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System stabilization via policy gradient (PG) methods has drawn increasing attention in both control and machine learning communities. In this paper, we study their convergence and sample complexity for stabilizing linear time-invariant…
Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…
Generalized method of moments estimators based on higher-order moment conditions derived from independent shocks can be used to identify and estimate the simultaneous interaction in structural vector autoregressions. This study highlights…
Recently, numerous end-to-end optimized image compression neural networks have been developed and proved themselves as leaders in rate-distortion performance. The main strength of these learnt compression methods is in powerful nonlinear…
Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random…
We study the problem of multiclass classification for settings where data features $\mathbf{x}$ and their labels $\mathbf{y}$ are uncertain. We identify that distributionally robust one-vs-all (OVA) classifiers often struggle in settings…
One-dimensional convolution is a widely used deep learning technique in prestack amplitude variation with offset (AVO) inversion; however, it lacks lateral continuity. Although two-dimensional convolution improves lateral continuity, due to…
In many applications, we have access to the complete dataset but are only interested in the prediction of a particular region of predictor variables. A standard approach is to find the globally best modeling method from a set of candidate…
In the presence of confounders, the ordinary least squares (OLS) estimator is known to be biased. This problem can be remedied by using the two-stage least squares (TSLS) estimator, based on the availability of valid instrumental variables…
This paper develops theoretical results regarding noisy 1-bit compressed sensing and sparse binomial regression. We show that a single convex program gives an accurate estimate of the signal, or coefficient vector, for both of these models.…
Spontaneous wavefunction collapse models offer a solution to the quantum measurement problem, by modifying the Schr\"odinger equation with nonlinear and stochastic terms. The Continuous Spontaneous Localisation (CSL) model is the most…
This paper investigates a partially linear spatial autoregressive panel data model that incorporates fixed effects, constant and time-varying regression coefficients, and a time-varying spatial lag coefficient. A two-stage least squares…
In the first part of this work, we develop a novel scheme for solving nonparametric regression problems. That is the approximation of possibly low regular and noised functions from the knowledge of their approximate values given at some…
Given any domain $X\subseteq \mathbb{R}^d$ and a probability measure $\rho$ on $X$, we study the problem of approximating in $L^2(X,\rho)$ a given function $u:X\to\mathbb{R}$, using its noiseless pointwise evaluations at random samples. For…
We consider the problem of learning linear prediction models with model misspecification bias. In such case, the collinearity among input variables may inflate the error of parameter estimation, resulting in instability of prediction…
Support vector machine (SVM) has attracted great attentions for the last two decades due to its extensive applications, and thus numerous optimization models have been proposed. To distinguish all of them, in this paper, we introduce a new…
The linear Support Vector Machine (SVM) is a classic classification technique in machine learning. Motivated by applications in modern high dimensional statistics, we consider penalized SVM problems involving the minimization of a…
Relevance vector machine (RVM) can be seen as a probabilistic version of support vector machines which is able to produce sparse solutions by linearly weighting a small number of basis functions instead using all of them. Regardless of a…
Spline quantile regression (SQR) is a method introduced recently by Li and Megiddo (2026) for linear quantile regression where the regression coefficients are treated as smooth functions of the quantile level. With the coefficients…
A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward its grand mean. In this paper, a more general…