Related papers: Statistical Translation, Heat Kernels and Expected…
Text embeddings have become central to computational social science and psychology, enabling scalable measurement of meaning and mixed-method inference. Yet most representation learning is optimized and evaluated for prediction and…
When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…
In recent years, various kernels have been proposed in the context of persistent homology to deal with persistence diagrams in supervised learning approaches. In this paper, we consider the idea of variably scaled kernels, for approximating…
In distributed and federated learning, heterogeneity across data sources remains a major obstacle to effective model aggregation and convergence. We focus on feature heterogeneity and introduce energy distance as a sensitive measure for…
We use a suitable version of the so-called "kernel trick" to devise two-sample (homogeneity) tests, especially focussed on high-dimensional and functional data. Our proposal entails a simplification related to the important practical…
Semantic correspondence, the task of determining relationships between different parts of images, underpins various applications including 3D reconstruction, image-to-image translation, object tracking, and visual place recognition. Recent…
The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…
The goal of universal machine translation is to learn to translate between any pair of languages, given a corpus of paired translated documents for \emph{a small subset} of all pairs of languages. Despite impressive empirical results and an…
We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method…
In this paper, we propose Complex Diffusion Maps (CDM), a novel diffusion mapping framework that aims to reveal the dominant complex harmonics of high-dimensional data. Inspired by the local Gaussian kernel relevant to the heat equation and…
The expansiveness of compositional phase space is too vast to fully search using current theoretical tools for many emergent problems in condensed matter physics. The reliance on a deep chemical understanding is one method to identify local…
Multivariate time series forecasting poses challenges as the variables are intertwined in time and space, like in the case of traffic signals. Defining signals on graphs relaxes such complexities by representing the evolution of signals…
Parallel texts (bitexts) have properties that distinguish them from other kinds of parallel data. First, most words translate to only one other word. Second, bitext correspondence is noisy. This article presents methods for biasing…
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…
Image retrieval relies heavily on the quality of the data modeling and the distance measurement in the feature space. Building on the concept of image manifold, we first propose to represent the feature space of images, learned via neural…
Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
Persistent homology allows us to create topological summaries of complex data. In order to analyse these statistically, we need to choose a topological summary and a relevant metric space in which this topological summary exists. While…
Many real-world graphs or networks are temporal, e.g., in a social network persons only interact at specific points in time. This information directs dissemination processes on the network, such as the spread of rumors, fake news, or…
We obtain sharp two-sided heat kernel estimates on spaces with varying dimension, in which two spaces of general dimension are connected at one point. On these spaces, if the dimensions of the two constituent parts are different, the volume…