Quaternion Valued Risk Diversification

Sugitomo, Seisuke; Maeta, Keiichi

doi:10.3390/e22040390

Cited by 3 publications

(1 citation statement)

References 14 publications

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“…Another fundamental property of quaternion-valued learning is the Hamilton product, which has recently favored the proliferation of convolutional neural networks in the quaternion domain [ 35 , 36 , 37 , 38 ]. Due to their capabilities, quaternion-valued learning methods have been applied in several applications, including spoken language understanding [ 39 ], color image processing [ 40 , 41 ], 3D audio [ 42 , 43 ], speech recognition [ 44 ], image generation [ 45 ], quantum mechanics [ 46 ], risk diversification [ 47 ], gait data analysis [ 48 ].…”

Section: Introductionmentioning

confidence: 99%

An Information-Theoretic Perspective on Proper Quaternion Variational Autoencoders

Grassucci

Comminiello

Uncini

2021

Entropy

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Variational autoencoders are deep generative models that have recently received a great deal of attention due to their ability to model the latent distribution of any kind of input such as images and audio signals, among others. A novel variational autoncoder in the quaternion domain H, namely the QVAE, has been recently proposed, leveraging the augmented second order statics of H-proper signals. In this paper, we analyze the QVAE under an information-theoretic perspective, studying the ability of the H-proper model to approximate improper distributions as well as the built-in H-proper ones and the loss of entropy due to the improperness of the input signal. We conduct experiments on a substantial set of quaternion signals, for each of which the QVAE shows the ability of modelling the input distribution, while learning the improperness and increasing the entropy of the latent space. The proposed analysis will prove that proper QVAEs can be employed with a good approximation even when the quaternion input data are improper.

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Section: Introductionmentioning

confidence: 99%

An Information-Theoretic Perspective on Proper Quaternion Variational Autoencoders

Grassucci

Comminiello

Uncini

2021

Entropy

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Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays

Chen

Zhang

Xue

2022

Mathematics and Computers in Simulation

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GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio

Nakagawa

Uchiyama²

2020

Mathematics

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There are three distinguishing features in the financial time series, such as stock prices, are as follows: (1) Non-normality, (2) serial correlation, and (3) leverage effect. All three points need to be taken into account to model the financial time series. However, multivariate financial time series modeling involves a large number of stocks, with many parameters to be estimated. Therefore, there are few examples of multivariate financial time series modeling that explicitly deal with higher-order moments. Furthermore, there is no multivariate financial time series model that takes all three characteristics above into account. In this study, we propose the generalized orthogonal (GO)-Glosten, Jagannathan, and Runkle GARCH (GJR) model which extends the GO-generalized autoregressive conditional heteroscedasticity (GARCH) model and incorporates the three features of the financial time series. We confirm the effectiveness of the proposed model by comparing the performance of risk-based portfolios with higher-order moments. The results show that the performance with our proposed model is superior to that with baseline methods, and indicate that estimation methods are important in risk-based portfolios with higher moments.

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Quaternion Valued Risk Diversification

Cited by 3 publications

References 14 publications

An Information-Theoretic Perspective on Proper Quaternion Variational Autoencoders

An Information-Theoretic Perspective on Proper Quaternion Variational Autoencoders

Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays

GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio

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