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Inferring network structures remains an interesting question for its importance on the understanding and controlling collective dynamics of complex systems. The existing shrinking methods such as Lasso-type estimation can not suitably…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
Common regularization algorithms for linear regression, such as LASSO and Ridge regression, rely on a regularization hyperparameter that balances the tradeoff between minimizing the fitting error and the norm of the learned model…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression…
Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended…
As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…
Separation in logistic regression is a common problem causing failure of the iterative estimation process when finding maximum likelihood estimates. Firth's correction (FC) was proposed as a solution, providing estimates also in presence of…
We introduce a new online convex optimization algorithm that adaptively chooses its regularization function based on the loss functions observed so far. This is in contrast to previous algorithms that use a fixed regularization function…
In [1], the distributed linear-quadratic problem with fixed communication topology (DFT-LQ) and the sparse feedback LQ problem (SF-LQ) are formulated into a nonsmooth and nonconvex optimization problem with affine constraints. Moreover, a…
This paper presents a parametric solution to piecewise linear regression through the Adaptive Block Gradient Descent (ABGD) algorithm. The heart of the method is the parametrization of piecewise linear functions as the difference of…
It is well known that quantile regression model minimizes the portfolio extreme risk, whenever the attention is placed on the estimation of the response variable left quantiles. We show that, by considering the entire conditional…
Given a set of 2-dimensional (2-D) scattering points, which are usually obtained from the edge detection process, the aim of ellipse fitting is to construct an elliptic equation that best fits the collected observations. However, some of…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly…
Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm…
Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…
We provide theory for computing the lower semi-continuous convex envelope of functionals of the type f(x) plus an l2 misfit, and discuss applications to various non-convex optimization problems. The latter term is a data fit term whereas f…