Related papers: Some theory for ordinal embedding
The first goal of this paper is to prove a sharp condition to guarantee of having a positive proportion of all congruence classes of triangles in given sets in $\mathbb{F}_q^2$. More precisely, for $A, B, C\subset \mathbb{F}_q^2$, if…
Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine…
When the number of subjects, $n$, is large, paired comparisons are often sparse. Here, we study statistical inference in a class of paired comparison models parameterized by a set of merit parameters, under an Erd\"{o}s--R\'{e}nyi…
Analysis of the convergence rates of modern convex optimization algorithms can be achived through binary means: analysis of emperical convergence, or analysis of theoretical convergence. These two pathways of capturing information diverge…
Categorical compositional distributional model of Coecke et al. (2010) suggests a way to combine grammatical composition of the formal, type logical models with the corpus based, empirical word representations of distributional semantics.…
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
Similarity comparisons of the form "Is object a more similar to b than to c?" are useful for computer vision and machine learning applications. Unfortunately, an embedding of $n$ points is specified by $n^3$ triplets, making collecting…
The main contribution of this dissertation is the introduction of new or improved approximation algorithms and data structures for several similarity search problems. We examine the furthest neighbor query, the annulus query, distance…
With the increasing popularity of graph-based methods for dimensionality reduction and representation learning, node embedding functions have become important objects of study in the literature. In this paper, we take an axiomatic approach…
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
Cross-lingual or cross-domain correspondences play key roles in tasks ranging from machine translation to transfer learning. Recently, purely unsupervised methods operating on monolingual embeddings have become effective alignment tools.…
This paper have two parts. In the first part we discuss word embeddings. We discuss the need for them, some of the methods to create them, and some of their interesting properties. We also compare them to image embeddings and see how word…
Embedders play a central role in machine learning, projecting any object into numerical representations that can, in turn, be leveraged to perform various downstream tasks. The evaluation of embedding models typically depends on…
While there has been substantial progress in learning suitable distance metrics, these techniques in general lack transparency and decision reasoning, i.e., explaining why the input set of images is similar or dissimilar. In this work, we…
This paper investigates theoretical properties of subsampling and hashing as tools for approximate Euclidean norm-preserving embeddings for vectors with (unknown) additive Gaussian noises. Such embeddings are sometimes called…
Quantitative bounds for random embeddings of $\mathbb{R}^{k}$ into Lorentz sequence spaces are given, with improved dependence on $\varepsilon$.
We address the classical problem of hierarchical clustering, but in a framework where one does not have access to a representation of the objects or their pairwise similarities. Instead, we assume that only a set of comparisons between…
In this paper, we address the problem of measuring and analysing sensation, the subjective magnitude of one's experience. We do this in the context of the method of triads: the sensation of the stimulus is evaluated via relative judgments…