Expert Aggregation for Financial Forecasting

Machine learning algorithms dedicated to financial time series forecasting have gained a lot of interest over the last few years. One difficulty lies in the choice between several algorithms, as their estimation accuracy may be unstable through time. In this paper, we propose to apply an online aggregation-based forecasting model combining several machine learning techniques to build a portfolio which dynamically adapts itself to market conditions. We apply this aggregation technique to the construction of a long-short-portfolio of individual stocks ranked on their financial characteristics and we demonstrate how aggregation outperforms single algorithms both in terms of performances and of stability

An Open Source C++ Implementation of Multi-Threaded Gaussian Mixture Models, k-Means and Expectation Maximisation

Modelling of multivariate densities is a core component in many signal processing, pattern recognition and machine learning applications. The modelling is often done via Gaussian mixture models (GMMs), which use computationally expensive and potentially unstable training algorithms. We provide an overview of a fast and robust implementation of GMMs in the C++ language, employing multi-threaded versions of the Expectation Maximisation (EM) and k-means training algorithms. Multi-threading is achieved through reformulation of the EM and k-means algorithms into a MapReduce-like framework. Furthermore, the implementation uses several techniques to improve numerical stability and modelling accuracy. We demonstrate that the multi-threaded implementation achieves a speedup of an order of magnitude on a recent 16 core machine, and that it can achieve higher modelling accuracy than a previously well-established publically accessible implementation. The multi-threaded implementation is included as a user-friendly class in recent releases of the open source Armadillo C++ linear algebra library. The library is provided under the permissive Apache~2.0 license, allowing unencumbered use in commercial products

A General Framework for Learning Mean-Field Games

This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and demonstrates that naively combining reinforcement learning with the fixed-point approach in classical MFGs yields unstable algorithms. It then proposes value-based and policy-based reinforcement learning algorithms (GMF-V and GMF-P, respectively) with smoothed policies, with analysis of their convergence properties and computational complexities. Experiments on an equilibrium product pricing problem demonstrate that GMF-V-Q and GMF-P-TRPO, two specific instantiations of GMF-V and GMF-P, respectively, with Q-learning and TRPO, are both efficient and robust in the GMFG setting. Moreover, their performance is superior in convergence speed, accuracy, and stability when compared with existing algorithms for multi-agent reinforcement learning in the $N$-player setting.Comment: 43 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1901.0958

Stochastic trapping in a solvable model of on-line independent component analysis

Previous analytical studies of on-line Independent Component Analysis (ICA) learning rules have focussed on asymptotic stability and efficiency. In practice the transient stages of learning will often be more significant in determining the success of an algorithm. This is demonstrated here with an analysis of a Hebbian ICA algorithm which can find a small number of non-Gaussian components given data composed of a linear mixture of independent source signals. An idealised data model is considered in which the sources comprise a number of non-Gaussian and Gaussian sources and a solution to the dynamics is obtained in the limit where the number of Gaussian sources is infinite. Previous stability results are confirmed by expanding around optimal fixed points, where a closed form solution to the learning dynamics is obtained. However, stochastic effects are shown to stabilise otherwise unstable sub-optimal fixed points. Conditions required to destabilise one such fixed point are obtained for the case of a single non-Gaussian component, indicating that the initial learning rate \eta required to successfully escape is very low (\eta = O(N^{-2}) where N is the data dimension) resulting in very slow learning typically requiring O(N^3) iterations. Simulations confirm that this picture holds for a finite system.Comment: 17 pages, 3 figures. To appear in Neural Computatio