Related papers: Testing that a Local Optimum of the Likelihood is …
We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions. Under restricted strong convexity on the loss and suitable regularity conditions on the…
This paper presents a novel strategy for high-fidelity image restoration by characterizing both local smoothness and nonlocal self-similarity of natural images in a unified statistical manner. The main contributions are three-folds. First,…
This paper present the mathematical fundaments and experimental study of an algorithm used to find the optimal position for the camera lens to obtain a maximum of details. This information can be further applied to a appropriate system to…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
Optimizing proper loss functions is popularly believed to yield predictors with good calibration properties; the intuition being that for such losses, the global optimum is to predict the ground-truth probabilities, which is indeed…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
In confirmatory clinical trials with small sample sizes, hypothesis tests based on asymptotic distributions are often not valid and exact non-parametric procedures are applied instead. However, the latter are based on discrete test…
The objective of this paper is to provide, for the problem of univariate symmetry (with respect to specified or unspecified location), a concept of optimality, and to construct tests achieving such optimality. This requires embedding…
We study a hypothesis testing problem in which data is compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
We present global convergence rates for a line-search method which is based on random first-order models and directions whose quality is ensured only with certain probability. We show that in terms of the order of the accuracy, the…
In several interesting applications one is faced with the problem of simultaneous binary hypothesis testing and parameter estimation. Although such joint problems are not infrequent, there exist no systematic analysis in the literature that…
Modern state estimation is often formulated as an optimization problem and solved using efficient local search methods. These methods at best guarantee convergence to local minima, but, in some cases, global optimality can also be…
Numerical optimization for the inverse design of photonic structures is a tool which is providing increasingly convincing results -- even though the wave nature of problems in photonics makes them particularly complex. In the meantime, the…
Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…
A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high…
When images are statistically described by a generative model we can use this information to develop optimum techniques for various image restoration problems as inpainting, super-resolution, image coloring, generative model inversion, etc.…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust…
Optimisation problems are ubiquitous in particle and astrophysics, and involve locating the optimum of a complicated function of many parameters that may be computationally expensive to evaluate. We describe a number of global optimisation…