相关论文: Stochastic geometry to generalize the Mondrian Pro…

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…

Random forests are a popular class of algorithms used for regression and classification. The algorithm introduced by Breiman in 2001 and many of its variants are ensembles of randomized decision trees built from axis-aligned partitions of…

Since the seminal work by Nagel and Weiss, the iteration stable (STIT) tessellations have attracted considerable interest in stochastic geometry as a natural and flexible, yet analytically tractable model for hierarchical spatial…

This report is concerned with the Mondrian process and its applications in machine learning. The Mondrian process is a guillotine-partition-valued stochastic process that possesses an elegant self-consistency property. The first part of the…

Three-dimensional random tessellations that are stable under iteration (STIT tessellations) are considered. They arise as a result of subsequent cell division, which implies that their cells are not face-to-face. The edges of the…

We study rotation-robust learning for image inputs using Convolutional Model Trees (CMTs) [1], whose split and leaf coefficients can be structured on the image grid and transformed geometrically at deployment time. In a controlled MNIST…

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…

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…

Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

Shape modelling (with methods that output shapes) is a new and important task in Bayesian nonparametrics and bioinformatics. In this work, we focus on Bayesian nonparametric methods for capturing shapes by partitioning a space using curves.…

In this paper planar STIT tesselations with weighted axis-parallel cutting directions are considered. They are known also as weighted planar Mondrian tesselations in the machine learning literature, where they are used in random forest…

Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…

The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in $\mathbb{R}^d$, which form a rather new, rich and flexible class of random tessellations considered in stochastic…

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…

Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…

Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…

A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…

Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…

The fluctuation effect of gradient expectation and variance caused by parameter update between consecutive iterations is neglected or confusing by current mainstream gradient optimization algorithms.Using this fluctuation effect, combined…