Related papers: Negative association, ordering and convergence of …
For obtaining optimal first-order convergence guarantee for stochastic optimization, it is necessary to use a recurrent data sampling algorithm that samples every data point with sufficient frequency. Most commonly used data sampling…
In this paper, we study the convergence to the stable equilibrium for Kuramoto oscillators. Specifically, we derive estimates on the rate of convergence to the global equilibrium for solutions of the Kuramoto-Sakaguchi equation in a large…
We present weak approximations schemes of any order for the Heston model that are obtained by using the method developed by Alfonsi and Bally (2021). This method consists in combining approximation schemes calculated on different random…
In this paper, we propose a novel $K$-nearest neighbor resampling procedure for estimating the performance of a policy from historical data containing realized episodes of a decision process generated under a different policy. We provide…
In many real-world binary classification tasks (e.g. detection of certain objects from images), an available dataset is imbalanced, i.e., it has much less representatives of a one class (a minor class), than of another. Generally, accurate…
Rejection sampling is a well-known method to sample from a target distribution, given the ability to sample from a given distribution. The method has been first formalized by von Neumann (1951) and has many applications in classical…
To obtain strong convergence rates of numerical schemes, an overwhelming majority of existing works impose a global monotonicity condition on coefficients of SDEs. Nevertheless, there are still many SDEs from applications that do not have…
We introduce a new algorithm for finding robust circular coordinates on data that is expected to exhibit recurrence, such as that which appears in neuronal recordings of C. elegans. Techniques exist to create circular coordinates on a…
The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…
We study dropout regularization in continuous-time models through the lens of random-batch methods -- a family of stochastic sampling schemes originally devised to reduce the computational cost of interacting particle systems. We construct…
In this work we explore the fundamental structure-adaptiveness of state of the art randomized first order algorithms on regularized empirical risk minimization tasks, where the solution has intrinsic low-dimensional structure (such as…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is…
The general method of the reduction in the number of coupling parameters is discussed. Using renormalization group invariance, theories with several independent couplings are related to a set of theories with a single coupling parameter.…
Convergence rates in spectral regularization methods quantify the approximation error in inverse problems as a function of the noise level or the number of sampling points. Classical strong convergence rate results typically rely on source…
Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by…
In a previous paper, an implementable algorithm was introduced to compute discrete solutions of sweeping processes (i.e. specific first order differential inclusions). The convergence of this numerical scheme was proved thanks to…
We introduce a detailed analysis of the convergence of first-order methods with composite noise (sum of relative and absolute) in gradient for convex and smooth function minimization. This paper illustrates instances of practical problems…
We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…
We consider in this work the convergence of Random Batch Method proposed in our previous work [Jin et al., J. Comput. Phys., 400(1), 2020] for interacting particles to the case of disparate species and weights. We show that the strong error…