arXiv research

A new method for unsupervised disentanglement using axis-aligned cliffs.

Two-dimensional embeddings remain the dominant approach to visualize high dimensional data. The choice of embeddings ranges from highly non-linear ones, which can capture complex relationships but are difficult to interpret quantitatively, to axis-aligned projections, which are easy to interpret but are limited to biva…

Space partitioning methods such as random forests and the Mondrian process are powerful machine learning methods for multi-dimensional and relational data, and are based on recursively cutting a domain. The flexibility of these methods is often limited by the requirement that the cuts be axis aligned. The Ostomachion p…

GTBO uses group testing to optimize high-dimensional functions efficiently.

Oblique BART improves tree-based predictions.

BO method identifies sparse subspaces for efficient high-dimensional optimization.

New kernel interprets 3D anisotropic data with rotations and improved predictions.

Decision forests, including Random Forests and Gradient Boosting Trees, have recently demonstrated state-of-the-art performance in a variety of machine learning settings. Decision forests are typically ensembles of axis-aligned decision trees; that is, trees that split only along feature dimensions. In contrast, many r…

Deep models have advanced prediction in many domains, but their lack of interpretability remains a key barrier to the adoption in many real world applications. There exists a large body of work aiming to help humans understand these black box functions to varying levels of granularity -- for example, through distillati…

Axis-aligned subspace clustering generally entails searching through enormous numbers of subspaces (feature combinations) and evaluation of cluster quality within each subspace. In this paper, we tackle the problem of identifying subsets of features with the most significant contribution to the formation of the local n…

We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative approaches, our algorithm is non-iterative, so is not vulnerable to a bad choice of init…

New method learns representations for decision forests using input perturbation.

Proves nonemptyness of domains for specific group actions.

We introduce canonical correlation forests (CCFs), a new decision tree ensemble method for classification and regression. Individual canonical correlation trees are binary decision trees with hyperplane splits based on local canonical correlation coefficients calculated during training. Unlike axis-aligned alternatives…

GTBO uses group testing to optimize high-dimensional functions efficiently.

We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a `small' deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of disc…

Cut-DeepONet handles discontinuities and sharp transitions in neural operators.

Study proves existence of equilibrium in incomplete economies with discontinuous volatility.

New domains of discontinuity found for Anosov representations.

As early as 1972, Penrose - in a purely formal way - introduced a "discontinuous coordinate transformation", which relates a continuous representation of the metric of impulsive pp-waves to a discontinuous one. On the basis of the invertibility concept for generalized functions developed recently by the first author, w…

Study the discontinuity of functions not embeddable in Euclidean space.

Study new symmetries in non-symmetric spaces and discontinuous groups.

Bayesian nonparametric method partitions shapes using curves.

Paper finds surface groups can deform in reductive symmetric spaces.

New random forest variants achieve optimal performance in high dimensions.

New method estimates active subspaces for jump-discontinuous functions.

This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of pseudo-Riemannian manifolds with constant curvatures, and discuss what kind of …

The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.

Paper analyzes error in stochastic approximation for discontinuous functions.

Bayesian emulator tackles models with discontinuities efficiently.

We characterise completely when limit sets, as parametrised by Cannon-Thurston maps, move discontinuously for a sequence of algebraically convergent quasi-Fuchsian groups.

We show that there is a complete connected 2-dimensional Riemannian manifold with discontinuous isoperimetric profile, answering a question of Nardulli and Pansu.

Volunteer labor can temporarily yield lower benefits to charities than its costs. In such instances, organizations may wish to defer volunteer donations to a later date. Exploiting a discontinuity in blood donations' eligibility criteria, we show that deferring donors reduces their future volunteerism. In our setting, …

We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of …

Study proves rigid spectral properties of planets with metric discontinuities.

We study the properly discontinuous and isometric actions on the unit sphere of infinite dimensional Hilbert spaces and we get some new examples of Hilbert manifold with costant positive sectional curvature. We prove some necessary conditions for a group to act isometrically and properly discontinuously and in the case…

In this paper, we present a method for the accurate estimation of the derivative (aka.~sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression. The method is an improvement of the approach presented in [Risk Magazine April 2018]. T…

This work models overnight rates with jumps and discontinuities, extending classical short-rate models.

Quasi-experimental research designs, such as regression discontinuity and interrupted time series, allow for causal inference in the absence of a randomized controlled trial, at the cost of additional assumptions. In this paper, we provide a framework for discontinuity-based designs using Bayesian model comparison and …

The study explores deformations of discrete subgroups in non-compact homogeneous spaces.

Paper analyzes SGHMC for non-convex optimization with discontinuous gradients.

This paper tackles discontinuous neural networks for better approximation of piecewise continuous functions.

In the present paper, we prove that no infinite group acts isometrically, effectively, and properly discontinuously on a certain class of Lorentzian manifolds that are not necessarily homogeneous.

Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.

In this article we study properly discontinuous actions on Hilbert manifolds giving new examples of complete Hilbert manifolds with nonnegative, respectively nonpositive, sectional curvature with infinite fundamental group. We also get examples of complete infinite dimensional Kähler manifolds with positive holomorphic…

Let $X$ be a CAT(0) space, and $G$ a discrete cyclic group of isometries of $X$. We investigate the domain of discontinuity for the action of $G$ on the boundary $\partial X$.

Estimates discontinuous optimal transport maps between a discrete and continuous distribution.

This work uses stochastic geometry to improve STIT processes in machine learning.