Representation learning in finance

Finance studies often employ heterogeneous datasets from different sources with different structures and frequencies. Some data are noisy, sparse, and unbalanced with missing values; some are unstructured, containing text or networks. Traditional techniques often struggle to combine and effectively extract information from these datasets. This work explores representation learning as a proven machine learning technique in learning informative embedding from complex, noisy, and dynamic financial data. This dissertation proposes novel factorization algorithms and network modeling techniques to learn the local and global representation of data in two specific financial applications: analysts’ earnings forecasts and asset pricing. Financial analysts’ earnings forecast is one of the most critical inputs for security valuation and investment decisions. However, it is challenging to fully utilize this type of data due to the missing values. This work proposes one matrix-based algorithm, “Coupled Matrix Factorization,” and one tensor-based algorithm, “Nonlinear Tensor Coupling and Completion Framework,” to impute missing values in analysts’ earnings forecasts and then use the imputed data to predict firms’ future earnings. Experimental analysis shows that missing value imputation and representation learning by coupled matrix/tensor factorization from the observed entries improve the accuracy of firm earnings prediction. The results confirm that representing financial time-series in their natural third-order tensor form improves the latent representation of the data. It learns high-quality embedding by overcoming information loss of flattening data in spatial or temporal dimensions. Traditional asset pricing models focus on linear relationships among asset pricing factors and often ignore nonlinear interaction among firms and factors. This dissertation formulates novel methods to identify nonlinear asset pricing factors and develops asset pricing models that capture global and local properties of data. First, this work proposes an artificial neural network “auto enco der” based model to capture the latent asset pricing factors from the global representation of an equity index. It also shows that autoencoder effectively identifies communal and non-communal assets in an index to facilitate portfolio optimization. Second, the global representation is augmented by propagating information from local communities, where the network determines the strength of this information propagation. Based on the Laplacian spectrum of the equity market network, a network factor “Z-score” is proposed to facilitate pertinent information propagation and capture dynamic changes in network structures. Finally, a “Dynamic Graph Learning Framework for Asset Pricing” is proposed to combine both global and local representations of data into one end-to-end asset pricing model. Using graph attention mechanism and information diffusion function, the proposed model learns new connections for implicit networks and refines connections of explicit networks. Experimental analysis shows that the proposed model incorporates information from negative and positive connections, captures the network evolution of the equity market over time, and outperforms other state-of-the-art asset pricing and predictive machine learning models in stock return prediction. In a broader context, this is a pioneering work in FinTech, particularly in understanding complex financial market structures and developing explainable artificial intelligence models for finance applications. This work effectively demonstrates the application of machine learning to model financial networks, capture nonlinear interactions on data, and provide investors with powerful data-driven techniques for informed decision-making

Noise and nonlinearities in high-throughput data

High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based approaches have proved useful in extracting hidden information within such networks and for estimating missing data, but these methods are based essentially on linear assumptions. The physical models of matching, when applicable, often suggest non-linear mechanisms, that may sometimes be identified as noise. The use of non-linear models in data analysis, however, may require the introduction of many parameters, which lowers the statistical weight of the model. According to the quality of data, a simpler linear analysis may be more convenient than more complex approaches. In this paper, we show how a simple non-parametric Bayesian model may be used to explore the role of non-linearities and noise in synthetic and experimental data sets.Comment: 12 pages, 3 figure

Data-driven Identification and Prediction of Power System Dynamics Using Linear Operators

In this paper, we propose linear operator theoretic framework involving Koopman operator for the data-driven identification of power system dynamics. We explicitly account for noise in the time series measurement data and propose robust approach for data-driven approximation of Koopman operator for the identification of nonlinear power system dynamics. The identified model is used for the prediction of state trajectories in the power system. The application of the framework is illustrated using an IEEE nine bus test system.Comment: Accepted for publication in IEEE Power and Energy System General Meeting 201

Predicting Spatio-Temporal Time Series Using Dimension Reduced Local States

We present a method for both cross estimation and iterated time series prediction of spatio temporal dynamics based on reconstructed local states, PCA dimension reduction, and local modelling using nearest neighbour methods. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio-Cherry-Fenton model, and the Kuramoto-Sivashinsky model

State and parameter estimation using Monte Carlo evaluation of path integrals

Transferring information from observations of a dynamical system to estimate the fixed parameters and unobserved states of a system model can be formulated as the evaluation of a discrete time path integral in model state space. The observations serve as a guiding potential working with the dynamical rules of the model to direct system orbits in state space. The path integral representation permits direct numerical evaluation of the conditional mean path through the state space as well as conditional moments about this mean. Using a Monte Carlo method for selecting paths through state space we show how these moments can be evaluated and demonstrate in an interesting model system the explicit influence of the role of transfer of information from the observations. We address the question of how many observations are required to estimate the unobserved state variables, and we examine the assumptions of Gaussianity of the underlying conditional probability.Comment: Submitted to the Quarterly Journal of the Royal Meteorological Society, 19 pages, 5 figure