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Existing error-bound-based analyses for stochastic algorithms that exhibit certain descent properties, such as randomized coordinate descent and randomized projection methods, are often limited in scope and typically lead to overly…
An application area of vertex enumeration problem (VEP) is the usage within objective space based linear/convex {vector} optimization algorithms whose aim is to generate (an approximation of) the Pareto frontier. In such algorithms, VEP,…
We study the problem of optimizing a function under a \emph{budgeted number of evaluations}. We only assume that the function is \emph{locally} smooth around one of its global optima. The difficulty of optimization is measured in terms of…
When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…
Practical identifiability is a critical concern in data-driven modeling of mathematical systems. In this paper, we propose a novel framework for practical identifiability analysis to evaluate parameter identifiability in mathematical models…
Accurately estimating decision boundaries in black box systems is critical when ensuring safety, quality, and feasibility in real-world applications. However, existing methods iteratively refine boundary estimates by sampling in regions of…
We study the eigenvalues and eigenfunctions of a differential operator that governs the asymptotic behavior of the unsupervised learning algorithm known as Locally Linear Embedding when a large data set is sampled from an interval or disc.…
The paper is concerned with a class of nonlinear free boundary problems, which are usually solved by variational methods based on primal (or primal-dual) variational settings. We deduce and investigate special relations (error identities).…
Predictability is an emerging metric that quantifies the highest possible prediction accuracy for a given time series, being widely utilized in assessing known prediction algorithms and characterizing intrinsic regularities in human…
We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to…
Edge detection is widely and fundamental feature used in various algorithms in computer vision to determine the edges in an image. The edge detection algorithm is used to determine the edges in an image which are further used by various…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
While texture analysis is largely addressed for images, the comparison of the geometric reliefs on surfaces embedded in the 3D space is still an open challenge. Starting from the Local Binary Pattern (LBP) description originally defined for…
We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. BnB-PEP poses the problem of finding the optimal…
Image classification is an essential part of computer vision which assigns a given input image to a specific category based on the similarity evaluation within given criteria. While promising classifiers can be obtained through deep…
One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data.…
The sign-constrained Stiefel manifold in $\mathbb{R}^{n\times r}$ is a segment of the Stiefel manifold with fixed signs (nonnegative or nonpositive) for some columns of the matrices. It includes the nonnegative Stiefel manifold as a special…
This paper presents an entirely unsupervised interest point training framework by jointly learning detector and descriptor, which takes an image as input and outputs a probability and a description for every image point. The objective of…
Edge detection (ED) is a fundamental perceptual process in computer vision, forming the structural basis for high-level reasoning tasks such as segmentation, recognition, and scene understanding. Despite substantial progress achieved by…