相关论文: Asymmetric scale functions for $t$-digests

Knowing which parts of a complex system have identical roles simplifies computations and reveals patterns in its network structure. Group theory has been applied to study symmetries in unweighted networks. However, in real-world weighted…

The design and implementation of efficient concurrent data structures have seen significant attention. However, most of this work has focused on concurrent data structures providing good \emph{worst-case} guarantees. In real workloads,…

Recent works have highlighted scale invariance or symmetry that is present in the weight space of a typical deep network and the adverse effect that it has on the Euclidean gradient based stochastic gradient descent optimization. In this…

We consider gradient-based optimisation of wide, shallow neural networks, where the output of each hidden node is scaled by a positive parameter. The scaling parameters are non-identical, differing from the classical Neural Tangent Kernel…

Inspired by the structure of spherical harmonics, we propose the truncated kernel stochastic gradient descent (T-kernel SGD) algorithm with a least-square loss function for spherical data fitting. T-kernel SGD introduces a novel…

In many problems in machine learning and operations research, we need to optimize a function whose input is a random variable or a probability density function, i.e. to solve optimization problems in an infinite dimensional space. On the…

Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients…

This work studies the learning ability of consensus and diffusion distributed learners from continuous streams of data arising from different but related statistical distributions. Four distinctive features for diffusion learners are…

Existing asynchronous distributed optimization algorithms often use diminishing step-sizes that cause slow practical convergence, or fixed step-sizes that depend on an assumed upper bound of delays. Not only is such a delay bound hard to…

Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…

Elliptical slice sampling is a widely used gradient-free Markov chain Monte Carlo algorithm that is tuning-free and capable of adapting to local characteristics of the target distribution. However, its primary limitation is that sampling…

The family of temporal difference (TD) methods span a spectrum from computationally frugal linear methods like TD({\lambda}) to data efficient least squares methods. Least square methods make the best use of available data directly…

In environmental studies, many data are typically skewed and it is desired to have a flexible statistical model for this kind of data. In this paper, we study a class of skewed distributions by invoking arguments as described by Ferreira…

There has been a growing effort in studying the distributed optimization problem over a network. The objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. Literature…

There has been a recent explosion in the size of stored data, partially due to advances in storage technology, and partially due to the growing popularity of cloud-computing and the vast quantities of data generated. This motivates the need…

Persistence diagrams are common objects in the field of Topological Data Analysis. They are topological summaries that capture both topological and geometric structure within data. Recently there has been a surge of interest in developing…

Dataset distillation seeks to synthesize a compact distilled dataset, enabling models trained on it to achieve performance comparable to models trained on the full dataset. Recent methods for large-scale datasets focus on matching global…

Gradient descent and stochastic gradient descent are central to modern machine learning, yet their behavior under large step sizes remains theoretically unclear. Recent work suggests that acceleration often arises near the edge of…

Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\em exactly} invariant under Euclidean scaling? This requires working in the continuum…

We study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance,…