified in terms of hidden layer outputs, which are not themselves optimization variables. In contrast to prevalent methods that optimize them indirectly through model weights, we propose inserting proximal mapping as a new layer to the deep network, which directly and explicitly produces well regularized hidden layer outputs. The resulting technique is shown well connected to kernel warping and dropout, and novel algorithms were developed for robust temporal learning and multiview modeling, both outperforming state-of-the-art methods. 

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