Related papers: Discrepancy Minimization via a Self-Balancing Walk

We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change…

This paper is an attempt to set a justification for making use of some dicrepancy indexes, starting from the classical Maximum Likelihood definition, and adapting the corresponding basic principle of inference to situations where…

We study, in d-dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants and moments rather than a direct study of the probability…

Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution.…

This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…

We consider the fundamental problem of allocating $T$ indivisible items that arrive over time to $n$ agents with additive preferences, with the goal of minimizing envy. This problem is tightly connected to online multicolor discrepancy:…

We introduce a new algorithmic framework for discrepancy minimization based on regularization. We demonstrate how varying the regularizer allows us to re-interpret several breakthrough works in algorithmic discrepancy, ranging from…

e consider the experimental design problem in an online environment, an important practical task for reducing the variance of estimates in randomized experiments which allows for greater precision, and in turn, improved decision making. In…

Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are…

In [1], the authors consider a random walk $(Z_{n,1},\ldots,Z_{n,K+1})\in \mathbb{Z}^{K+1}$ with the constraint that each coordinate of the walk is at distance one from the following one. A functional central limit theorem for the first…

This paper studies the addition of linear constraints to the Support Vector Regression (SVR) when the kernel is linear. Adding those constraints into the problem allows to add prior knowledge on the estimator obtained, such as finding…

We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when…

We study random walks on metric spaces with contracting isometries. In this first article of the series, we establish sharp deviation inequalities by adapting Gou\"ezel's pivotal time construction. As an application, we establish the…

We study a unified approach and algorithm for constructive discrepancy minimization based on a stochastic process. By varying the parameters of the process, one can recover various state-of-the-art results. We demonstrate the flexibility of…

We prove existence and uniqueness of a solution to the problem of minimizing the logarithmic energy of vector potentials associated to a $d$-tuple of positive measures supported on closed subsets of the complex plane. The assumptions we…

We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the…

We consider a latent space model for dynamic networks, where our objective is to estimate the pairwise inner products plus the intercept of the latent positions. To balance posterior inference and computational scalability, we consider a…

Let $G$ be a finitely generated group of polynomial volume growth equipped with a word-length $|\cdot|$. The goal of this paper is to develop techniques to study the behavior of random walks driven by symmetric measures $\mu$ such that, for…

In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically…

Lower bounds involving $f$-divergences between the underlying probability measures are proved for the minimax risk in estimation problems. Our proofs just use simple convexity facts. Special cases and straightforward corollaries of our…