We focus on minimizing nonconvex finite-sum functions that typically arise in machine learning problems. In an attempt to solve this problem, the adaptive cubic regularized Newton method has shown its strong global convergence guarantees and ability to escape from strict saddle points. This method uses a trust region-like scheme to determine if an iteration is successful or not, and updates only when it is successful.In this paper, we suggest an algorithm combining negative curvature with the adaptive cubic regularized Newton method to update even at unsuccessful iterations. We call this new method Stochastic Adaptive cubic regularization with Negative Curvature (SANC). Unlike the previous method, in order to attain stochastic gradient and Hessian estimators, the SANC algorithm uses independent sets of data points of consistent size over all iterations. It makes the SANC algorithm more practical to apply for solving large-scale machine learning problems. To the best of our knowledge, this is the first approach that combines the negative curvature method with the adaptive cubic regularized Newton method. Finally, we provide experimental results including neural networks problems supporting the efficiency of our method.
Public companies in the US stock market must annually report their activities and financial performances to the SEC by filing the so-called 10-K form. Recent studies have demonstrated that changes in the textual content of the corporate annual filing (10-K) can convey strong signals of companies’ future returns. In this study, we combine natural language processing techniques and network science to introduce a novel 10-K-based network, named Lazy Network, that leverages year-on-year changes in companies’ 10-Ks detected using a neural network embedding model. The Lazy Network aims to capture textual changes derived from financial or economic changes on the equity market. Leveraging the Lazy Network, we present a novel investment strategy that attempts to select the least disrupted and stable companies by capturing the peripheries of the Lazy Network. We show that this strategy earns statistically significant risk-adjusted excess returns. Specifically, the proposed portfolios yield up to 95 basis points in monthly five-factor alphas (over 12% annually), outperforming similar strategies in the literature.
Navigating unmanned aerial vehicles in precarious environments is of great importance. It is necessary to rely on alternative information processing techniques to attain spatial information that is required for navigation in such settings. This paper introduces a novel deep learning-based approach for navigating that exclusively relies on synthetic aperture radar (SAR) images. The proposed method utilizes deep neural networks (DNNs) for image matching, retrieval, and registration. To this end, we introduce Deep Cosine Similarity Neural Networks (DCSNNs) for mapping SAR images to a global descriptive feature vector. We also introduce a fine-tuning algorithm for DC-SNNs, and DCSNNs are used to generate a database of feature vectors for SAR images that span a geographic area of interest, which, in turn, are compared against a feature vector of an inquiry image. Images similar to the inquiry are retrieved from the database by using a scalable distance measure between the feature vector outputs of DCSNN. Methods for reranking the retrieved SAR images that are used to update position coordinates of an inquiry SAR image by estimating from the best retrieved SAR image are also introduced. Numerical experiments comparing with baselines on the Polarimetric SAR (PolSAR) images are presented.
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