Hellinger distance based probability distribution approach to performance monitoring of nonlinear control systems

Control performance monitoring has attracted great attention in both academia and industry over the past two decades. However, most research efforts have been devoted to the performance monitoring of linear control systems, without considering the pervasive nonlinearities(e.g. valve stiction) present in most industrial control systems. In this work, a novel probability distribution distance based index is proposed to monitor the performance of non-linear control systems. The proposed method uses Hellinger distance to evaluate change of control system performance. Several simulation examples are given to illustrate the effectiveness of the proposed method.

One-against-all-based Hellinger distance decision tree for multiclass imbalanced learning

Since traditional machine learning methods are sensitive to skewed distribution and do not consider the characteristics in multiclass imbalance problems,the skewed distribution of multiclass data poses a major challenge to machine learning algorithms.To tackle such issues,we propose a new splitting criterion of the decision tree based on the one-against-all-based Hellinger distance(OAHD).Two crucial elements are included in OAHD.First,the one-against-all scheme is integrated into the process of computing the Hellinger distance in OAHD,thereby extending the Hellinger distance decision tree to cope with the multiclass imbalance problem.Second,for the multiclass imbalance problem,the distribution and the number of distinct classes are taken into account,and a modified Gini index is designed.Moreover,we give theoretical proofs for the properties of OAHD,including skew insensitivity and the ability to seek a purer node in the decision tree.Finally,we collect 20 public real-world imbalanced data sets from the Knowledge Extraction based on Evolutionary Learning(KEEL)repository and the University of California,Irvine(UCI)repository.Experimental and statistical results show that OAHD significantly improves the performance compared with the five other well-known decision trees in terms of Precision,F-measure,and multiclass area under the receiver operating characteristic curve(MAUC).Moreover,through statistical analysis,the Friedman and Nemenyi tests are used to prove the advantage of OAHD over the five other decision trees.

Derivation of quantum Chernoff metric with perturbation expansion method

We investigate a measure of distinguishability defined by the quantum Chernoff bound, which naturally induces the quantum Chernoff metric over a manifold of quantum states. Based on a quantum statistical model, we alternatively derive this metric by means of perturbation expansion. Moreover, we show that the quantum Chernoff metric coincides with the infinitesimal form of the quantum Hellinger distance, and reduces to the variant version of the quantum Fisher information for the single-parameter case. We also give the exact form of the quantum Chernoff metric for a qubit system containing a single parameter.

On the rate of convergence of the maximum likelihood estimator of a k-monotone density

Bounds for the bracketing entropy of the classes of bounded k-monotone functions on [0,A] are obtained under both the Hellinger distance and the Lp(Q) distance,where 1 p < ∞ and Q is a probability measure on [0,A].The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a k-monotone density.