Related papers: Discrepancy Minimization via a Self-Balancing Walk

We study an online vector balancing problem, in which $n$ independent Gaussian random vectors $\boldsymbol{\zeta}(1),\dots,\boldsymbol{\zeta}(n) \sim \mathcal{N}(0, I_n)$, each of dimension $n$, arrive one at a time. The goal is to choose…

The objective of the matrix selection problem is to select a submatrix $A_{S}\in \mathbb{R}^{n\times k}$ from $A\in \mathbb{R}^{n\times m}$ such that its minimum singular value is maximized. In this paper, we employ the interlacing…

The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We…

We consider a one-dimensional simple symmetric exclusion process in equilibrium, constituting a dynamic random environment for a nearest-neighbor random walk that on occupied/vacant sites has two different local drifts to the right. We…

The search for binary sequences with a high figure of merit, known as the low autocorrelation binary sequence ($labs$}) problem, represents a formidable computational challenge. To mitigate the computational constraints of the problem, we…

There are many real-world classification problems wherein the issue of data imbalance (the case when a data set contains substantially more samples for one/many classes than the rest) is unavoidable. While under-sampling the problematic…

While test-time reasoning enables language models (LMs) to tackle complex tasks, searching or planning in natural language can be slow, costly, and error-prone. But even when LMs struggle to emulate the precise reasoning steps needed to…

Imbalanced problems can arise in different real-world situations, and to address this, certain strategies in the form of resampling or balancing algorithms are proposed. This issue has largely been studied in the context of classification,…

Monte Carlo sampling has become a major vehicle for approximate inference in Bayesian networks. In this paper, we investigate a family of related simulation approaches, known collectively as quasi-Monte Carlo methods based on deterministic…

We consider the Vector Scheduling problem on identical machines: we have m machines, and a set J of n jobs, where each job j has a processing-time vector $p_j\in \mathbb{R}^d_{\geq 0}$. The goal is to find an assignment $\sigma:J\to [m]$ of…

We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…

We investigate random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramer's condition. We prove moderate deviation principles in dimensions two and larger, covering…

We present a systematic method for constructing stochastic processes by modifying simpler, analytically solvable random walks on discrete lattices. Our framework integrates the Doob $h$-transformation with the Montroll defect theory,…

We study an infinite system of independent symmetric random walks on a hierarchical group, in particular, the c-random walks. Such walks are used, e.g., in population genetics. The number variance problem consists in investigating if the…

We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…

We prove decoupling inequalities for random polynomials in independent random variables with coefficients in vector space. We use various means of comparison, including rearrangement invariant norms (e.g., Orlicz and Lorentz norms), tail…

We consider a branching random walk on $\mathbb{R}$ with a stationary and ergodic environment $\xi=(\xi_n)$ indexed by time $n\in\mathbb{N}$. Let $Z_n$ be the counting measure of particles of generation $n$. For the case where the…

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…

In one-dimensional random walks, the waiting time for each direction transitions is the same, even in the presence of bias, as a consequence of the microscopic-reversibility. We study the symmetry breaking of forward/ backward transition…

Although stochastic models driven by latent Markov processes are widely used, the classical importance sampling methods based on the exponential tilting for these models suffers from the difficulties in computing the eigenvalues and…