Related papers: Towards Continuous-time Causal Foundation Models

This paper considers a safe trajectory tracking of the Stefan problem with a second-order moving boundary dynamics. The model is given by a parabolic Partial Differential Equation (PDE) defined on a time-varying domain of moving boundary…

Effective multivariate time series forecasting often benefits from accurately modeling complex inter-variable dependencies. However, existing attention- or graph-based methods face three key issues: (a) strong temporal self-dependencies are…

Travel Time Estimation (TTE) is indispensable in intelligent transportation system (ITS). It is significant to achieve the fine-grained Trajectory-based Travel Time Estimation (TTTE) for multi-city scenarios, namely to accurately estimate…

Assurance of asymptotic trajectory tracking in robotic manipulators with a smooth control law in the presence of unmodeled dynamics or external disturbance is a challenging problem. Recently, it is asserted that it is achieved via a…

Learning the dynamic causal structure of time series is a challenging problem. Most existing approaches rely on distributional or structural invariance to uncover underlying causal dynamics, assuming stationary or partially stationary…

Discovering causal direction from temporal observational data is particularly challenging for symbolic sequences, where functional models and noise assumptions are often unavailable. We propose a novel \emph{Dictionary Based Pattern Entropy…

In this paper, we develop a generic methodology to encode hierarchical causality structure among observed variables into a neural network in order to improve its predictive performance. The proposed methodology, called causality-informed…

The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator. SDEs to be considered are unique…

New biological assays like Perturb-seq link highly parallel CRISPR interventions to a high-dimensional transcriptomic readout, providing insight into gene regulatory networks. Causal gene regulatory networks can be represented by directed…

The use of observational time series data to assess the impact of multi-time point interventions is becoming increasingly common as more health and activity data are collected and digitized via wearables, social media, and electronic health…

Most existing methods that address out-of-distribution (OOD) generalization for node classification on graphs primarily focus on a specific type of data biases, such as label selection bias or structural bias. However, anticipating the type…

Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of…

Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting…

We propose a geometric model-free causality measurebased on multivariate delay embedding that can efficiently detect linear and nonlinear causal interactions between time series with no prior information. We then exploit the proposed causal…

Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the…

Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these systems are…

We propose a constraint-based algorithm, which automatically determines causal relevance thresholds, to infer causal networks from data. We call these topological thresholds. We present two methods for determining the threshold: the first…

This paper proposes a novel model inference procedure to identify system matrix from a single noisy trajectory over a finite-time interval. The proposed inference procedure comprises an observation data processor, a redundant data processor…

Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal…

We develop a Bayesian inference method for discretely-observed stochastic differential equations (SDEs). Inference is challenging for most SDEs, due to the analytical intractability of the likelihood function. Nevertheless, forward…