Related papers: Linear Spherical Sliced Optimal Transport: A Fast …
The inherent safety alignment of Large Language Models (LLMs) is prone to erosion during fine-tuning, even when using seemingly innocuous datasets. While existing defenses attempt to mitigate this via data selection, they typically rely on…
We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named…
The growing use of wide angle image capture devices and the need for fast and accurate image analysis in computer visions have enforced the need for dedicated under-representation approaches. Most recent decomposition methods segment an…
Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…
We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency.…
Robust road segmentation is a key challenge in self-driving research. Though many image-based methods have been studied and high performances in dataset evaluations have been reported, developing robust and reliable road segmentation is…
We introduce an innovative method for incremental nonparametric probabilistic inference in high-dimensional state spaces. Our approach leverages \slices from high-dimensional surfaces to efficiently approximate posterior distributions of…
In medical imaging, scans often reveal objects with varied contrasts but consistent internal intensities or textures. This characteristic enables the use of low-frequency approximations for tasks such as segmentation and deformation field…
Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this…
We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
We propose a novel amortized optimization method for predicting optimal transport (OT) plans across multiple pairs of measures by leveraging Kantorovich potentials derived from sliced OT. We introduce two amortization strategies:…
Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis. In numerous applications, it is necessary to align and jointly embed multiple datasets from different studies or experimental…
Traditional multi-view learning methods often rely on two assumptions: ($i$) the samples in different views are well-aligned, and ($ii$) their representations in latent space obey the same distribution. Unfortunately, these two assumptions…
Most of existing superpixel methods are designed to segment standard planar images as pre-processing for computer vision pipelines. Nevertheless, the increasing number of applications based on wide angle capture devices, mainly generating…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…
We propose a new unsupervised anomaly detection method based on the sliced-Wasserstein distance for training data selection in machine learning approaches. Our filtering technique is interesting for decision-making pipelines deploying…
In this essay, we discuss the notion of optimal transport on geodesic measure spaces and the associated (2-)Wasserstein distance. We then examine displacement convexity of the entropy functional on the space of probability measures. In…
Roof-mounted spinning LiDAR sensors are widely used by autonomous vehicles. However, most semantic datasets and algorithms used for LiDAR sequence segmentation operate on $360^\circ$ frames, causing an acquisition latency incompatible with…
Salient object detection (SOD) aims to segment visually prominent regions in images and serves as a foundational task for various computer vision applications. We posit that SOD can now reach near-supervised accuracy without a single…