Related papers: Learning Sparse Dynamical Systems from a Single Sa…
We consider a problem of estimating a sparse group of sparse normal mean vectors. The proposed approach is based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their…
For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if $\rho=\lim\frac{p}{n}=0$, where $p$ is the dimension…
The Ho-Kalman algorithm has been widely employed for the identification of discrete-time linear time-invariant (LTI) systems. In this paper, we investigate the pole estimation error for the Ho-Kalman algorithm based on finite input/output…
The central problem we address in this work is estimation of the parameter support set S, the set of indices corresponding to nonzero parameters, in the context of a sparse parametric likelihood model for discrete multivariate time series.…
Sparsity-based approaches have been popular in many applications in image processing and imaging. Compressed sensing exploits the sparsity of images in a transform domain or dictionary to improve image recovery from undersampled…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…
Predicting how a dynamical unit evolves over time - how an individual ages, an epidemic spreads, or a physical system degrades - typically requires dense longitudinal tracking. When only extremely sparse or entirely cross-sectional data is…
How can we learn the laws underlying the dynamics of stochastic systems when their trajectories are sampled sparsely in time? Existing methods either require temporally resolved high-frequency observations, or rely on geometric arguments…
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…
Analyzing the urban trajectory in cities has become an important topic in data mining. How can we model the human mobility consisting of stay and travel from the raw trajectory data? How can we infer such a mobility model from the single…
Utilizing the information in observations of a complex system to make accurate predictions through a quantitative model when observations are completed at time $T$, requires an accurate estimate of the full state of the model at time $T$.…
In these lectures notes, we review our recent works addressing various problems of finding the nearest stable system to an unstable one. After the introduction, we provide some preliminary background, namely, defining Port-Hamiltonian…
In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…
We discuss two new methods of recovery of sparse signals from noisy observation based on $\ell_1$- minimization. They are closely related to the well-known techniques such as Lasso and Dantzig Selector. However, these estimators come with…
Identification of nonlinear dynamical systems has been popularized by sparse identification of the nonlinear dynamics (SINDy) via the sequentially thresholded least squares (STLS) algorithm. Many extensions SINDy have emerged in the…
System identification plays a crucial role in physics and machine learning for discovering governing equations directly from data. A powerful approach is the Sparse Identification of Nonlinear Dynamics (SINDy) method, which assumes that…
Enabling fast and accurate physical simulations with data has become an important area of computational physics to aid in inverse problems, design-optimization, uncertainty quantification, and other various decision-making applications.…
In this paper we revisit random linear under-determined systems with sparse solutions. We consider $\ell_1$ optimization heuristic known to work very well when used to solve these systems. A collection of fundamental results that relate to…
In this work, a new two-stage identification method based on dynamic programming and sparsity inducing is proposed for switched linear systems. Our method achieves sparsity inducing in the identification of switched linear systems by the…
We introduce a novel procedure that, given sparse data generated from a stationary deterministic nonlinear dynamical system, can characterize specific local and/or global dynamic behavior with rigorous probability guarantees. More…