Related papers: Probabilistic Voronoi Diagrams for Probabilistic M…
In the past decades, great progress has been made in the field of optical and particle-based measurement techniques for experimental analysis of fluid flows. Particle Image Velocimetry (PIV) technique is widely used to identify flow…
We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other…
The fastest indexes for Approximate Nearest Neighbor Search today are also the slowest to build: graph-based methods like HNSW and Vamana achieve state-of-the-art query performance but have large construction times due to relying on…
K-Nearest Neighbours (k-NN) is a popular classification and regression algorithm, yet one of its main limitations is the difficulty in choosing the number of neighbours. We present a Bayesian algorithm to compute the posterior probability…
Identifying safe areas is a key point to guarantee trust for systems that are based on Deep Neural Networks (DNNs). To this end, we introduce the AllDNN-Verification problem: given a safety property and a DNN, enumerate the set of all the…
Similarity search is a fundamental building block for information retrieval on a variety of datasets. The notion of a neighbor is often based on binary considerations, such as the k nearest neighbors. However, considering that data is often…
Approximate nearest neighbor (ANN) search is a fundamental problem in many areas of data mining, machine learning and computer vision. The performance of traditional hierarchical structure (tree) based methods decreases as the…
Worst-case dynamic PDN noise analysis is an essential step in PDN sign-off to ensure the performance and reliability of chips. However, with the growing PDN size and increasing scenarios to be validated, it becomes very time- and…
Particle Image Velocimetry (PIV) is a widely used technique for flow measurement that traditionally relies on cross-correlation to track the displacement. Recent advances in deep learning-based methods have significantly improved the…
We investigate the classes of functions whose minimization diagrams can be approximated efficiently in \Re^d. We present a general framework and a data-structure that can be used to approximate the minimization diagram of such functions.…
Deep neural networks are frequently used by autonomous systems for their ability to learn complex, non-linear data patterns and make accurate predictions in dynamic environments. However, their use as black boxes introduces risks as the…
Machine learning models perform well across domains such as diagnostics, weather forecasting, NLP, and autonomous driving, but their limited uncertainty handling restricts use in safety-critical settings. Traditional neural networks often…
In this paper, we propose an online path planning architecture that extends the model predictive control (MPC) formulation to consider future location uncertainties for safer navigation through cluttered environments. Our algorithm combines…
Anomaly detection aims to identify data instances that deviate significantly from majority of data, which has been widely used in fraud detection, network security, and industrial quality control. Existing methods struggle with datasets…
In many real-world applications such as business planning and sensor data monitoring, one important, yet challenging, the task is to rank objects(e.g., products, documents, or spatial objects) based on their ranking scores and efficiently…
Improving on the Voronoi cell based techniques of Micciancio and Voulgaris (SIAM J. Comp. 13), and Sommer, Feder and Shalvi (SIAM J. Disc. Math. 09), we give a Las Vegas $\tilde{O}(2^n)$ expected time and space algorithm for CVPP (the…
Probabilistic forecasts are essential for various downstream applications such as business development, traffic planning, and electrical grid balancing. Many of these probabilistic forecasts are performed on time series data that contain…
Given a countable set of points in a continuous space, Voronoi tessellation is an intuitive way of partitioning the space according to the distance to the individual points. As a powerful approach to obtain structural information, it has a…
This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded…
We study the problem of processing continuous k nearest neighbor (CkNN) queries over moving objects on road networks, which is an essential operation in a variety of applications. We are particularly concerned with scenarios where the…