arXiv research

BOFiP optimizes high-dimensional functions by distributing them into sub-spaces and using game theory.

A new method for one-class classifiers using spanning trees and sub-spaces.

Improved SSD for faster and more accurate goodness-of-fit tests and model learning.

Motivated by the equation satisfied by the extremals of certain Hardy-Sobolev type inequalities, we show sharp $L^q$ regularity for finite energy solutions of p-laplace equations involving critical exponents and possible singularity on a sub-space of $\mathbb{R}^n$, which imply asymptotic behavior of the solutions at i…

The Martin boundary of a Cartan-Hadamard manifold describes a fine geometric structure at infinity, which is a sub-space of positive harmonic functions. We describe conditions which ensure that some points of the sphere at infinity belong to the Martin boundary as well. In the case of the universal cover of a compact m…

Proves transitivity of real Anosov diffeomorphisms with specific properties.

Analogously to the concept of a curvature of curve and surface, in the differential geometry, in the main part of this paper the concept of the curvature of the hyper-dimensional vector spaces of Riemannian metric is generally defined. The defined concept of the curvature of Riemannian spaces of higher dimensions M: M>…

We explain some interesting relations in the degree three bounded cohomology of surface groups. Specifically, we show that if two faithful Kleinian surface group representations are quasi-isometric, then their bounded fundamental classes are the same in bounded cohomology. This is novel in the setting that one end is d…

We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is preserved. We propose DVSDR, a deep variational approach for sufficient dimensionality r…

The paper extends graph-based semi-supervised learning to infinite-dimensional Wasserstein space.

Introduces Conditional Action Trees to simplify RL action spaces.

Unified Bayesian Optimisation for mixed variables improves performance.

Transforms data into separable subspaces for clustering.

New optimal prior avoids bias in complex models with limited data.

New BO method efficiently optimizes high-dimensional functions by automatically selecting variables.

The vulnerability of machine learning systems to adversarial attacks questions their usage in many applications. In this paper, we propose a randomized diversification as a defense strategy. We introduce a multi-channel architecture in a gray-box scenario, which assumes that the architecture of the classifier and the t…

In the supervised high dimensional settings with a large number of variables and a low number of individuals, one objective is to select the relevant variables and thus to reduce the dimension. That subspace selection is often managed with supervised tools. However, some data can be missing, compromising the validity o…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of this measure is concentrated on a lower dimensional subspace, meaning that certai…

Two Bayesian optimization methods tackle dynamic design spaces with mixed variables.

A new boosting method reduces overfitting and negative transfer in transfer learning.

HRF enhances tree diversity in random forests to improve performance.

Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by the classes (or categories). To this end, we set up a model in which each class i…

Algorithm improves SVM classification in non-Euclidean spaces.

Extreme multi-label classification refers to supervised multi-label learning involving hundreds of thousands or even millions of labels. Datasets in extreme classification exhibit fit to power-law distribution, i.e. a large fraction of labels have very few positive instances in the data distribution. Most state-of-the-…

LOTOS improves ensemble robustness by promoting orthogonal transformations.

We present a large-scale study of commonality in liquidity and resilience across assets in an ultra high-frequency (millisecond-timestamped) Limit Order Book (LOB) dataset from a pan-European electronic equity trading facility. We first show that extant work in quantifying liquidity commonality through the degree of ex…

WeakNAS uses a set of weaker predictors to find top architectures with fewer samples.