Related papers: Random Projection Trees Revisited

While many phenomena in physics and engineering are formally high-dimensional, their long-time dynamics often live on a lower-dimensional manifold. The present work introduces an autoencoder framework that combines implicit regularization…

We adapt the idea of random projections applied to the output space, so as to enhance tree-based ensemble methods in the context of multi-label classification. We show how learning time complexity can be reduced without affecting…

Tree-based data structures are ubiquitous across applications. Therefore, a multitude of different tree implementations exist. However, while these implementations are diverse, they share a tree structure as the underlying data structure.…

The decision tree recursively partitions the input space into regions and derives axis-aligned decision boundaries from data. Despite its simplicity and interpretability, decision trees lack parameterized representation, which makes it…

Big Data is one of the major challenges of statistical science and has numerous consequences from algorithmic and theoretical viewpoints. Big Data always involve massive data but they also often include online data and data heterogeneity.…

Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…

Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is…

We present a new way of constructing an ensemble classifier, named the Guided Random Forest (GRAF) in the sequel. GRAF extends the idea of building oblique decision trees with localized partitioning to obtain a global partitioning. We show…

Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…

We study the local limit of the fixed-point forest, a tree structure associated to a simple sorting algorithm on permutations. This local limit can be viewed as an infinite random tree that can be constructed from a Poisson point process…

Deep learning optimization exhibits structure that is not captured by worst-case gradient bounds. Empirically, gradients along training trajectories are often temporally predictable and evolve within a low-dimensional subspace. In this work…

The wealth of data being gathered about humans and their surroundings drives new machine learning applications in various fields. Consequently, more and more often, classifiers are trained using not only numerical data but also complex data…

Multivariate histograms are difficult to construct due to the curse of dimensionality. Motivated by $k$-d trees in computer science, we show how to construct an efficient data-adaptive partition of Euclidean space that possesses the…

Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of…

While globally optimal empirical risk minimization (ERM) decision trees have become computationally feasible and empirically successful, rigorous theoretical guarantees for their statistical performance remain limited. In this work, we…

We develop a theoretical framework for the analysis of oblique decision trees, where the splits at each decision node occur at linear combinations of the covariates (as opposed to conventional tree constructions that force axis-aligned…

Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…

The induction of additional randomness in parallel and sequential ensemble methods has proven to be worthwhile in many aspects. In this manuscript, we propose and examine a novel random tree depth injection approach suitable for sequential…

We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…

As a flexible nonparametric learning tool, the random forests algorithm has been widely applied to various real applications with appealing empirical performance, even in the presence of high-dimensional feature space. Unveiling the…