Ziyang Jiang

Ziyang Jiang, Yiling Liu, Michael H. Klein et al.

Causal mediation analysis (CMA) is a powerful method to dissect the total effect of a treatment into direct and mediated effects within the potential outcome framework. This is important in many scientific applications to identify the underlying mechanisms of a treatment effect. However, in many scientific applications the mediator is unobserved, but there may exist related measurements. For example, we may want to identify how changes in brain activity or structure mediate an antidepressant's effect on behavior, but we may only have access to electrophysiological or imaging brain measurements. To date, most CMA methods assume that the mediator is one-dimensional and observable, which oversimplifies such real-world scenarios. To overcome this limitation, we introduce a CMA framework that can handle complex and indirectly observed mediators based on the identifiable variational autoencoder (iVAE) architecture. We prove that the true joint distribution over observed and latent variables is identifiable with the proposed method. Additionally, our framework captures a disentangled representation of the indirectly observed mediator and yields accurate estimation of the direct and mediated effects in synthetic and semi-synthetic experiments, providing evidence of its potential utility in real-world applications.

Ziyang Jiang, Tongshu Zheng, Yiling Liu et al.

It is challenging to guide neural network (NN) learning with prior knowledge. In contrast, many known properties, such as spatial smoothness or seasonality, are straightforward to model by choosing an appropriate kernel in a Gaussian process (GP). Many deep learning applications could be enhanced by modeling such known properties. For example, convolutional neural networks (CNNs) are frequently used in remote sensing, which is subject to strong seasonal effects. We propose to blend the strengths of deep learning and the clear modeling capabilities of GPs by using a composite kernel that combines a kernel implicitly defined by a neural network with a second kernel function chosen to model known properties (e.g., seasonality). We implement this idea by combining a deep network and an efficient mapping based on the Nystrom approximation, which we call Implicit Composite Kernel (ICK). We then adopt a sample-then-optimize approach to approximate the full GP posterior distribution. We demonstrate that ICK has superior performance and flexibility on both synthetic and real-world data sets. We believe that ICK framework can be used to include prior information into neural networks in many applications.