Differential Performance Debugging with Discriminant Regression Trees

Differential performance debugging is a technique to find performance problems. It applies in situations where the performance of a program is (unexpectedly) different for different classes of inputs. The task is to explain the differences in asymptotic performance among various input classes in terms of program internals. We propose a data-driven technique based on discriminant regression tree (DRT) learning problem where the goal is to discriminate among different classes of inputs. We propose a new algorithm for DRT learning that first clusters the data into functional clusters, capturing different asymptotic performance classes, and then invokes off-the-shelf decision tree learning algorithms to explain these clusters. We focus on linear functional clusters and adapt classical clustering algorithms (K-means and spectral) to produce them. For the K-means algorithm, we generalize the notion of the cluster centroid from a point to a linear function. We adapt spectral clustering by defining a novel kernel function to capture the notion of linear similarity between two data points. We evaluate our approach on benchmarks consisting of Java programs where we are interested in debugging performance. We show that our algorithm significantly outperforms other well-known regression tree learning algorithms in terms of running time and accuracy of classification.Comment: To Appear in AAAI 201

Kernel methods for detecting coherent structures in dynamical data

We illustrate relationships between classical kernel-based dimensionality reduction techniques and eigendecompositions of empirical estimates of reproducing kernel Hilbert space (RKHS) operators associated with dynamical systems. In particular, we show that kernel canonical correlation analysis (CCA) can be interpreted in terms of kernel transfer operators and that it can be obtained by optimizing the variational approach for Markov processes (VAMP) score. As a result, we show that coherent sets of particle trajectories can be computed by kernel CCA. We demonstrate the efficiency of this approach with several examples, namely the well-known Bickley jet, ocean drifter data, and a molecular dynamics problem with a time-dependent potential. Finally, we propose a straightforward generalization of dynamic mode decomposition (DMD) called coherent mode decomposition (CMD). Our results provide a generic machine learning approach to the computation of coherent sets with an objective score that can be used for cross-validation and the comparison of different methods