Related papers: Tree-Wasserstein Distance for High Dimensional Dat…
We present a framework that allows for the non-asymptotic study of the $2$-Wasserstein distance between the invariant distribution of an ergodic stochastic differential equation and the distribution of its numerical approximation in the…
Clustering is a data analysis method for extracting knowledge by discovering groups of data called clusters. Among these methods, state-of-the-art density-based clustering methods have proven to be effective for arbitrary-shaped clusters.…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
Despite the notable advancements in numerous Transformer-based models, the task of long multi-horizon time series forecasting remains a persistent challenge, especially towards explainability. Focusing on commonly used saliency maps in…
How to extract useful insights from data is always a challenge, especially if the data is multidimensional. Often, the data can be organized according to certain hierarchical structure that are stemmed either from data collection process or…
Smoothing and filtering two-dimensional sequences are fundamental tasks in fields such as computer vision. Conventional filtering algorithms often rely on the selection of the filtering window, limiting their applicability in certain…
Lightweight Temporal Compression (LTC) is among the lossy stream compression methods that provide the highest compression rate for the lowest CPU and memory consumption. As such, it is well suited to compress data streams in…
While time series prediction is an important, actively studied problem, the predictive accuracy of time series models is complicated by non-stationarity. We develop a fast and effective approach to allow for non-stationarity in the…
Trajectory similarity is a cornerstone of trajectory data management and analysis. Traditional similarity functions often suffer from high computational complexity and a reliance on specific distance metrics, prompting a shift towards deep…
The Gromov--Wasserstein (GW) distance and its fused extension (FGW) are powerful tools for comparing heterogeneous data. Their computation is, however, challenging since both distances are based on non-convex, quadratic optimal transport…
For more than three decades, measurement of terrace width distributions (TWDs) of vicinal crystal surfaces have been recognized as arguably the best way to determine the dimensionless strength $\tilde{A}$ of the elastic repulsion between…
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…
Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation…
The synergy between extremely large-scale antenna arrays and terahertz technology in sixth-generation networks establishes a near-field wideband transmission environment, enabling the generation of highly focused beams. To leverage this…
Dimension reduction (DR) methods provide systematic approaches for analyzing high-dimensional data. A key requirement for DR is to incorporate global dependencies among original and embedded samples while preserving clusters in the…
In recent years, reversible data hiding has attracted much more attention than before. Reversibility signifies that the original media can be recovered without any loss from the marked media after extracting the embedded message. This paper…
Determining the appropriate number of clusters in unsupervised learning is a central problem in statistics and data science. Traditional validity indices such as Calinski-Harabasz, Silhouette, and Davies-Bouldin-depend on centroid-based…
Discrete diffusion models have recently shown great promise for modeling complex discrete data, with masked diffusion models (MDMs) offering a compelling trade-off between quality and generation speed. MDMs denoise by progressively…
Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…
Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way…