相关论文: Recognising Multidimensional Euclidean Preferences

Two-dimensional transition metal dichalcogenides (TMDs) can adopt one of several possible structures, with the most common being the trigonal prismatic and octahedral symmetry phases. Since the structure determines the electronic…

Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large…

Complex networks representing social interactions, brain activities, molecular structures have been studied widely to be able to understand and predict their characteristics as graphs. Models and algorithms for these networks are used in…

This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise…

Hierarchical data is common in many domains like life sciences and e-commerce, and its embeddings often play a critical role. While hyperbolic embeddings offer a theoretically grounded approach to representing hierarchies in low-dimensional…

Current practice in parameter space exploration in euclidean space is dominated by randomized sampling or design of experiment methods. The biggest issue with these methods is not keeping track of what part of parameter space has been…

The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a…

In the signal processing and statistics literature, the minimum description length (MDL) principle is a popular tool for choosing model complexity. Successful examples include signal denoising and variable selection in linear regression,…

We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted,…

Laplacian-based methods are popular for the dimensionality reduction of data lying in $\mathbb{R}^N$. Several theoretical results for these algorithms depend on the fact that the Euclidean distance locally approximates the geodesic distance…

Policy gradient methods equipped with deep neural networks have achieved great success in solving high-dimensional reinforcement learning (RL) problems. However, current analyses cannot explain why they are resistant to the curse of…

We introduce an Attention Overload Model that captures the idea that alternatives compete for the decision maker's attention, and hence the attention that each alternative receives decreases as the choice problem becomes larger. Using this…

We consider the problem of preference based reinforcement learning (PbRL), where, unlike traditional reinforcement learning, an agent receives feedback only in terms of a 1 bit (0/1) preference over a trajectory pair instead of absolute…

Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself…

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…

In neural networks, it is often desirable to work with various representations of the same space. For example, 3D rotations can be represented with quaternions or Euler angles. In this paper, we advance a definition of a continuous…

We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.

Predicting user responses, such as clicks and conversions, is of great importance and has found its usage in many Web applications including recommender systems, web search and online advertising. The data in those applications is mostly…

Many decision-making problems feature multiple objectives where it is not always possible to know the preferences of a human or agent decision-maker for different objectives. However, demonstrated behaviors from the decision-maker are often…

Preference are central to decision making by both machines and humans. Representing, learning, and reasoning with preferences is an important area of study both within computer science and across the sciences. When working with preferences…