Related papers: Statistical Translation, Heat Kernels and Expected…
Applying kernel methods to matchings is challenging due to their discrete, non-Euclidean nature. In this paper, we develop a principled framework for constructing geometric kernels that respect the natural geometry of the space of…
We introduce the diffusion and superposition distances as two metrics to compare signals supported in the nodes of a network. Both metrics consider the given vectors as initial temperature distributions and diffuse heat trough the edges of…
We consider the problem of translating high-level textual descriptions to formal representations in technical documentation as part of an effort to model the meaning of such documentation. We focus specifically on the problem of learning…
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science. However, since the (metric) space of…
Heat transfer can differ distinctly at the nanoscale from that at the macroscale. Recent advancement in computational and experimental techniques has enabled a large number of interesting observations and understanding of heat transfer…
Metric and kernel learning are important in several machine learning applications. However, most existing metric learning algorithms are limited to learning metrics over low-dimensional data, while existing kernel learning algorithms are…
In recent years, quantities derived from the heat equation have become popular in shape processing and analysis of triangulated surfaces. Such measures are often robust with respect to different kinds of perturbations, including…
Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…
How we choose to represent our data has a fundamental impact on our ability to subsequently extract information from them. Machine learning promises to automatically determine efficient representations from large unstructured datasets, such…
The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora. Past distances between documents suffer from either an inability to incorporate semantic similarities between words or from…
Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this…
Graph signals are widely used to describe vertex attributes or features in graph-structured data, with applications spanning the internet, social media, transportation, sensor networks, and biomedicine. Graph signal processing (GSP) has…
The purpose of this paper is to establish a new continuous-time on-diagonal lower estimate of heat kernel for large time on graphs. To achieve the goal, we first give an upper bound of heat kernel in natural graph metric, and then use this…
Extractive summarization for long documents is challenging due to the extended structured input context. The long-distance sentence dependency hinders cross-sentence relations modeling, the critical step of extractive summarization. This…
We argue that translation quality alone is not a sufficient metric for measuring knowledge transfer in multilingual neural machine translation. To support this claim, we introduce Representational Transfer Potential (RTP), which measures…
Quantum contextual sets have been recognized as resources for universal quantum computation, quantum steering and quantum communication. Therefore, we focus on engineering the sets that support those resources and on determining their…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
Machine learning models are only as good as the data to which they are fit. As such, it is always preferable to use as much data as possible in training models. What data can be used for fitting a model depends a lot on the formulation of…
The huge amount of information stored in text form makes methods that deal with texts really interesting. This thesis focuses on dealing with texts using compression distances. More specifically, the thesis takes a small step towards…
Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…