相关论文: A Meaner King uses Biased Bases

The many-normal-means problem is a classic example that motivates the development of many important inferential procedures in the history of statistics. In this short note, we consider a further special case of the problem, which involves…

A variety of problems in distributed control involve a networked system of autonomous agents cooperating to carry out some complex task in a decentralized fashion, e.g., orienting a flock of drones, or aggregating data from a network of…

Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on…

This paper considers distributed average consensus using finite-bit bounded quantizer with possibly unbounded data. Under the framework of the alternating direction method of multipliers (ADMM), we develop distributed averaging algorithms…

Non-stabilizerness, or magic, is a fundamental resource for quantum computation, enabling quantum algorithms to surpass classical capabilities. Despite its importance, characterizing magic remains challenging due to the intricate geometry…

Shannon defined the mutual information between two variables. We illustrate why the true mutual information between a variable and the predictions made by a prediction algorithm is not a suitable measure of prediction quality, but the…

Consider a coin tossing experiment which consists of tossing one of two coins at a time, according to a renewal process. The first coin is fair and the second has probability $1/2 + \theta$, $\theta \in [-1/2,1/2]$, $\theta$ unknown but…

We present an axiomatic approach to the mean and discuss generalizations of the mean, including one due to Kolmogorov based on the Weak Law of Large Numbers. We offer examples and counterexamples, describe conventional and unconventional…

Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…

The problem of quantizing a circularly-symmetric complex Gaussian random variable is considered. For this purpose, we design two non-uniform quantizers, a high-rate-, and a Lloyd-Max-, quantizer that are both based on the (golden angle)…

We consider the problem of mutually unbiased bases as a polynomial optimization problem over the reals. We heavily reduce it using known symmetries before exploring it using two methods, combining a number of optimization techniques. The…

In a quantum system having a finite number $N$ of orthogonal states, two orthonormal bases $\{a_i\}$ and $\{b_j\}$ are called mutually unbiased if all inner products $<a_i|b_j>$ have the same modulus $1/\sqrt{N}$. This concept appears in…

Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…

In this work, we revisit the problem of active sequential prediction-powered mean estimation, where at each round one must decide the query probability of the ground-truth label upon observing the covariates of a sample. Furthermore, if the…

In this work we consider an agent based model in order to study the wealth distribution problem where the interchange is determined with a symmetric zero sum game. Simultaneously, the agents update their way of play trying to learn the…

We establish a theory of quantum-to-classical rate distortion coding. In this setting, a sender Alice has many copies of a quantum information source. Her goal is to transmit classical information about the source, obtained by performing a…

We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…

We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…

This paper introduces \emph{biased mean regression}, estimating the \emph{biased mean}, i.e., $\mathbb{E}[Y] + x$, where $x \in \mathbb{R}$. The approach addresses a fundamental statistical problem that covers numerous applications. For…

The assumption of free will - the ability of an experimentalist to make random choices - is central to proving the indeterminism of quantum resources, the primary tool in quantum cryptography. Relaxing the assumption in a Bell test allows…