Related papers: Fast and principled equation discovery from chaos …

We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their…

Causal discovery is fundamental to scientific research, yet traditional statistical algorithms face significant challenges, including expensive data collection, redundant computation for known relations, and unrealistic assumptions. While…

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…

We present a Bayesian algorithm to combine optical imaging of unresolved objects from distinct epochs and observation platforms for orbit determination and tracking. By propagating the non-Gaussian uncertainties we are able to optimally…

Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…

Parameter calibration is essential for reducing uncertainty and improving predictive fidelity in physics-based models, yet it is often limited by the high computational cost of model evaluations. Bayesian calibration methods provide a…

The combination of machine learning (ML) and sparsity-promoting techniques is enabling direct extraction of governing equations from data, revolutionizing computational modeling in diverse fields of science and engineering. The discovered…

Entropic Outlier Sparsification (EOS) is proposed as a robust computational strategy for the detection of data anomalies in a broad class of learning methods, including the unsupervised problems (like detection of non-Gaussian outliers in…

The paper introduces a novel methodology for the identification of coefficients of switched autoregressive linear models. We consider the case when the system's outputs are contaminated by possibly large values of measurement noise. It is…

This chapter introduces the Bayesian reflex -- an analogy with the autonomic nervous system -- as a unifying framework for online learning in AI. Bayesian online algorithms automatically maintain equilibrium in dynamic environments via…

Numerous Bayesian Network (BN) structure learning algorithms have been proposed in the literature over the past few decades. Each publication makes an empirical or theoretical case for the algorithm proposed in that publication and results…

In the recent past, psychological stress has been increasingly observed in humans, and early detection is crucial to prevent health risks. Stress detection using on-device deep learning algorithms has been on the rise owing to advancements…

Uncertainty estimation for unlabeled data is crucial to active learning. With a deep neural network employed as the backbone model, the data selection process is highly challenging due to the potential over-confidence of the model…

Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…

Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of…

Estimating time-varying graphical models are of paramount importance in various social, financial, biological, and engineering systems, since the evolution of such networks can be utilized for example to spot trends, detect anomalies,…

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity promoting…

Bayesian experimental design (BED) provides a principled framework for optimizing data collection by choosing experiments that are maximally informative about unknown parameters. However, existing methods cannot deal with the joint…

Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of…

Big data has become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt…