  The regression of multiple inter-connected sequence data is a problem in
various disciplines. Formally, we name the regression problem of multiple
inter-connected data entities as the "dynamic network regression" in this
paper. Within the problem of stock forecasting or traffic speed prediction, we
need to consider both the trends of the entities and the relationships among
the entities. A majority of existing approaches can't capture that information
together. Some of the approaches are proposed to deal with the sequence data,
like LSTM. The others use the prior knowledge in a network to get a fixed graph
structure and do prediction on some unknown entities, like GCN. To overcome the
limitations in those methods, we propose a novel graph neural network, namely
Graph Neural Lasso (GNL), to deal with the dynamic network problem. GNL extends
the GDU (gated diffusive unit) as the base neuron to capture the information
behind the sequence. Rather than using a fixed graph structure, GNL can learn
the dynamic graph structure automatically. By adding the attention mechanism in
GNL, we can learn the dynamic relations among entities within each network
snapshot. Combining these two parts, GNL is able to model the dynamic network
problem well. Experimental results provided on two networked sequence datasets,
i.e., Nasdaq-100 and METR-LA, show that GNL can address the network regression
problem very well and is also very competitive among the existing approaches.
