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Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
Entropically regularized optimal transport between probability measures supported on compact subsets of Euclidean space admits a representation as an information projection under moment inequality constraints. Exploiting this structure, I…
We study the regret performance of Sample Average Approximation (SAA) for data-driven newsvendor problems with general convex inventory costs. In literature, the optimality of SAA has not been fully established under both \alpha-global…
We show both adaptive and non-adaptive minimax rates of convergence for a family of weighted Laplacian-Eigenmap based nonparametric regression methods, when the true regression function belongs to a Sobolev space and the sampling density is…
The errors-in-variables (EIV) regression model, being more realistic by accounting for measurement errors in both the dependent and the independent variables, is widely adopted in applied sciences. The traditional EIV model estimators,…
We examine the rate of convergence of the Lasso estimator of lower dimensional components of the high-dimensional parameter. Under bounds on the $\ell_1$-norm on the worst possible sub-direction these rates are of order $\sqrt {|J| \log p /…
A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive…
Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…
Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex…
The Seemingly Unrelated Regressions (SUR) model is a wide used estimation procedure in econometrics, insurance and finance, where very often, the regression model contains more than one equation. Unknown parameters, regression coefficients…
Data valuation quantifies data importance, but existing methods cannot ensure validity in a single training process. The neural dynamic data valuation (NDDV) method [3] addresses this limitation. Based on NDDV, we are the first to explore…
While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an…
The classical hinge-loss support vector machines (SVMs) model is sensitive to outlier observations due to the unboundedness of its loss function. To circumvent this issue, recent studies have focused on non-convex loss functions, such as…
In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older…
Increasing practical interest has been shown in regression problems where the errors, or disturbances, are centred in a way that reflects particular characteristics of the mechanism that generated the data. In economics this occurs in…
We study the nonparametric estimation of the jump density of a renewal reward process from one discretely observed sample path over [0,T]. We consider the regime when the sampling rate goes to 0. The main difficulty is that a renewal reward…
It is shown that over-parameterized neural networks can achieve minimax optimal rates of convergence (up to logarithmic factors) for learning functions from certain smooth function classes, if the weights are suitably constrained or…
Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least…
Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…
We consider the framework of non-stationary Online Convex Optimization where a learner seeks to control its dynamic regret against an arbitrary sequence of comparators. When the loss functions are strongly convex or exp-concave, we…