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We study the semiparametric efficient estimation of a class of linear functionals in settings where a complete multivariate dataset is supplemented by additional datasets recording subsets of the variables of interest. These datasets are…
We consider the exact solution of problem $(QP)$ that consists in minimizing a quadratic function subject to quadratic constraints. Starting from the classical convex relaxation that uses the McCormick's envelopes, we introduce 12…
Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. This…
Let $\mathcal{P} \subset [0,1)^S$ be a finite point set of cardinality $N$ in an $S$-dimensional cube, and let $f:[0,1)^S \to \mathbb{R}$ be an integrable function. A QMC integration of $f$ by $\mathcal{P}$ is the average of values of $f$…
Practitioners wishing to experience the efficiency gains from using low discrepancy sequences need correct, robust, well-written software. This article, based on our MCQMC 2020 tutorial, describes some of the better quasi-Monte Carlo (QMC)…
The problem of minimizing an entropy functional subject to linear constraints is a useful example of partially finite convex programming. In the 1990s, Borwein and Lewis provided broad and easy-to-verify conditions that guarantee strong…
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…
In this paper we present a new multilevel quasi-interpolation algorithm for smooth periodic functions using scaled Gaussians as basis functions. Recent research in this area has focussed upon implementations using basis function with finite…
A control in feedback form is derived for linear quadratic, time-invariant optimal control problems subject to parabolic partial differential equations with coefficients depending on a countably infinite number of uncertain parameters. It…
Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…
In this paper, we study the adaptive submodular cover problem under the worst-case setting. This problem generalizes many previously studied problems, namely, the pool-based active learning and the stochastic submodular set cover. The input…
Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…
Real-world machine learning applications may require functions that are fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for…
In structured prediction problems where we have indirect supervision of the output, maximum marginal likelihood faces two computational obstacles: non-convexity of the objective and intractability of even a single gradient computation. In…
We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free…
A longstanding problem related to floating-point implementation of numerical programs is to provide efficient yet precise analysis of output errors. We present a framework to compute lower bounds on largest absolute roundoff errors, for a…
We study the off-policy evaluation (OPE) problem in an infinite-horizon Markov decision process with continuous states and actions. We recast the $Q$-function estimation into a special form of the nonparametric instrumental variables (NPIV)…
In a recent paper by the authors, it is shown that there exists a quasi-Monte Carlo (QMC) rule which achieves the best possible rate of convergence for numerical integration in a reproducing kernel Hilbert space consisting of smooth…
Estimation of convex functions finds broad applications in engineering and science, while convex shape constraint gives rise to numerous challenges in asymptotic performance analysis. This paper is devoted to minimax optimal estimation of…
We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to…