Related papers: Fast Ergodic Search with Kernel Functions
This paper develops KL-Ergodic Exploration from Equilibrium ($\text{KL-E}^3$), a method for robotic systems to integrate stability into actively generating informative measurements through ergodic exploration. Ergodic exploration enables…
We study the following range searching problem in high-dimensional Euclidean spaces: given a finite set $P\subset \mathbb{R}^d$, where each $p\in P$ is assigned a weight $w_p$, and radius $r>0$, we need to preprocess $P$ into a data…
Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have…
Clustering, as an unsupervised technique, plays a pivotal role in various data analysis applications. Among clustering algorithms, Spectral Clustering on Euclidean Spaces has been extensively studied. However, with the rapid evolution of…
We formulate and optimally solve a new generalized Set Similarity Search problem, which assumes the size of the database and query sets are known in advance. By creating polylog copies of our data-structure, we optimally solve any symmetric…
We make the first steps towards an understanding of the ergodic properties of a rational map defined over a complete algebraically closed non-archimedean field. For such a rational map R, we construct a natural invariant probability measure…
Existing high-dimensional Bayesian optimization (BO) methods aim to overcome the curse of dimensionality by carefully encoding structural assumptions, from locality to sparsity to smoothness, into the optimization procedure. Surprisingly,…
Understanding and explaining the predictions of Graph Neural Networks (GNNs), is crucial for enhancing their safety and trustworthiness. Subgraph-level explanations are gaining attention for their intuitive appeal. However, most existing…
Random walk based node embedding algorithms learn vector representations of nodes by optimizing an objective function of node embedding vectors and skip-bigram statistics computed from random walks on the network. They have been applied to…
The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…
We propose a family of search directions based on primal-dual entropy in the context of interior-point methods for linear optimization. We show that by using entropy based search directions in the predictor step of a predictor-corrector…
We develop an algorithm to explore an environment to generate a measurement model for use in future localization tasks. Ergodic exploration with respect to the likelihood of a particular class of measurement (e.g., a contact detection…
Gaussian Process (GP) kernels are central to Bayesian optimization (BO), yet designing effective kernels for high-dimensional problems still relies on extensive manual engineering. Existing automated approaches struggle in high dimensions…
In the d-Euclidean Distance Matrix Completion (d-EDMC) problem, one aims to determine whether a given partial matrix of pairwise distances can be extended to a full Euclidean distance matrix in d dimensions. This problem is a cornerstone of…
We propose an approximation algorithm for efficient correlation search in time series data. In our method, we use Fourier transform and neural network to embed time series into a low-dimensional Euclidean space. The given space is learned…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…
The mathematical definitions of distinct concepts that are needed in building an ergodicity detection algorithm are introduced in a framework. This algorithmic framework is expressed in a discrete setting in an accessible manner for broader…
Unconstrained optimization problems are typically solved using iterative methods, which often depend on line search techniques to determine optimal step lengths in each iteration. This paper introduces a novel line search approach.…
Many important geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given a set of relative measurements between them. This problem is typically formulated as…