Optimal Control of Brownian Inventory Models with Convex Inventory Cost: Discounted Cost Case

We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be negative when there is a backlog. At any time, the inventory level can be adjusted by a positive or negative amount, which incurs a fixed positive cost and a proportional cost. The challenge is to find an adjustment policy that balances the inventory cost and adjustment cost to minimize the expected total discounted cost. We provide a tutorial on using a three-step lower-bound approach to solving the optimal control problem under a discounted cost criterion. In addition, we prove that a four-parameter control band policy is optimal among all feasible policies. A key step is the constructive proof of the existence of a unique solution to the free boundary problem. The proof leads naturally to an algorithm to compute the four parameters of the optimal control band policy

Optimal Bayes Classifiers for Functional Data and Density Ratios

Bayes classifiers for functional data pose a challenge. This is because probability density functions do not exist for functional data. As a consequence, the classical Bayes classifier using density quotients needs to be modified. We propose to use density ratios of projections on a sequence of eigenfunctions that are common to the groups to be classified. The density ratios can then be factored into density ratios of individual functional principal components whence the classification problem is reduced to a sequence of nonparametric one-dimensional density estimates. This is an extension to functional data of some of the very earliest nonparametric Bayes classifiers that were based on simple density ratios in the one-dimensional case. By means of the factorization of the density quotients the curse of dimensionality that would otherwise severely affect Bayes classifiers for functional data can be avoided. We demonstrate that in the case of Gaussian functional data, the proposed functional Bayes classifier reduces to a functional version of the classical quadratic discriminant. A study of the asymptotic behavior of the proposed classifiers in the large sample limit shows that under certain conditions the misclassification rate converges to zero, a phenomenon that has been referred to as "perfect classification". The proposed classifiers also perform favorably in finite sample applications, as we demonstrate in comparisons with other functional classifiers in simulations and various data applications, including wine spectral data, functional magnetic resonance imaging (fMRI) data for attention deficit hyperactivity disorder (ADHD) patients, and yeast gene expression data

Online Deception Detection Refueled by Real World Data Collection

The lack of large realistic datasets presents a bottleneck in online deception detection studies. In this paper, we apply a data collection method based on social network analysis to quickly identify high-quality deceptive and truthful online reviews from Amazon. The dataset contains more than 10,000 deceptive reviews and is diverse in product domains and reviewers. Using this dataset, we explore effective general features for online deception detection that perform well across domains. We demonstrate that with generalized features - advertising speak and writing complexity scores - deception detection performance can be further improved by adding additional deceptive reviews from assorted domains in training. Finally, reviewer level evaluation gives an interesting insight into different deceptive reviewers' writing styles.Comment: 10 pages, Accepted to Recent Advances in Natural Language Processing (RANLP) 201