Additive models have attracted much attention for high-dimensional regression estimation and variable selection. However, the existing models are usually limited to the single-task learning framework under the mean squared error (MSE) criterion, where the utilization of variable structure depends heavily on a priori knowledge among variables. For high-dimensional observations in real environment, e.g., Coronal Mass Ejections (CMEs) data, the learning performance of previous methods may be degraded seriously due to the complex non-Gaussian noise and the insufficiency of a prior knowledge on variable structure.

Existing melody harmonization models have made great progress in improving the quality of generated harmonies, but most of them ignored the emotions beneath the music. Meanwhile, the variability of harmonies generated by previous methods is insufficient. To solve these problems, we propose a novel LSTM-based Hierarchical Variational Auto-Encoder (LHVAE) to investigate the influence of emotional conditions on melody harmonization, while improving the quality of generated harmonies and capturing the abundant variability of chord progressions. Specifically, LHVAE incorporates latent variables and emotional conditions at different levels (piece- and bar-level) to model the global and local music properties. Additionally, we introduce an attention-based melody context vector at each step to better learn the correspondence between melodies and harmonies. Objective experimental results show that our proposed model outperforms other LSTM-based models. Through subjective evaluation, we conclude that only altering the types of chords hardly changes the overall emotion of the music. The qualitative analysis demonstrates the ability of our model to generate variable harmonies.

Self-supervised learning is an empirically successful approach to unsupervised learning based on creating artificial supervised learning problems. A popular self-supervised approach to representation learning is contrastive learning, which leverages naturally occurring pairs of similar and dissimilar data points, or multiple views of the same data. This work provides a theoretical analysis of contrastive learning in the multi-view setting, where two views of each datum are available. The main result is that linear functions of the learned representations are nearly optimal on downstream prediction tasks whenever the two views provide redundant information about the label.