Neural Information Processing Systems http://nips.cc/

Kernel machines such as kernel SVM and kernel ridge regression usually construct high quality models; however, their use in real-world applications remains limited due to the high prediction cost.

Given an n -vertex weighted tree with structural diameter S and a subset of m vertices, we present a technique to compute a corresponding m \times m Gram matrix of the pseudoinverse of the graph Laplacian in O(n m 2 m S) time. We discuss the application of this technique to fast label prediction on a generic graph. We approximate the graph with a spanning tree and then we predict with the kernel perceptron. We address the approximation of the graph with either a minimum spanning tree or a shortest path tree. The fast computation of the pseudoinverse enables us to address prediction problems on large graphs.

Given an $n$-vertex weighted tree with structural diameter $S$ and a subset of $m$ vertices, we present a technique to compute a corresponding $m \times m$ Gram matrix of the pseudoinverse of the graph Laplacian in $O(n m 2 m S)$ time. We discuss the application of this technique to fast label prediction on a generic graph. We approximate the graph with a spanning tree and then we predict with the kernel perceptron. We address the approximation of the graph with either a minimum spanning tree or a shortest path tree. The fast computation of the pseudoinverse enables us to address prediction problems on large graphs.

Kernel machines such as kernel SVM and kernel ridge regression usually construct high quality models; however, their use in real-world applications remains limited due to the high prediction cost. First, we show that by adding "pseudo landmark points" to the classical Nystr om kernel approximation in an elegant way, we can significantly reduce the prediction error without much additional prediction cost. Second, we provide a new theoretical analysis on bounding the error of the solution computed by using Nystr om kernel approximation method, and show that the error is related to the weighted kmeans objective function where the weights are given by the model computed from the original kernel. This theoretical insight suggests a new landmark point selection technique for the situation where we have knowledge of the original model. Based on these two insights, we provide a divide-and-conquer framework for improving the prediction speed.

Discovering the underlying physical behavior of complex systems is a crucial, but less well-understood topic in many engineering disciplines. This study proposes a finite-difference inspired convolutional neural network framework to learn hidden partial differential equations from given data and iteratively estimate future dynamical behavior. The methodology designs the filter sizes such that they mimic the finite difference between the neighboring points. By learning the governing equation, the network predicts the future evolution of the solution by using only a few trainable parameters. In this paper, we provide numerical results to compare the efficiency of the second-order Trust-Region Conjugate Gradient (TRCG) method with the first-order ADAM optimizer.