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We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence…
This article introduces a functional method for lower-dimensional smooth representations in terms of time-varying dissimilarities. The method incorporates dissimilarity representation in multidimensional scaling and smoothness approach of…
The present work investigates the segmentation of textures by formulating it as a strongly convex optimization problem, aiming to favor piecewise constancy of fractal features (local variance and local regularity) widely used to model…
In computer graphics, smooth data reconstruction on 2D or 3D manifolds usually refers to subdivision problems. Such a method is only valid based on dense sample points. The manifold usually needs to be triangulated into meshes (or patches)…
We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique…
We consider solving nonconvex composite optimization problems in which the sum of a smooth function and a nonsmooth function is minimized. Many of convergence analyses of proximal gradient-type methods rely on global descent property…
This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…
Deep learning models benefit from rich (e.g., multi-modal) input features. However, multimodal models might be challenging to deploy, because some inputs may be missing at inference. Current popular solutions include marginalization,…
The recently introduced Gradient Methods with Memory use a subset of the past oracle information to create an accurate model of the objective function that enables them to surpass the Gradient Method in practical performance. The model…
In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly…
This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…
Pushing forward the understanding of general non-unitary dynamics in controlled quantum platforms has been fueled by the recent discovery of measurement-induced phases and phase transitions. So far, these transitions remained largely…
3D volumetric reconstruction from incomplete or noisy measurements is a fundamental problem in medical imaging and computational tomography. Deep image prior (DIP)-based methods have recently shown strong capability for solving inverse…
Some prominent discretisation methods such as finite elements provide a way to approximate a function of $d$ variables from $n$ values it takes on the nodes $x_i$ of the corresponding mesh. The accuracy is $n^{-s_a/d}$ in $L^2$-norm, where…
Self-supervised multi-frame monocular depth estimation relies on the geometric consistency between successive frames under the assumption of a static scene. However, the presence of moving objects in dynamic scenes introduces inevitable…
This work introduces the Gaussian integration to address a smoothing problem of a nonlinear stochastic state space model. The probability densities of states at each time instant are assumed to be Gaussian, and their means and covariances…
A significant portion of the data today, e.g, social networks, web connections, etc., can be modeled by graphs. A proper analysis of graphs with Machine Learning (ML) algorithms has the potential to yield far-reaching insights into many…
Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…