Related papers: Mixed-Curvature Decision Trees and Random Forests

Decision trees are renowned for their ability to achieve high predictive performance while remaining interpretable, especially on tabular data. Traditionally, they are constructed through recursive algorithms, where they partition the data…

The effectiveness of Symmetric Positive Definite (SPD) manifold features has been proven in various computer vision tasks. However, due to the non-Euclidean geometry of these features, existing Euclidean machineries cannot be directly used.…

Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…

Representing token embeddings as probability distributions over learned manifolds allows for more flexible contextual inference, reducing representational rigidity while enhancing semantic granularity. Comparative evaluations demonstrate…

Classical metric and non-metric multidimensional scaling (MDS) variants are widely known manifold learning (ML) methods which enable construction of low dimensional representation (projections) of high dimensional data inputs. However,…

We introduce a notion of the Euclidean- and the Minkowski rank for arbitrary metric spaces and we study their behaviour with respect to products. We show that the Minkowski rank is additive with respect to metric products, while additivity…

Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…

Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a…

We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued…

Decision trees and their ensembles are very popular models of supervised machine learning. In this paper we merge the ideas underlying decision trees, their ensembles and FCA by proposing a new supervised machine learning model which can be…

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean…

We introduce an algorithm that performs a one-directional mesh overset of a parallel forest of octrees with another distributed mesh of unrelated partition. The forest mesh consists of several adaptively refined octrees. Individual smooth…

We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss.…

We consider the problem of reconstructing an embedding of a compact connected Riemannian manifold in a Euclidean space up to an almost isometry, given the information on intrinsic distances between points from its ``sufficiently large''…

A novel method, named Curvature-Augmented Manifold Embedding and Learning (CAMEL), is proposed for high dimensional data classification, dimension reduction, and visualization. CAMEL utilizes a topology metric defined on the Riemannian…

Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…

Several first order stochastic optimization methods commonly used in the Euclidean domain such as stochastic gradient descent (SGD), accelerated gradient descent or variance reduced methods have already been adapted to certain Riemannian…

We study deterministic online embeddings of metrics spaces into normed spaces and into trees against an adaptive adversary. Main results include a polynomial lower bound on the (multiplicative) distortion of embedding into Euclidean spaces,…

We propose a novel algorithm for optimizing multivariate linear threshold functions as split functions of decision trees to create improved Random Forest classifiers. Standard tree induction methods resort to sampling and exhaustive search…

Random Forests are one of the most popular classifiers in machine learning. The larger they are, the more precise is the outcome of their predictions. However, this comes at a cost: their running time for classification grows linearly with…