205 research outputs found
Multi-way Graph Signal Processing on Tensors: Integrative analysis of irregular geometries
Graph signal processing (GSP) is an important methodology for studying data
residing on irregular structures. As acquired data is increasingly taking the
form of multi-way tensors, new signal processing tools are needed to maximally
utilize the multi-way structure within the data. In this paper, we review
modern signal processing frameworks generalizing GSP to multi-way data,
starting from graph signals coupled to familiar regular axes such as time in
sensor networks, and then extending to general graphs across all tensor modes.
This widely applicable paradigm motivates reformulating and improving upon
classical problems and approaches to creatively address the challenges in
tensor-based data. We synthesize common themes arising from current efforts to
combine GSP with tensor analysis and highlight future directions in extending
GSP to the multi-way paradigm.Comment: In review for IEEE Signal Processing Magazin
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
Tensor Completion for Weakly-dependent Data on Graph for Metro Passenger Flow Prediction
Low-rank tensor decomposition and completion have attracted significant
interest from academia given the ubiquity of tensor data. However, the low-rank
structure is a global property, which will not be fulfilled when the data
presents complex and weak dependencies given specific graph structures. One
particular application that motivates this study is the spatiotemporal data
analysis. As shown in the preliminary study, weakly dependencies can worsen the
low-rank tensor completion performance. In this paper, we propose a novel
low-rank CANDECOMP / PARAFAC (CP) tensor decomposition and completion framework
by introducing the -norm penalty and Graph Laplacian penalty to model
the weakly dependency on graph. We further propose an efficient optimization
algorithm based on the Block Coordinate Descent for efficient estimation. A
case study based on the metro passenger flow data in Hong Kong is conducted to
demonstrate improved performance over the regular tensor completion methods.Comment: Accepted at AAAI 202
Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach
Traffic speed is central to characterizing the fluidity of the road network.
Many transportation applications rely on it, such as real-time navigation,
dynamic route planning, and congestion management. Rapid advances in sensing
and communication techniques make traffic speed detection easier than ever.
However, due to sparse deployment of static sensors or low penetration of
mobile sensors, speeds detected are incomplete and far from network-wide use.
In addition, sensors are prone to error or missing data due to various kinds of
reasons, speeds from these sensors can become highly noisy. These drawbacks
call for effective techniques to recover credible estimates from the incomplete
data. In this work, we first identify the issue as a spatiotemporal kriging
problem and propose a Laplacian enhanced low-rank tensor completion (LETC)
framework featuring both lowrankness and multi-dimensional correlations for
large-scale traffic speed kriging under limited observations. To be specific,
three types of speed correlation including temporal continuity, temporal
periodicity, and spatial proximity are carefully chosen and simultaneously
modeled by three different forms of graph Laplacian, named temporal graph
Fourier transform, generalized temporal consistency regularization, and
diffusion graph regularization. We then design an efficient solution algorithm
via several effective numeric techniques to scale up the proposed model to
network-wide kriging. By performing experiments on two public million-level
traffic speed datasets, we finally draw the conclusion and find our proposed
LETC achieves the state-of-the-art kriging performance even under low
observation rates, while at the same time saving more than half computing time
compared with baseline methods. Some insights into spatiotemporal traffic data
modeling and kriging at the network level are provided as well
A dual framework for low-rank tensor completion
One of the popular approaches for low-rank tensor completion is to use the
latent trace norm regularization. However, most existing works in this
direction learn a sparse combination of tensors. In this work, we fill this gap
by proposing a variant of the latent trace norm that helps in learning a
non-sparse combination of tensors. We develop a dual framework for solving the
low-rank tensor completion problem. We first show a novel characterization of
the dual solution space with an interesting factorization of the optimal
solution. Overall, the optimal solution is shown to lie on a Cartesian product
of Riemannian manifolds. Furthermore, we exploit the versatile Riemannian
optimization framework for proposing computationally efficient trust region
algorithm. The experiments illustrate the efficacy of the proposed algorithm on
several real-world datasets across applications.Comment: Aceepted to appear in Advances of Nueral Information Processing
Systems (NIPS), 2018. A shorter version appeared in the NIPS workshop on
Synergies in Geometric Data Analysis 201
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