Related papers: The Bregman Variational Dual-Tree Framework

Decision diagrams (DDs) have emerged as an efficient tool for simulating quantum circuits due to their capacity to exploit data redundancies in quantum states and quantum operations, enabling the efficient computation of probability…

A (Euclidean) greedy drawing of a graph is a drawing in which, for any two vertices $s,t$ ($s \neq t$), there is a neighbor vertex of $s$ that is closer to $t$ than to $s$ in the Euclidean distance. Greedy drawings are important in the…

We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…

Now a days many algorithms are invented or being inventing to find the solution for Euclidean Minimum Spanning Tree, EMST, problem, as its applicability is increasing in much wide range of fields containing spatial or spatio temporal data…

Proximities are at the heart of almost all machine learning methods. If the input data are given as numerical vectors of equal lengths, euclidean distance, or a Hilbertian inner product is frequently used in modeling algorithms. In a more…

Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these,…

A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a…

The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value…

Learning useful representations is a key ingredient to the success of modern machine learning. Currently, representation learning mostly relies on embedding data into Euclidean space. However, recent work has shown that data in some domains…

Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…

There is a strong interest in studying the correspondence between Euclidean quantum fields and neural networks. This correspondence takes different forms depending on the type of networks considered. In this work, we study this…

Nowadays with a growing number of online controlling systems in the organization and also a high demand of monitoring and stats facilities that uses data streams to log and control their subsystems, data stream mining becomes more and more…

In this work, we propose a novel Bregman ADMM with nonlinear dual update to solve the Bethe variational problem (BVP), a key optimization formulation in graphical models and statistical physics. Our algorithm provides rigorous convergence…

Analyzing changes in network evolution is central to statistical network inference, as underscored by recent challenges of predicting and distinguishing pandemic-induced transformations in organizational and communication networks. We…

The performance of unsupervised methods such as clustering depends on the choice of distance metric between features, or ground metric. Commonly, ground metrics are decided with heuristics or learned via supervised algorithms. However,…

Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…

Many probabilistic models of interest in scientific computing and machine learning have expensive, black-box likelihoods that prevent the application of standard techniques for Bayesian inference, such as MCMC, which would require access to…

Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…

In this paper, we present a new algorithm that extends RRT* and RT-RRT* for online path planning in complex, dynamic environments. Sampling-based approaches often perform poorly in environments with narrow passages, a feature common to many…

Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…