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A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for…
Recent advances in engineering technologies have enabled the collection of a large number of longitudinal features. This wealth of information presents unique opportunities for researchers to investigate the complex nature of diseases and…
Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…
Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…
Biomechanics and human movement research often involves measuring multiple kinematic or kinetic variables regularly throughout a movement, yielding data that present as smooth, multivariate, time-varying curves and are naturally amenable to…
We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution…
Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected with measurement errors on discretized grids. In order to accurately smooth noisy functional…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
Large-scale longitudinal molecular profiling is now firmly established in biomedical research, prompted by the need to uncover coordinated biomarker trajectories reflecting the dynamics of underlying biological mechanisms and characterise…
The effectiveness of single-model sequential recommendation architectures, while scalable, is often limited when catering to "power users" in sparse or niche domains. Our previous research, PinnerFormerLite, addressed this by using a fixed…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…
Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…
In this paper, a novel method to adaptively approximate the solution to stochastic differential equations, which is based on compressive sampling and sparse recovery, is introduced. The proposed method consider the problem of sparse…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…
Its conceptual appeal and effectiveness has made latent factor modeling an indispensable tool for multivariate analysis. Despite its popularity across many fields, there are outstanding methodological challenges that have hampered practical…