Related papers: An information-based model selection criterion for…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…
We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and…
The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…
This work studies the theoretical rules of feature selection in linear discriminant analysis (LDA), and a new feature selection method is proposed for sparse linear discriminant analysis. An $l_1$ minimization method is used to select the…
The sparse identification of nonlinear dynamics (SINDy) approach can discover the governing equations of dynamical systems based on measurement data, where the dynamical model is identified as the sparse linear combination of the given…
Data-driven discovery of PDEs has made tremendous progress recently, and many canonical PDEs have been discovered successfully for proof-of-concept. However, determining the most proper PDE without prior references remains challenging in…
Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…
In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is…
Instruction tuning data are often quantity-saturated due to the large volume of data collection and fast model iteration, leaving data selection important but underexplored. Existing quality-driven data selection methods, such as LIMA…
In the classical setting of self-selection, the goal is to learn $k$ models, simultaneously from observations $(x^{(i)}, y^{(i)})$ where $y^{(i)}$ is the output of one of $k$ underlying models on input $x^{(i)}$. In contrast to mixture…
Sparse sampling schemes have the potential to dramatically reduce image acquisition time while simultaneously reducing radiation damage to samples. However, for a sparse sampling scheme to be useful it is important that we are able to…
Supervised learning algorithms are nowadays successfully scaling up to datasets that are very large in volume, leveraging the potential of in-memory cluster-computing Big Data frameworks. Still, massive datasets with a number of…
The demand of computational resources for the modeling process increases as the scale of the datasets does, since traditional approaches for regression involve inverting huge data matrices. The main problem relies on the large data size,…
We propose a parsimonious topic model for text corpora. In related models such as Latent Dirichlet Allocation (LDA), all words are modeled topic-specifically, even though many words occur with similar frequencies across different topics.…
We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…
As machine learning systems become democratized, it becomes increasingly important to help users easily debug their models. However, current data tools are still primitive when it comes to helping users trace model performance problems all…
This paper addresses the problem of data-driven model discrimination for unknown switched systems with unknown linear temporal logic (LTL) specifications, representing tasks, that govern their mode sequences, where only sampled data of the…
The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…
Discovering the governing equations of a dynamical system from observed trajectories provides deeper insight into its structure than mere prediction of future states. We present a data-driven approach to model discovery based on…
We consider the high-dimensional discriminant analysis problem. For this problem, different methods have been proposed and justified by establishing exact convergence rates for the classification risk, as well as the l2 convergence results…