Related papers: SNEkhorn: Dimension Reduction with Symmetric Entro…
Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…
The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…
Current machine learning systems are brittle in the face of distribution shifts (DS), where the target distribution that the system is tested on differs from the source distribution used to train the system. This problem of robustness to DS…
Designing optimal soft modular robots is difficult, due to non-trivial interactions between morphology and controller. Evolutionary algorithms (EAs), combined with physical simulators, represent a valid tool to overcome this issue. In this…
The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…
Stochastic Neighbor Embedding (SNE) methods minimize the divergence between the similarity matrix of a high-dimensional data set and its counterpart from a low-dimensional embedding, leading to widely applied tools for data visualization.…
Entity alignment (EA) plays an important role in automatically integrating knowledge graphs (KGs) from multiple sources. Recent approaches based on Graph Neural Network (GNN) obtain entity representation from relation information and have…
Entropically regularized optimal transport between probability measures supported on compact subsets of Euclidean space admits a representation as an information projection under moment inequality constraints. Exploiting this structure, I…
Graph neural networks (GNNs) have become a prevalent framework for graph tasks. Many recent studies have proposed the use of graph convolution methods over the numerous subgraphs of each graph, a concept known as subgraph graph neural…
We propose a novel Fr\'echet sufficient dimension reduction (SDR) method based on kernel distance covariance, tailored for metric space-valued responses such as count data, probability densities, and other complex structures. The method…
Sinkhorn algorithm is the de-facto standard approximation algorithm for optimal transport, which has been applied to a variety of applications, including image processing and natural language processing. In theory, the proof of its…
The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
Recently, linear regression models incorporating an optimal transport (OT) loss have been explored for applications such as supervised unmixing of spectra, music transcription, and mass spectrometry. However, these task-specific approaches…
Data augmentation (DA) has been widely used to improve the generalization of deep neural networks. While existing DA methods have proven effective, they often rely on augmentation operations with random magnitudes to each sample. However,…
Modern neural networks (NNs) often do not generalize well in the presence of a "covariate shift"; that is, in situations where the training and test data distributions differ, but the conditional distribution of classification labels…
Multi-Agent Reinforcement Learning is widely used for multi-robot coordination, where simple graphs typically model pairwise interactions. However, such representations fail to capture higher-order collaborations, limiting effectiveness in…
Autoencoders are a type of unsupervised neural networks, which can be used to solve various tasks, e.g., dimensionality reduction, image compression, and image denoising. An AE has two goals: (i) compress the original input to a…
Graph neural networks (GNNs) have shown advantages in graph-based analysis tasks. However, most existing methods have the homogeneity assumption and show poor performance on heterophilic graphs, where the linked nodes have dissimilar…
A key operation for massive data series collection analysis is similarity search. According to recent studies, SAX-based indexes offer state-of-the-art performance for similarity search tasks. However, their performance lags under…