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A novel approach is proposed to establish a sharp upper bound on the expected supremum of a separable martingale random field, serving as an alternative to classical universal chaining-based methods. The proposed approach begins by deriving…

We obtain explicit error bounds for the $d$-dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling, or is a non-linear statistic of independent random…

In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…

Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them…

Stochastic estimators are fundamental to large-scale optimization, where population quantities must be inferred from noisy oracle observations. Although influential methods such as momentum, SPIDER, STORM, and PAGE have been highly…

We study the canonical quantity-based network revenue management (NRM) problem where the decision-maker must irrevocably accept or reject each arriving customer request with the goal of maximizing the total revenue given limited resources.…

A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…

We present three simple algorithms to uniformly generate `Fibonacci words' (i.e., some words that are enumerated by Fibonacci numbers), Schr{\"o}der trees of size $n$ and Motzkin left factors of size $n$ and final height $h$. These…

The problem of using proximity (similarity or dissimilarity) data for the purpose of "adding a point to a vector diagram" was first studied by J.C. Gower in 1968. Since then, a number of methods -- mostly kernel methods -- have been…

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization…

Von Neumann's classic "multiplexing" method is unique in achieving high-threshold fault-tolerant classical computation (FTCC), but has several significant barriers to implementation: i) the extremely complex circuits required by randomized…

The wide and rapid adoption of deep learning by practitioners brought unintended consequences in many situations such as in the infamous case of Google Photos' racist image recognition algorithm; thus, necessitated the utilization of the…

We propose a genetic-algorithm-based method to find the unitary transformations for any desired quantum computation. We formulate a simple genetic algorithm by introducing the "genetic parameter vector" of the unitary transformations to be…

In this note, we develop a novel algorithm for generating random numbers from a distribution with a probability density function proportional to $\sin^k(x)$, $x \in (0,\pi)$ and $k \geq 1$. Our algorithm is highly efficient and is based on…

We study random number generators (RNGs), both in the fixed to variable-length (FVR) and the variable to fixed-length (VFR) regimes, in a universal setting in which the input is a finite memory source of arbitrary order and unknown…

Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…

Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step…

Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other…

$2^K$ factorial designs are widely adopted by statisticians and the broader scientific community. In this short note, under the potential outcomes framework (Neyman, 1923; Rubin, 1974), we adopt the partial identification approach and…

We apply the stochastic approximation method to construct a large class of recursive kernel estimators of a probability density, including the one introduced by Hall and Patil (1994). We study the properties of these estimators and compare…