Compound Poisson Processes, Latent Shrinkage Priors and Bayesian Nonconvex Penalization

arXiv.org Machine Learning

In this paper we discuss Bayesian nonconvex penalization for sparse learning problems. We explore a nonparametric formulation for latent shrinkage parameters using subordinators which are one-dimensional L\'{e}vy processes. We particularly study a family of continuous compound Poisson subordinators and a family of discrete compound Poisson subordinators. We exemplify four specific subordinators: Gamma, Poisson, negative binomial and squared Bessel subordinators. The Laplace exponents of the subordinators are Bernstein functions, so they can be used as sparsity-inducing nonconvex penalty functions. We exploit these subordinators in regression problems, yielding a hierarchical model with multiple regularization parameters. We devise ECME (Expectation/Conditional Maximization Either) algorithms to simultaneously estimate regression coefficients and regularization parameters. The empirical evaluation of simulated data shows that our approach is feasible and effective in high-dimensional data analysis.


Nonconvex Penalization Using Laplace Exponents and Concave Conjugates

Neural Information Processing Systems

In this paper we study sparsity-inducing nonconvex penalty functions using Lévy processes. We define such a penalty as the Laplace exponent of a subordinator. Accordingly,we propose a novel approach for the construction of sparsityinducing nonconvexpenalties. Particularly, we show that the nonconvex logarithmic (LOG) and exponential (EXP) penalty functions are the Laplace exponents of Gamma and compound Poisson subordinators, respectively. Additionally, we explore the concave conjugate of nonconvex penalties. We find that the LOG and EXP penalties are the concave conjugates of negative Kullback-Leiber (KL) distance functions.Furthermore, the relationship between these two penalties is due to asymmetricity of the KL distance.


Improved EEMD-based crude oil price forecasting using LSTM networks

#artificialintelligence

The inadequacy of traditional forecasting model based on EEMD in practical work. For WTI, the first four IMFs decomposed by EEMD are suitable as inputs. Considering the actual demand of crude oil price forecasting, a novel model based on ensemble empirical mode decomposition (EEMD) and long short-term memory (LSTM) is proposed. In practical work, the model trained by historical data will be used in later data. Then the forecasting models based on EEMD need re-execute EEMD to update decomposition results of price series after getting new data.


Multivariate Forecasting of Crude Oil Spot Prices using Neural Networks

arXiv.org Machine Learning

Abstract--Crude oil is a major component in most advanced economies of the world. Accurately predicting and understanding thebehavior of crude oil prices is important for economists, analysts, forecasters, and traders, to name a few. The price of crude oil has declined in the past decade and is seeing a phase of stability; but will this stability last? This work is an empirical study on how multivariate analysis may be employed to predict crude oil spot prices using neural networks. The concept of using neural networks showed promising potential. A very simple neural network model was able to perform on par with ARIMA models - the state-of-the-art model in time-series forecasting. Advanced neural network models using larger datasets may be used in the future to extend this proofof-concept toa full scale framework. I. INTRODUCTION Crude oil spot prices saw a tremendous uptick in the first decade of the 21 Since 2014, crude oil prices have fallen and may have stabilized now. However, there has always been a constant interest in accurately predicting crude oil prices; given that crude oil drives a major portion of the economy. Economists, scientists, data analysts, and traders are all interested in models that give them the best accuracy.


Beyond One-Step-Ahead Forecasting: Evaluation of Alternative Multi-Step-Ahead Forecasting Models for Crude Oil Prices

arXiv.org Artificial Intelligence

An accurate prediction of crude oil prices over long future horizons is challenging and of great interest to governments, enterprises, and investors. This paper proposes a revised hybrid model built upon empirical mode decomposition (EMD) based on the feed-forward neural network (FNN) modeling framework incorporating the slope-based method (SBM), which is capable of capturing the complex dynamic of crude oil prices. Three commonly used multi-step-ahead prediction strategies proposed in the literature, including iterated strategy, direct strategy, and MIMO (multiple-input multiple-output) strategy, are examined and compared, and practical considerations for the selection of a prediction strategy for multi-step-ahead forecasting relating to crude oil prices are identified. The weekly data from the WTI (West Texas Intermediate) crude oil spot price are used to compare the performance of the alternative models under the EMD-SBM-FNN modeling framework with selected counterparts. The quantitative and comprehensive assessments are performed on the basis of prediction accuracy and computational cost. The results obtained in this study indicate that the proposed EMD-SBM-FNN model using the MIMO strategy is the best in terms of prediction accuracy with accredited computational load.