Related papers: Testing that a Local Optimum of the Likelihood is …
The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
We propose the superiorization of incremental algorithms for tomographic image reconstruction. The resulting methods follow a better path in its way to finding the optimal solution for the maximum likelihood problem in the sense that they…
We propose a method for verifying that a given feasible point for a polynomial optimization problem is globally optimal. The approach relies on the Lasserre hierarchy and the result of Lasserre regarding the importance of the convexity of…
We investigate the problem of testing the global null in the high-dimensional regression models when the feature dimension $p$ grows proportionally to the number of observations $n$. Despite a number of prior work studying this problem,…
Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
Recently there has been sustained interest in modifying prediction algorithms to satisfy fairness constraints. These constraints are typically complex nonlinear functionals of the observed data distribution. Focusing on the path-specific…
We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for…
Combining test statistics from independent trials or experiments is a popular method of meta-analysis. However, there is very limited theoretical understanding of the power of the combined test, especially in high-dimensional models…
Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
We study finite element approximations of second-order elliptic problems with measure-valued right-hand sides supported on lower-dimensional sets. The exact solution generally lacks $H^1$-regularity due to the source singularity, which…
Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for…
This article concerns tests for location parameters in cases where the data dimension is larger than the sample size. We propose a family of tests based on the optimality arguments in Le Cam (1986) under elliptical symmetric. The asymptotic…
In numerous practical applications, especially in medical image reconstruction, it is often infeasible to obtain a large ensemble of ground-truth/measurement pairs for supervised learning. Therefore, it is imperative to develop unsupervised…
In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal control problems involve uncertainty, we need to use a few…
The optimization problem behind neural networks is highly non-convex. Training with stochastic gradient descent and variants requires careful parameter tuning and provides no guarantee to achieve the global optimum. In contrast we show…