Related papers: Trajectory Generator Matching for Time Series

Generative models have shown great promise as trajectory planners, given their affinity to modeling complex distributions and guidable inference process. Previous works have successfully applied these in the context of robotic manipulation…

We investigate the generative capabilities of the Schr\"odinger Bridge (SB) approach for time series. The SB framework formulates time series synthesis as an entropic optimal interpolation transport problem between a reference probability…

Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…

Temporally indexed data are essential in a wide range of fields and of interest to machine learning researchers. Time series data, however, are often scarce or highly sensitive, which precludes the sharing of data between researchers and…

Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE…

Current Generative Adversarial Network (GAN)-based approaches for time series generation face challenges such as suboptimal convergence, information loss in embedding spaces, and instability. To overcome these challenges, we introduce an…

Modeling real-world multidimensional time series can be particularly challenging when these are sporadically observed (i.e., sampling is irregular both in time and across dimensions)-such as in the case of clinical patient data. To address…

Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising…

This paper explores the application of Stochastic Differential Equations (SDE) to interpret the text generation process of Large Language Models (LLMs) such as GPT-4. Text generation in LLMs is modeled as a stochastic process where each…

Imagine generating a city's electricity demand pattern based on weather, the presence of an electric vehicle, and location, which could be used for capacity planning during a winter freeze. Such real-world time series are often enriched…

Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…

We derive the divergence-kernel formula for the linear response of random dynamical systems. Specifically, the pathwise expression is for the parameter-derivative of the marginal or stationary density, not an averaged observable. Our…

This paper focuses on the analysis of sequential image data, particularly brain imaging data such as MRI, fMRI, CT, with the motivation of understanding the brain aging process and neurodegenerative diseases. To achieve this goal, we…

The recent deep generative models for static graphs that are now being actively developed have achieved significant success in areas such as molecule design. However, many real-world problems involve temporal graphs whose topology and…

We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method…

We explore whether useful temporal neural generative models can be learned from sequential data without back-propagation through time. We investigate the viability of a more neurocognitively-grounded approach in the context of unsupervised…

This paper explores the challenges and benefits of a trainable destruction process in diffusion samplers -- diffusion-based generative models trained to sample an unnormalised density without access to data samples. Contrary to the majority…

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

Time-lapse image sequences offer visually compelling insights into dynamic processes that are too slow to observe in real time. However, playing a long time-lapse sequence back as a video often results in distracting flicker due to random…