Consider learning a generative model for time-series data. The sequential setting poses a unique challenge: Not only should the generator capture the dynamics of (stepwise) transitions, but its open-loop rollouts should also preserve the distribution of (multi-step) trajectories. On one hand, autoregressive models trained by MLE allow learning and computing explicit transition distributions, but suffer from compounding error during rollouts. On the other hand, adversarial models based on GAN training alleviate such exposure bias, but transitions are implicit and hard to assess. In this work, we study a generative framework that seeks to combine the strengths of both: Motivated by a moment-matching objective to mitigate compounding error, we optimize a local (but forward-looking), where the reinforcement signal is provided by a global (but stepwise-decomposable) trained by contrastive estimation.

Abstract--Score-based generative models (SGMs) have demonstrated unparalleled sampling quality and diversity in numerous fields, such as image generation, voice synthesis, and tabular data synthesis, etc. Inspired by those outstanding results, we apply SGMs to synthesize time-series by learning its conditional score function. T o this end, we present a conditional score network for time-series synthesis, deriving a denoising score matching loss tailored for our purposes. In particular, our presented denoising score matching loss is the conditional denoising score matching loss for time-series synthesis. In addition, our framework is such flexible that both regular and irregular time-series can be synthesized with minimal changes to our model design. Finally, we obtain exceptional synthesis performance on various time-series datasets, achieving state-of-the-art sampling diversity and quality. Time-series frequently occurs in our daily lives, e.g., stock data, climate data, and so on. Especially, time-series forecasting and classification are popular research topics in the field of machine learning [1], [2]. In many cases, however, time-series samples are incomplete and/or the number of samples is insufficient, in which case training machine learning models cannot be fulfilled in a robust way. To overcome the limitation, time-series synthesis has been studied actively recently [3], [4]. These synthesis models have been designed in various ways, including variational autoencoders (V AEs) and generative adversarial networks (GANs) [5]-[7].

Consider learning a generative model for time-series data. The sequential setting poses a unique challenge: Not only should the generator capture the conditional dynamics of (stepwise) transitions, but its open-loop rollouts should also preserve the joint distribution of (multi-step) trajectories. On one hand, autoregressive models trained by MLE allow learning and computing explicit transition distributions, but suffer from compounding error during rollouts. On the other hand, adversarial models based on GAN training alleviate such exposure bias, but transitions are implicit and hard to assess. In this work, we study a generative framework that seeks to combine the strengths of both: Motivated by a moment-matching objective to mitigate compounding error, we optimize a local (but forward-looking) transition policy, where the reinforcement signal is provided by a global (but stepwise-decomposable) energy model trained by contrastive estimation.

Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models fall short in learning sequence data with sharp transitions - common in many real-world systems - due to numerical challenges during optimization. In this work, we propose LS4, a generative model for sequences with latent variables evolving according to a state space ODE to increase modeling capacity. Inspired by recent deep state space models (S4), we achieve speedups by leveraging a convolutional representation of LS4 which bypasses the explicit evaluation of hidden states. We show that LS4 significantly outperforms previous continuous-time generative models in terms of marginal distribution, classification, and prediction scores on real-world datasets in the Monash Forecasting Repository, and is capable of modeling highly stochastic data with sharp temporal transitions. LS4 sets state-of-the-art for continuous-time latent generative models, with significant improvement of mean squared error and tighter variational lower bounds on irregularly-sampled datasets, while also being x100 faster than other baselines on long sequences.

Score-based generative models (SGMs) are generative models that are in the spotlight these days. Time-series frequently occurs in our daily life, e.g., stock data, climate data, and so on. Especially, time-series forecasting and classification are popular research topics in the field of machine learning. SGMs are also known for outperforming other generative models. As a result, we apply SGMs to synthesize time-series data by learning conditional score functions. We propose a conditional score network for the time-series generation domain. Furthermore, we also derive the loss function between the score matching and the denoising score matching in the time-series generation domain. Finally, we achieve state-of-the-art results on real-world datasets in terms of sampling diversity and quality.

For health prognostic task, ever-increasing efforts have been focused on machine learning-based methods, which are capable of yielding accurate remaining useful life (RUL) estimation for industrial equipment or components without exploring the degradation mechanism. A prerequisite ensuring the success of these methods depends on a wealth of run-to-failure data, however, run-to-failure data may be insufficient in practice. That is, conducting a substantial amount of destructive experiments not only is high costs, but also may cause catastrophic consequences. Out of this consideration, an enhanced RUL framework focusing on data self-generation is put forward for both non-cyclic and cyclic degradation patterns for the first time. It is designed to enrich data from a data-driven way, generating realistic-like time-series to enhance current RUL methods. First, high-quality data generation is ensured through the proposed convolutional recurrent generative adversarial network (CR-GAN), which adopts a two-channel fusion convolutional recurrent neural network. Next, a hierarchical framework is proposed to combine generated data into current RUL estimation methods. Finally, the efficacy of the proposed method is verified through both non-cyclic and cyclic degradation systems. With the enhanced RUL framework, an aero-engine system following non-cyclic degradation has been tested using three typical RUL models. State-of-art RUL estimation results are achieved by enhancing capsule network with generated time-series. Specifically, estimation errors evaluated by the index score function have been reduced by 21.77%, and 32.67% for the two employed operating conditions, respectively. Besides, the estimation error is reduced to zero for the Lithium-ion battery system, which presents cyclic degradation.