Related papers: Sparse Equation Matching: A Derivative-Free Learni…

Long Short-Term Memory (LSTM) has achieved state-of-the-art performances on a wide range of tasks. Its outstanding performance is guaranteed by the long-term memory ability which matches the sequential data perfectly and the gating…

We propose a general dynamic reduced-order modeling framework for typical experimental data: time-resolved sensor data and optional non-time-resolved PIV snapshots. This framework contains four steps. First, the sensor signals are lifted to…

Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…

We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…

Sparse signal representations based on linear combinations of learned atoms have been used to obtain state-of-the-art results in several practical signal processing applications. Approximation methods are needed to process high-dimensional…

SEMMS (Scalable Empirical-Bayes Model for Marker Selection) is a variable-selection procedure for generalized linear models that uses a three-component normal mixture prior on regression coefficients. In its original form, SEMMS assumes…

In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…

Various studies that address the compressed sensing problem with Multiple Measurement Vectors (MMVs) have been recently carried. These studies assume the vectors of the different channels to be jointly sparse. In this paper, we relax this…

Robust physics discovery is of great interest for many scientific and engineering fields. Inspired by the principle that a representative model is the one simplest possible, a new model selection criteria considering both model's Parsimony…

Model discovery aims to uncover governing differential equations of dynamical systems directly from experimental data. Benchmarking such methods is essential for tracking progress and understanding trade-offs in the field. While prior…

In recent years, knowledge graph embedding becomes a pretty hot research topic of artificial intelligence and plays increasingly vital roles in various downstream applications, such as recommendation and question answering. However,…

Neural Stochastic Differential Equations (Neural SDEs) have emerged as powerful mesh-free generative models for continuous stochastic processes, with critical applications in fields such as finance, physics, and biology. Previous…

Generally, discretization of partial differential equations (PDEs) creates a sequence of linear systems $A_k x_k = b_k, k = 0, 1, 2, ..., N$ with well-known and structured sparsity patterns. Preconditioners are often necessary to achieve…

We present a boosting-based method to learn additive Structural Equation Models (SEMs) from observational data, with a focus on the theoretical aspects of determining the causal order among variables. We introduce a family of score…

We propose Energy-based generator matching (EGM), a modality-agnostic approach to train generative models from energy functions in the absence of data. Extending the recently proposed generator matching, EGM enables training of arbitrary…

Predicting the behavior of ultra-large complex systems, from climate to biological and technological networks, is a central unsolved challenge. Existing approaches face a fundamental trade-off: equation discovery methods provide…

Large-scale association analysis between multivariate responses and predictors is of great practical importance, as exemplified by modern business applications including social media marketing and crisis management. Despite the rapid…

We investigate the use of sequence analysis for behavior modeling, emphasizing that sequential context often outweighs the value of aggregate features in understanding human behavior. We discuss framing common problems in fields like…

This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…

Data-driven methods have recently made great progress in the discovery of partial differential equations (PDEs) from spatial-temporal data. However, several challenges remain to be solved, including sparse noisy data, incomplete candidate…