Related papers: Computationally Efficient Estimators for Dimension…
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…
In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately…
This paper proposes a robust and computationally efficient estimation framework for fitting parametric distributions based on trimmed L-moments. Trimmed L-moments extend classical L-moment theory by downweighting or excluding extreme order…
This work is about parameter estimation for a fast-slow stochastic system with non-Gaussian $\alpha$-stable L\'evy noise. When the observations are only available for slow components, a system parameter is estimated and the accuracy for…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…
Stability selection is a widely adopted resampling-based framework for high-dimensional variable selection. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability…
Least absolute deviation regression is applied using a fixed number of points for all values of the index to estimate the index and scale parameter of the stable distribution using regression methods based on the empirical characteristic…
Phase estimation protocols provide a fundamental benchmark for the field of quantum metrology. The latter represents one of the most relevant applications of quantum theory, potentially enabling the capability of measuring unknown physical…
We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…
Robust methods, though ubiquitous in practice, are yet to be fully understood in the context of regularized estimation and high dimensions. Even simple questions become challenging very quickly. For example, classical statistical theory…
The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
The likelihood functions for discretely observed nonlinear continuous-time models based on stochastic differential equations are not available except for a few cases. Various parameter estimation techniques have been proposed, each with…
Robust estimators of location and dispersion are often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data outside an ellipsoid based in the associated Mahalanobis distance. Here…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
The main purpose of this article is to prove that, under certain assumptions in a linear prediction setting, optimal methods based upon model reduction and even an optimal predictor can be provided. The optimality is formulated in terms of…
With the advent of large-scale quantum annealing devices, several challenges have emerged. For example, it has been shown that the performance of a device can be significantly affected by several degrees of freedom when programming the…
The development of modern technology has enabled data collection of unprecedented size, which poses new challenges to many statistical estimation and inference problems. This paper studies the maximum score estimator of a semi-parametric…