  The architectures of deep neural networks (DNN) rely heavily on the
underlying grid structure of variables, for instance, the lattice of pixels in
an image. For general high dimensional data with variables not associated with
a grid, the multi-layer perceptron and deep belief network are often used.
However, it is frequently observed that those networks do not perform
competitively and they are not helpful for identifying important variables. In
this paper, we propose a framework that imposes on blocks of variables a chain
structure obtained by step-wise greedy search so that the DNN architecture can
leverage the constructed grid. We call this new neural network Deep
Variable-Block Chain (DVC). Because the variable blocks are used for
classification in a sequential manner, we further develop the capacity of
selecting variables adaptively according to a number of regions trained by a
decision tree. Our experiments show that DVC outperforms other generic DNNs and
other strong classifiers. Moreover, DVC can achieve high accuracy at much
reduced dimensionality and sometimes reveals drastically different sets of
relevant variables for different regions.
