Related papers: Information-Geometric Set Embeddings (IGSE): From …
We study the problem of learning permutation invariant representations that can capture "flexible" notions of containment. We formalize this problem via a measure theoretic definition of multisets, and obtain a theoretically-motivated…
This work presents an innovative method for point set self-embedding, that encodes the structural information of a dense point set into its sparser version in a visual but imperceptible form. The self-embedded point set can function as the…
Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly…
Word embeddings -- distributed representations of words -- in deep learning are beneficial for many tasks in natural language processing (NLP). However, different embedding sets vary greatly in quality and characteristics of the captured…
Current work in lexical distributed representations maps each word to a point vector in low-dimensional space. Mapping instead to a density provides many interesting advantages, including better capturing uncertainty about a representation…
Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be…
We consider the problem of learning to choose from a given set of objects, where each object is represented by a feature vector. Traditional approaches in choice modelling are mainly based on learning a latent, real-valued utility function,…
spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into…
In this paper, we show that coherent sets of gambles and coherent lower and upper previsions can be embedded into the algebraic structure of information algebra. This leads firstly, to a new perspective of the algebraic and logical…
Learning word embeddings using distributional information is a task that has been studied by many researchers, and a lot of studies are reported in the literature. On the contrary, less studies were done for the case of multiple languages.…
We have studied the concept of bipolarity of information in the soft sets. We have defined bipolar soft sets and basic operations of union, intersection and complementation for bipolar soft sets. Examples of bipolar soft sets and an…
Probabilistic graphical models allow us to encode a large probability distribution as a composition of smaller ones. It is oftentimes the case that we are interested in incorporating in the model the idea that some of these smaller…
By representing words with probability densities rather than point vectors, probabilistic word embeddings can capture rich and interpretable semantic information and uncertainty. The uncertainty information can be particularly meaningful in…
Many high dimensional integrals can be reduced to the problem of finding the relative measures of two sets. Often one set will be exponentially larger than the other, making it difficult to compare the sizes. A standard method of dealing…
Learned embeddings are widely used to obtain concise data representation and enable transfer learning between different data sets and tasks. In this paper, we present Silhouette, our approach that leverages publicly-available performance…
In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…
In a recent work we have shown how to construct an information algebra of coherent sets of gambles defined on general possibility spaces. Here we analyze the connection of such an algebra with the set algebra of subsets of the possibility…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
Structural equation modeling is widely used in IS research. However, inconsistent construct definitions impede the cumulative development of knowledge. In this work, we present an approach that aims at the integration of structural equation…
Probability intervals are an attractive tool for reasoning under uncertainty. Unlike belief functions, though, they lack a natural probability transformation to be used for decision making in a utility theory framework. In this paper we…