Related papers: Fast Ergodic Search with Kernel Functions
This paper formulates the problem of Extremum Seeking for optimization of cost functions defined on Riemannian manifolds. We extend the conventional extremum seeking algorithms for optimization problems in Euclidean spaces to optimization…
Large Language Models (LLMs) have achieved impressive progress in natural language processing, but their limited ability to retain long-term context constrains performance on document-level or multi-turn tasks. Retrieval-Augmented…
To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison…
Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…
The searching procedure of neural architecture search (NAS) is notoriously time consuming and cost prohibitive.To make the search space continuous, most existing gradient-based NAS methods relax the categorical choice of a particular…
Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…
Approximate Nearest Neighbor (ANN) search in high-dimensional Euclidean spaces is a fundamental problem with a wide range of applications. However, there is currently no ANN method that performs well in both indexing and query answering…
In both industrial and service domains, a central benefit of the use of robots is their ability to quickly and reliably execute repetitive tasks. However, even relatively simple peg-in-hole tasks are typically subject to stochastic…
Spherical k-Means is frequently used to cluster document collections because it performs reasonably well in many settings and is computationally efficient. However, the time complexity increases linearly with the number of clusters k, which…
Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…
Ordinal embedding aims at finding a low dimensional representation of objects from a set of constraints of the form "item $j$ is closer to item $i$ than item $k$". Typically, each object is mapped onto a point vector in a low dimensional…
The challenge to fully exploit the potential of existing and upcoming scientific instruments like large single-dish radio telescopes is to process the collected massive data effectively and efficiently. As a "quasi 2D stencil computation"…
Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability…
We study the problem of searching for a target at some unknown location in $\mathbb{R}^d$ when additional information regarding the position of the target is available in the form of predictions. In our setting, predictions come as…
Establishing associations between the structure and the generalisation ability of deep neural networks (DNNs) is a challenging task in modern machine learning. Producing solutions to this challenge will bring progress both in the…
A methodology is developed for data analysis based on empirically constructed geodesic metric spaces. For a probability distribution, the length along a path between two points can be defined as the amount of probability mass accumulated…
Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…
This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows…
This work addresses approximate nearest neighbor search applied in the domain of large-scale image retrieval. Within the group testing framework we propose an efficient off-line construction of the search structures. The linear-time…
We present a computational study of a visualization method for invariant sets based on ergodic partition theory, first proposed in [1,2]. The algorithms for computation of the time averages of observables on phase space are developed and…