Related papers: The Mondrian Process for Machine Learning
We introduce the Mondrian kernel, a fast random feature approximation to the Laplace kernel. It is suitable for both batch and online learning, and admits a fast kernel-width-selection procedure as the random features can be re-used…
Ensembles of randomized decision trees, usually referred to as random forests, are widely used for classification and regression tasks in machine learning and statistics. Random forests achieve competitive predictive performance and are…
Random forests are popular methods for regression and classification analysis, and many different variants have been proposed in recent years. One interesting example is the Mondrian random forest, in which the underlying constituent trees…
Introduced by Breiman, Random Forests are widely used classification and regression algorithms. While being initially designed as batch algorithms, several variants have been proposed to handle online learning. One particular instance of…
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…
The stable under iterated tessellation (STIT) process is a stochastic process that produces a recursive partition of space with cut directions drawn independently from a distribution over the sphere. The case of random axis-aligned cuts is…
Many real-world regression problems demand a measure of the uncertainty associated with each prediction. Standard decision forests deliver efficient state-of-the-art predictive performance, but high-quality uncertainty estimates are…
Random Forests have been extensively used in regression and classification, inspiring the development of various forest-based methods. Among these, Mondrian Forests, derived from the Mondrian process, mark a significant advancement.…
We establish the consistency of an algorithm of Mondrian Forests, a randomized classification algorithm that can be implemented online. First, we amend the original Mondrian Forest algorithm, that considers a fixed lifetime parameter.…
The Mondrian process represents an elegant and powerful approach for space partition modelling. However, as it restricts the partitions to be axis-aligned, its modelling flexibility is limited. In this work, we propose a self-consistent…
Random Forests (RF) is one of the algorithms of choice in many supervised learning applications, be it classification or regression. The appeal of such tree-ensemble methods comes from a combination of several characteristics: a remarkable…
Random feature maps are used to decrease the computational cost of kernel machines in large-scale problems. The Mondrian kernel is one such example of a fast random feature approximation of the Laplace kernel, generated by a computationally…
We propose a computationally efficient algorithm for gradient-based linear dimension reduction and high-dimensional regression. The algorithm initially computes a Mondrian forest and uses this estimator to identify a relevant feature…
This work studies the statistical implications of using features comprised of general linear combinations of covariates to partition the data in randomized decision tree and forest regression algorithms. Using random tessellation theory in…
Supervised learning algorithms generally assume the availability of enough memory to store their data model during the training and test phases. However, in the Internet of Things, this assumption is unrealistic when data comes in the form…
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…
Random forest regression is a powerful non-parametric method that adapts to local data characteristics through data-driven partitioning, making it effective across diverse application domains. However, the piecewise constant nature of…
Mondrian Forests are a powerful data stream classification method, but their large memory footprint makes them ill-suited for low-resource platforms such as connected objects. We explored using reduced-precision floating-point…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
The Binary Space Partitioning~(BSP)-Tree process is proposed to produce flexible 2-D partition structures which are originally used as a Bayesian nonparametric prior for relational modelling. It can hardly be applied to other learning tasks…