Related papers: On the Convergence of the Mean Shift Algorithm in …
We study the convergence of a random iterative sequence of a family of operators on infinite dimensional Hilbert spaces, inspired by the Stochastic Gradient Descent (SGD) algorithm in the case of the noiseless regression, as studied in [1].…
In this paper, we revisit a well-known distributed projected subgradient algorithm which aims to minimize a sum of cost functions with a common set constraint. In contrast to most of existing results, weight matrices of the time-varying…
We investigate an algorithm named histogram transform ensembles (HTE) density estimator whose effectiveness is supported by both solid theoretical analysis and significant experimental performance. On the theoretical side, by decomposing…
Pairwise network comparison is essential for various applications, including neuroscience, disease research, and dynamic network analysis. While existing literature primarily focuses on comparing entire network structures, we address a…
In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called…
Stochastic gradient descent (SGD) algorithm is the method of choice in many machine learning tasks thanks to its scalability and efficiency in dealing with large-scale problems. In this paper, we focus on the shuffling version of SGD which…
Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be…
Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
In this article, we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis. Monotonic convergence for a general class of multiplicative algorithms for $D$-optimality has been…
We study non-stationary averaging processes, where each term of a sequence is a weighted average of previous terms, namely $a_{n+1} = \sum_{j=1}^n p_n(j) a_j$. Our results extend classical theory in two distinct regimes. First, we prove a…
This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
We describe a simple geometric transformation of triangles which leads to an efficient and effective algorithm to smooth triangle and tetrahedral meshes. Our focus lies on the convergence properties of this algorithm: we prove the…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…
Assume that we observe a large number of curves, all of them with identical, although unknown, shape, but with a different random shift. The objective is to estimate the individual time shifts and their distribution. Such an objective…