The effectiveness of biosignal generation and data augmentation with biosignal generative models based on generative adversarial networks (GANs), which are a type of deep learning technique, was demonstrated in our previous paper. GAN-based generative models only learn the projection between a random distribution as input data and the distribution of training data.Therefore, the relationship between input and generated data is unclear, and the characteristics of the data generated from this model cannot be controlled. This study proposes a method for generating time-series data based on GANs and explores their ability to generate biosignals with certain classes and characteristics. Moreover, in the proposed method, latent variables are analyzed using canonical correlation analysis (CCA) to represent the relationship between input and generated data as canonical loadings. Using these loadings, we can control the characteristics of the data generated by the proposed method. The influence of class labels on generated data is analyzed by feeding the data interpolated between two class labels into the generator of the proposed GANs. The CCA of the latent variables is shown to be an effective method of controlling the generated data characteristics. We are able to model the distribution of the time-series data without requiring domain-dependent knowledge using the proposed method. Furthermore, it is possible to control the characteristics of these data by analyzing the model trained using the proposed method. To the best of our knowledge, this work is the first to generate biosignals using GANs while controlling the characteristics of the generated data.

Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional representations of high dimensional objects, we propose to quantify the estimation loss of CCA by the excess prediction loss defined through a prediction-after-dimension-reduction framework. Such framework suggests viewing CCA estimation as estimating the subspaces spanned by the canonical variates. Interestedly, the proposed error metrics derived from the excess prediction loss turn out to be closely related to the principal angles between the subspaces spanned by the population and sample canonical variates respectively. We characterize the non-asymptotic minimax rates under the proposed metrics, especially the dependency of the minimax rates on the key quantities including the dimensions, the condition number of the covariance matrices, the canonical correlations and the eigen-gap, with minimal assumptions on the joint covariance matrix. To the best of our knowledge, this is the first finite sample result that captures the effect of the canonical correlations on the minimax rates.