Related papers: Optimization from Structured Samples for Coverage …

We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated…

The problem we consider is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust…

We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic…

We formulate selecting the best optimizing system (SBOS) problems and provide solutions for those problems. In an SBOS problem, a finite number of systems are contenders. Inside each system, a continuous decision variable affects the…

In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We…

For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…

We address an optimization problem where the cost function is the expectation of a random mapping. To tackle the problem two approaches based on the approximation of the objective function by consensus-based particle optimization methods on…

Score-based diffusion models have become a foundational paradigm for modern generative modeling, demonstrating exceptional capability in generating samples from complex high-dimensional distributions. Despite the dominant adoption of…

Nowadays, sampling-based Approximate Query Processing (AQP) is widely regarded as a promising way to achieve interactivity in big data analytics. To build such an AQP system, finding the minimal sample size for a query regarding given error…

Particle-optimization-based sampling (POS) is a recently developed effective sampling technique that interactively updates a set of particles. A representative algorithm is the Stein variational gradient descent (SVGD). We prove, under…

We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using…

The stochastic knapsack problem is the stochastic variant of the classical knapsack problem in which the algorithm designer is given a a knapsack with a given capacity and a collection of items where each item is associated with a profit…

Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter's distribution or…

Sign-Perturbed Sum (SPS) is a powerful finite-sample system identification algorithm which can construct confidence regions for the true data generating system with exact coverage probabilities, for any finite sample size. SPS was developed…

Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where…

In many fairness and distribution robustness problems, one has access to labeled data from multiple source distributions yet the test data may come from an arbitrary member or a mixture of them. We study the problem of constructing a…

Transfer learning is an essential technique for many machine learning/AI models of complex structures such as large language models and generative AI. The essence of transfer learning is to leverage knowledge from resolved source tasks for…

Deep learning models for medical imaging often exhibit overconfidence, creating safety risks in ambiguous diagnostic scenarios. While Conformal Prediction (CP) provides distribution-free statistical guarantees, standard methods such as…