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We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…
The concept of extended cloud requires efficient network infrastructure to support ecosystems reaching form the edge to the cloud(s). Standard approaches to network load balancing deliver static solutions that are insufficient for the…
Many real-world optimization problems are not naturally homogeneous vectors but composite design objects with heterogeneous parameters: integers, real values, Booleans, categoricals, complex-valued descriptors, and embedding vectors.…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
In this study, we investigate the computational complexity of some variants of generalized puzzles. We are provided with two sets S_1 and S_2 of polyominoes. The first puzzle asks us to form the same shape using polyominoes in S_1 and S_2.…
Evolutionary computation methods have been successfully applied to neural networks since two decades ago, while those methods cannot scale well to the modern deep neural networks due to the complicated architectures and large quantities of…
In this paper we introduce the so-called Generalized Naive Bayes structure as an extension of the Naive Bayes structure. We give a new greedy algorithm that finds a good fitting Generalized Naive Bayes (GNB) probability distribution. We…
Genetic Programming (GP) has found various applications. Understanding this type of algorithm from a theoretical point of view is a challenging task. The first results on the computational complexity of GP have been obtained for problems…
The theme of this book chapter is to discuss algorithms for identifying and reconstructing groups and clusters of galaxies out of the general galaxy distribution. I review the progress of detection techniques through time, from the very…
The puzzle method was introduced by Choi and Park as an effective method for finding non-singular characteristic maps over wedged simplicial complexes $K(J)$ obtained from a given simplicial complex $K$. We study further the mod 2 case of…
Robotic grasping is an essential and fundamental task and has been studied extensively over the past several decades. Traditional work analyzes physical models of the objects and computes force-closure grasps. Such methods require…
In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…
We introduce the Probabilistic Generative Adversarial Network (PGAN), a new GAN variant based on a new kind of objective function. The central idea is to integrate a probabilistic model (a Gaussian Mixture Model, in our case) into the GAN…
Neural architectures inspired by our own human cognitive system, such as the recently introduced world models, have been shown to outperform traditional deep reinforcement learning (RL) methods in a variety of different domains. Instead of…
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
Outlier recognition is a fundamental problem in data analysis and has attracted a great deal of attention in the past decades. However, most existing methods still suffer from several issues such as high time and space complexities or…
A new strategy for global geometry optimization of clusters is presented. Important features are a restriction of search space to favorable nearest-neighbor distance ranges, a suitable cluster growth representation with diminished…
An unconstrained crossword puzzle is a generalization of the constrained crossword problem. In this problem, only the word vocabulary, and optionally the grid dimensions are known. Hence, it not only requires the algorithm to determine the…
Geometry problem solving, a crucial aspect of mathematical reasoning, is vital across various domains, including education, the assessment of AI's mathematical abilities, and multimodal capability evaluation. The recent surge in deep…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…