Related papers: Theoretical bounds on data requirements for the ra…

The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to…

Current synoptic sky surveys monitor large areas of the sky to find variable and transient astronomical sources. As the number of detections per night at a single telescope easily exceeds several thousand, current detection pipelines make…

Neural representations have shown spectacular ability to compress complex signals in a fraction of the raw data size. In 3D computer graphics, the bulk of a scene's memory usage is due to polygons and textures, making them ideal candidates…

Convex codes were recently introduced as models for neural codes in the brain. Any convex code $\C$ has an associated minimal embedding dimension $d(\C)$, which is the minimal Euclidean space dimension such that the code can be realized by…

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…

Understanding the surrounding environment of the vehicle is still one of the challenges for autonomous driving. This paper addresses 360-degree road scene semantic segmentation using surround view cameras, which are widely equipped in…

The problem of determining finite subsets of characteristic planar model sets (mathematical quasicrystals) $\varLambda$, called cyclotomic model sets, by parallel $X$-rays is considered. Here, an $X$-ray in direction $u$ of a finite subset…

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…

Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks. Many of these methods, however, learn only closed surfaces and are…

This paper investigates the relationship between the universal approximation property of deep neural networks and topological characteristics of datasets. Our primary contribution is to introduce data topology-dependent upper bounds on the…

This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…

Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for…

Multiclass neural networks are a common tool in modern unsupervised domain adaptation, yet an appropriate theoretical description for their non-uniform sample complexity is lacking in the adaptation literature. To fill this gap, we propose…

Surface inspection systems are an important application domain for computer vision, as they are used for defect detection and classification in the manufacturing industry. Existing systems use hand-crafted features which require extensive…

The restriction problem is better understood for hypersurfaces and recent progresses have been made by bilinear and multilinear approaches and most recently polynomial partitioning method which is combined with those estimates. However, for…

Tree convex sets refer to a collection of sets such that each set in the collection is a subtree of a tree whose nodes are the elements of these sets. They extend the concept of row convex sets each of which is an interval over a total…

Approximating convex bodies is a fundamental question in geometry, which has a wide variety of applications. Given a convex body $K$ in $\textbf{R}^d$ for fixed $d$, the objective is to minimize the number of facets of an approximating…

Approximating convex bodies is a fundamental problem in geometry. Given a convex body $K$ in $\mathbb{R}^d$ for a fixed dimension $d$, the objective is to minimize the number of facets of an approximating polytope for a given Hausdorff…

In this study, a novel machine learning algorithm, restricted Boltzmann machine (RBM), is introduced. The algorithm is applied for the spectral classification in astronomy. RBM is a bipartite generative graphical model with two separate…

This paper argues that DNNs implement a computational Occam's razor -- finding the `simplest' algorithm that fits the data -- and that this could explain their incredible and wide-ranging success over more traditional statistical methods.…