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Symbolic regression (SR) is an area of interpretable machine learning that aims to identify mathematical expressions, often composed of simple functions, that best fit in a given set of covariates $X$ and response $y$. In recent years, deep…
To improve the robustness of graph neural networks (GNN), graph structure learning (GSL) has attracted great interest due to the pervasiveness of noise in graph data. Many approaches have been proposed for GSL to jointly learn a clean graph…
We present a sparse analogue to stochastic gradient descent that is guaranteed to perform well under similar conditions to the lasso. In the linear regression setup with irrepresentable noise features, our algorithm recovers the support set…
For the sparse vector model, we consider estimation of the target vector, of its L2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with…
In this paper we develop efficient first-order algorithms for the generalized trust-region subproblem (GTRS), which has applications in signal processing, compressed sensing, and engineering. Although the GTRS, as stated, is nonlinear and…
In sparse linear regression, the SLOPE estimator generalizes LASSO by penalizing different coordinates of the estimate according to their magnitudes. In this paper, we present a precise performance characterization of SLOPE in the…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…
Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…
Decision trees are important both as interpretable models amenable to high-stakes decision-making, and as building blocks of ensemble methods such as random forests and gradient boosting. Their statistical properties, however, are not well…
A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…
We develop a scalable algorithmic framework for sparse convex quantile regression (SCQR), addressing key computational challenges in the literature. Enhancing the classical CQR model, we introduce L2-norm regularization and an…
We consider distributed estimation of a Gaussian source in a heterogenous bandwidth constrained sensor network, where the source is corrupted by independent multiplicative and additive observation noises, with incomplete statistical…
Graph embedding is gaining its popularity for link prediction in complex networks and achieving excellent performance. However, limited work has been done in sparse networks that represent most of real networks. In this paper, we propose a…
Gaussian graphical regression is a powerful means that regresses the precision matrix of a Gaussian graphical model on covariates, permitting the numbers of the response variables and covariates to far exceed the sample size. Model fitting…
In this paper, we develop a new sequential regression modeling approach for data streams. Data streams are commonly found around us, e.g in a retail enterprise sales data is continuously collected every day. A demand forecasting model is an…
In recent years, a rich variety of regularization procedures have been proposed for high dimensional regression problems. However, tuning parameter choice and computational efficiency in ultra-high dimensional problems remain vexing issues.…
Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a discrete graphical model given i.i.d samples from its joint…
We study a high-dimensional regression model. Aim is to construct a confidence set for a given group of regression coefficients, treating all other regression coefficients as nuisance parameters. We apply a one-step procedure with the…
Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can…