相关论文: Using Spectral Submanifolds for Optimal Mode Selec…

Monotonicity constraints are powerful regularizers in statistical modelling. They can support fairness in computer-aided decision making and increase plausibility in data-driven scientific models. The seminal min-max (MM) neural network…

When analyzing parametric statistical models, a useful approach consists in modeling geometrically the parameter space. However, even for very simple and commonly used hierarchical models like statistical mixtures or stochastic deep neural…

State space models (SSM) have been widely applied for the analysis and visualization of large sequential datasets. Sequential Monte Carlo (SMC) is a very popular particle-based method to sample latent states from intractable posteriors.…

The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $\mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the…

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

Stochastic descent methods (of the gradient and mirror varieties) have become increasingly popular in optimization. In fact, it is now widely recognized that the success of deep learning is not only due to the special deep architecture of…

In recent years, feature selection has become a challenging problem in several machine learning fields, such as classification problems. Support Vector Machine (SVM) is a well-known technique applied in classification tasks. Various…

State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

Recent advances in machine unlearning have focused on developing algorithms to remove specific training samples from a trained model. In contrast, we observe that not all models are equally easy to unlearn. Hence, we introduce a family of…

Hidden Markov models (HMMs) are widely used statistical models for modeling sequential data. The parameter estimation for HMMs from time series data is an important learning problem. The predominant methods for parameter estimation are…

We study control systems invariant under a Lie group with application to the problem of nonlinear trajectory planning. A theory of symmetry reduction of exterior differential systems is employed to demonstrate how symmetry reduction and…

Statistical shape modeling (SSM) characterizes anatomical variations in a population of shapes generated from medical images. SSM requires consistent shape representation across samples in shape cohort. Establishing this representation…

State space models (SSMs) leverage linear, time-invariant (LTI) systems to effectively learn sequences with long-range dependencies. By analyzing the transfer functions of LTI systems, we find that SSMs exhibit an implicit bias toward…

Molecular dynamics simulations are indispensable for exploring the behavior of atoms and molecules. Grounded in quantum mechanical principles, quantum molecular dynamics provides high predictive power but its computational cost is dominated…

Hyperspectral images (HSI) contain a wealth of information over hundreds of contiguous spectral bands, making it possible to classify materials through subtle spectral discrepancies. However, the classification of this rich spectral…

This paper proposes an approach, Spectral Dynamics Embedding Control (SDEC), to optimal control for nonlinear stochastic systems. This method reveals an infinite-dimensional feature representation induced by the system's nonlinear…

In this article, we propose a new algorithm for supervised learning methods, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset of the original variables, an ideal…

Intelligent spectrum management is crucial for improving spectrum efficiency and achieving secure utilization of spectrum resources. However, existing intelligent spectrum management methods, typically based on small-scale models, suffer…

Recent advances in optimization methods used for training convolutional neural networks (CNNs) with kernels, which are normalized according to particular constraints, have shown remarkable success. This work introduces an approach for…