An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes

We propose an improved variant of the accelerated gradient optimization models for solving unconstrained minimization problems. Merging the positive features of either double direction, as well as double step size accelerated gradient models, we define an iterative method of a simpler form which is generally more effective. Performed convergence analysis shows that the defined iterative method is at least linearly convergent for uniformly convex and strictly convex functions. Numerical test results confirm the efficiency of the developed model regarding the CPU time, the number of iterations and the number of function evaluations metrics.

Financial Volatility Forecasting: A Sparse Multi-Head Attention Neural Network

Accurately predicting the volatility of financial asset prices and exploring its laws of movement have profound theoretical and practical guiding significance for financial market risk early warning, asset pricing, and investment portfolio design. The traditional methods are plagued by the problem of substandard prediction performance or gradient optimization. This paper proposes a novel volatility prediction method based on sparse multi-head attention (SP-M-Attention). This model discards the two-dimensional modeling strategy of time and space of the classic deep learning model. Instead, the solution is to embed a sparse multi-head attention calculation module in the network. The main advantages are that (i) it uses the inherent advantages of the multi-head attention mechanism to achieve parallel computing, (ii) it reduces the computational complexity through sparse measurements and feature compression of volatility, and (iii) it avoids the gradient problems caused by long-range propagation and therefore, is more suitable than traditional methods for the task of analysis of long time series. In the end, the article conducts an empirical study on the effectiveness of the proposed method through real datasets of major financial markets. Experimental results show that the prediction performance of the proposed model on all real datasets surpasses all benchmark models. This discovery will aid financial risk management and the optimization of investment strategies.

CNN-based Multi-Scale Gradient Optimization for Full-Waveform Inversion

<p>The seismic full waveform inversion (FWI), as one of important ways to obtain the seismic wave velocity, has made rapid development in the last decade. In response to problems of cycle-skipping artifacts, dependence on the initial model, and low-frequency information in FWI, researchers have made many improvements, such as multi-scale envelope inversion and low-frequency extension. Recently, deep learning has been also adopted seismic data processing and interpretation, because of its strong nonlinear mapping ability. However, these works depend on labels used for training heavily, especially for the velocity model in the inversion, which prevents them from real application. Referring to these studies, this work combines low-frequency extension commonly as well as multiscale inversion with deep learning, and proposes a multi-scale FWI gradient optimization method based on CNN. CNN we designed is trained to predict the inversion gradient corresponding to the low-frequency band data in FWI, so that multi-scale gradient optimization can be directly used in multi-scale inversion, expanding the low-frequency information in the actual data and reducing the calculation in FWI. With a specially designed dataset, CNN is trained to optimize the gradients computed from the high-frequency band data by predicting the gradients corresponding to the low-frequency band data and the gradients corresponding to the mid-frequency band data, respectively. The predicted gradients are used in different stages of the multi-scale inversion. The low-frequency gradients are used to invert the initial structural construction so as not to rely on a good initial model, and the high-frequency gradients are used to improve the accuracy of the inversion results. In this way, low-frequency expansion and multiscale inversion can be achieved simultaneously. Our method achieves good results on the initial model for a given uniform wave velocity, effectively alleviating the reliance on the initial model in FWI. This study provides a new idea of combining deep learning and full waveform inversion, which will be effectively used in seismic data processing.</p>

Survival Analysis on Rare Events Using Group-Regularized Multi-Response Cox Regression

Motivation The prediction performance of Cox proportional hazard model suffers when there are only few uncensored events in the training data. Results We propose a Sparse-Group regularized Cox regression method to improve the prediction performance of large-scale and high-dimensional survival data with few observed events. Our approach is applicable when there is one or more other survival responses that 1. has a large number of observed events; 2. share a common set of associated predictors with the rare event response. This scenario is common in the UK Biobank (Sudlow et al., 2015) dataset where records for a large number of common and less prevalent diseases of the same set of individuals are available. By analyzing these responses together, we hope to achieve higher prediction performance than when they are analyzed individually. To make this approach practical for large-scale data, we developed an accelerated proximal gradient optimization algorithm as well as a screening procedure inspired by Qian et al. (2020). Availability https://github.com/rivas-lab/multisnpnet-Cox Supplementary information Supplementary data are available at Bioinformatics online.