MM-DAG: Multi-task DAG Learning for Multi-modal Data -- with Application
  for Traffic Congestion Analysis
Tian Lan Ziyue Li Zhishuai Li Lei Bai Man Li Fugee Tsung Wolfgang Ketter Rui Zhao Chen Zhang
This paper proposes to learn Multi-task, Multi-modal Direct Acyclic Graphs
(MM-DAGs), which are commonly observed in complex systems, e.g., traffic,
manufacturing, and weather systems, whose variables are multi-modal with
scalars, vectors, and functions. This paper takes the traffic congestion
analysis as a concrete case, where a traffic intersection is usually regarded
as a DAG. In a road network of multiple intersections, different intersections
can only have some overlapping and distinct variables observed. For example, a
signalized intersection has traffic light-related variables, whereas
unsignalized ones do not. This encourages the multi-task design: with each DAG
as a task, the MM-DAG tries to learn the multiple DAGs jointly so that their
consensus and consistency are maximized. To this end, we innovatively propose a
multi-modal regression for linear causal relationship description of different
variables. Then we develop a novel Causality Difference (CD) measure and its
differentiable approximator. Compared with existing SOTA measures, CD can
penalize the causal structural difference among DAGs with distinct nodes and
can better consider the uncertainty of causal orders. We rigidly prove our
design's topological interpretation and consistency properties. We conduct
thorough simulations and one case study to show the effectiveness of our
MM-DAG. The code is available under https://github.com/Lantian72/MM-DAG