Research into the market graph is attracting increasing attention in stock market analysis. One of the important problems connected with the market graph is its identification from observations. The standard way of identifying the market graph is to use a simple procedure based on statistical estimations of Pearson correlations between pairs of stocks. Recently a new class of statistical procedures for market graph identification was introduced and the optimality of these procedures in the Pearson correlation Gaussian network was proved. However, the procedures obtained have a high reliability only for Gaussian multivariate distributions of stock attributes. One of the ways to correct this problem is to consider different networks generated by different measures of pairwise similarity of stocks. A new and promising model in this context is the sign similarity network. In this paper the market graph identification problem in the sign similarity network is reviewed. A new class of statistical procedures for the market graph identification is introduced and the optimality of these procedures is proved. Numerical experiments reveal an essential difference in the quality between optimal procedures in sign similarity and Pearson correlation networks. In particular, it is observed that the quality of the optimal identification procedure in the sign similarity network is not sensitive to the assumptions on the distribution of stock attributes.
This book constitutes extended, revised and selected papers from the 7th International Conference on Optimization Problems and Their Applications, OPTA 2018, held in Omsk, Russia in July 2018. The 27 papers presented in this volume were carefully reviewed and selected from a total of 73 submissions. The papers are listed in thematic sections, namely location problems, scheduling and routing problems, optimization problems in data analysis, mathematical programming, game theory and economical applications, applied optimization problems and metaheuristics.
The paper deals with unconstrained face recognition task for the small sample size problem based on computation of distances between high-dimensional off-the-shelf features extracted by deep convolution neural network. We present the novel statistical recognition method, which maximizes the likelihood (joint probabilistic density) of the distances to all reference images from the gallery set. This likelihood is estimated with the known asymptotically normal distribution of the Kullback–Leibler discrimination between nonnegative features. Our approach penalizes the individuals if their feature vectors do not behave like the features of observed image in the space of dissimilarities of the gallery images. We provide the experimental study with the LFW (Labeled Faces in the Wild), YTF (YouTube Faces) and IJB-A (IARPA Janus Benchmark A) datasets and the state-of-the-art deep learning-based feature extractors (VGG-Face, VGGFace2, ResFace-101, CenterFace and Light CNN). It is demonstrated, that the proposed approach can be applied with traditional distances in order to increase accuracy in 0.3–5.5% when compared to known methods, especially if the training and testing images are significantly different.