Graph-based semi-supervised learning methods combine the graph structure and labeled data to classify unlabeled data. In this work, we study the effect of a noisy oracle on classification. In particular, we derive the maximum a posteriori (MAP) estimator for clustering a degree corrected stochastic block model when a noisy oracle reveals a fraction of the labels. We then propose an algorithm derived from a continuous relaxation of the MAP, and we establish its consistency. Numerical experiments show that our approach achieves promising performance on synthetic and real data sets, even in the case of very noisy labeled data.

We consider the problem of parameter estimation for the superposition of square-root diffusions. We first derive the explicit formulas for the moments and auto-covariances based on which we develop our moment estimators. We then establish a central limit theorem for the estimators with the explicit formulas for the asymptotic covariance matrix. Finally, we conduct numerical experiments to validate our method.

This paper investigates the precise large deviations of the net loss process in a two-dimensional risk model with consistently varying tails and dependence structures, and gives some asymptotic formulas which hold uniformly for all x varying in t-intervals. The study is among the initial efforts to analyze potential risk via large deviation results for the net loss process of the two-dimensional risk model, and can provide a novel insight to assess the operation risk in a long run by fully considering the premium income factors of the insurance company.

In this paper, we define weighted failure rate and their means from the stand point of an application. We begin by emphasizing that the formation of n independent component series system having weighted failure rates with sum of weight functions being unity is same as a mixture of n distributions. We derive some parametric and non-parametric characterization results. We discuss on the form invariance property of baseline failure rate for a specific choice of weight function. Some bounds on means of aging functions are obtained. Here, we establish that weighted increasing failure rate average (IFRA) class is not closed under formation of coherent systems unlike the IFRA class. An interesting application of the present work is credited to the fact that the quantile version of means of failure rate is obtained as a special case of weighted means of failure rate.

In this paper, a new multivariate counting process model (called Multivariate Poisson Generalized Gamma Process) is developed and its main properties are studied. Some basic stochastic properties of the number of events in the new multivariate counting process are initially derived. It is shown that this new multivariate counting process model includes the multivariate generalized Pólya process as a special case. The dependence structure of the multivariate counting process model is discussed. Some results on multivariate stochastic comparisons are also obtained.

Motivated by the impact of emerging technologies on (toll) parks, this paper studies a problem of customers’ strategic behavior, social optimization, and revenue maximization for infinite-server queues. More specifically, we assume that a customer’s utility consists of a positive reward for receiving service minus a cost caused by the other customers in the system. In the observable setting, we show the existence, uniqueness, and expressions of the individual equilibrium threshold, the socially optimal threshold, and the optimal revenue threshold, respectively. Then, we prove that the optimal revenue threshold is smaller than the socially optimal threshold, which is smaller than the individual one. Furthermore, we also extend the cost functions to any finite polynomial function with nonnegative coefficients. In the unobservable setting, we derive the joining probabilities of individual equilibrium and optimal revenue. Finally, using numerical experiments, we complement our results and compare the social welfare and the revenue under these two information levels.

In this paper, we use an information theoretic approach called cumulative residual extropy (CRJ) to compare mixed used systems. We establish mixture representations for the CRJ of mixed used systems and then explore the measure and comparison results among these systems. We compare the mixed used systems based on stochastic orders and stochastically ordered conditional coefficients vectors. Additionally, we derive bounds for the CRJ of mixed used systems with independent and identically distributed components. We also propose the Jensen-cumulative residual extropy (JCRJ) divergence to calculate the complexity of systems. To demonstrate the utility of these results, we calculate and compare the CRJ and JCRJ divergence of mixed used systems in the Exponential model. Furthermore, we determine the optimal system configuration based on signature under a criterion function derived from JCRJ in the exponential model.