Correlated Attention in Transformers for Multivariate Time Series

Multivariate time series (MTS) analysis prevails in real-world applications such as finance, climate science and healthcare. The various self-attention mechanisms, the backbone of the state-of-the-art Transformer-based models, efficiently discover the temporal dependencies, yet cannot well capture the intricate cross-correlation between different features of MTS data, which inherently stems from complex dynamical systems in practice. To this end, we propose a novel correlated attention mechanism, which not only efficiently captures feature-wise dependencies, but can also be seamlessly integrated within the encoder blocks of existing well-known Transformers to gain efficiency improvement. In particular, correlated attention operates across feature channels to compute cross-covariance matrices between queries and keys with different lag values, and selectively aggregate representations at the sub-series level. This architecture facilitates automated discovery and representation learning of not only instantaneous but also lagged cross-correlations, while inherently capturing time series auto-correlation. When combined with prevalent Transformer baselines, correlated attention mechanism constitutes a better alternative for encoder-only architectures, which are suitable for a wide range of tasks including imputation, anomaly detection and classification. Extensive experiments on the aforementioned tasks consistently underscore the advantages of correlated attention mechanism in enhancing base Transformer models, and demonstrate our state-of-the-art results in imputation, anomaly detection and classification

On the Convergence to a Global Solution of Shuffling-Type Gradient Algorithms

Stochastic gradient descent (SGD) algorithm is the method of choice in many machine learning tasks thanks to its scalability and efficiency in dealing with large-scale problems. In this paper, we focus on the shuffling version of SGD which matches the mainstream practical heuristics. We show the convergence to a global solution of shuffling SGD for a class of non-convex functions under over-parameterized settings. Our analysis employs more relaxed non-convex assumptions than previous literature. Nevertheless, we maintain the desired computational complexity as shuffling SGD has achieved in the general convex setting.Comment: The 37th Conference on Neural Information Processing Systems (NeurIPS 2023

Generalizing DP-SGD with Shuffling and Batch Clipping

Classical differential private DP-SGD implements individual clipping with random subsampling, which forces a mini-batch SGD approach. We provide a general differential private algorithmic framework that goes beyond DP-SGD and allows any possible first order optimizers (e.g., classical SGD and momentum based SGD approaches) in combination with batch clipping, which clips an aggregate of computed gradients rather than summing clipped gradients (as is done in individual clipping). The framework also admits sampling techniques beyond random subsampling such as shuffling. Our DP analysis follows the $f$-DP approach and introduces a new proof technique which allows us to derive simple closed form expressions and to also analyse group privacy. In particular, for $E$ epochs work and groups of size $g$, we show a $\sqrt{g E}$ DP dependency for batch clipping with shuffling.Comment: Update disclaimer