Related papers: Simultaneous model discovery and state estimation …

We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…

To successfully work on variable selection, sparse model structure has become a basic assumption for all existing methods. However, this assumption is questionable as it is hard to hold in most of cases and none of existing methods may…

A greedy algorithm is proposed for sparse-sensor selection in reduced-order sensing that contains correlated noise in measurement. The sensor selection is carried out by maximizing the determinant of the Fisher information matrix in a…

The methodology discussed in this paper aims to enhance choice models' comprehensiveness and explanatory power for forecasting choice outcomes. To achieve these, we have developed a data-driven method that leverages machine learning…

The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…

Numerous practical medical problems often involve data that possess a combination of both sparse and non-sparse structures. Traditional penalized regularizations techniques, primarily designed for promoting sparsity, are inadequate to…

Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…

The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of…

A variational approach to reconstruction of phase and amplitude of a complex-valued object from Poissonian intensity observations is developed. The observation model corresponds to the typical optical setups with a phase modulation of…

The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…

In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated…

For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…

To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…

Designing sparse sampling strategies is one of the important components in having resilient estimation and control in networked systems as they make network design problems more cost-effective due to their reduced sampling requirements and…

Causal discovery between collections of time-series data can help diagnose causes of symptoms and hopefully prevent faults before they occur. However, reliable causal discovery can be very challenging, especially when the data acquisition…

The performance of machine learning and pattern recognition algorithms generally depends on data representation. That is why, much of the current effort in performing machine learning algorithms goes into the design of preprocessing…

The quasipotential function allows for comprehension and prediction of the escape mechanisms from metastable states in nonlinear dynamical systems. This function acts as a natural extension of the potential function for non-gradient systems…

Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…

We propose a general method called truncated gradient to induce sparsity in the weights of online learning algorithms with convex loss functions. This method has several essential properties: The degree of sparsity is continuous -- a…

The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis.…