相关论文: A Meaner King uses Biased Bases

An open quantum system leaks information into its environment. In some circumstances it is possible for an observer, say Alice, to recover that information, as a classical measurement record, in a variety of different ways, using different…

We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…

We propose an improved estimator for the multi-task averaging problem, whose goal is the joint estimation of the means of multiple distributions using separate, independent data sets. The naive approach is to take the empirical mean of each…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…

In recent papers, the theory of representations of finite groups has been proposed to analyzing the violation of Bell inequalities. In this paper, we apply this method to more complicated cases. For two partite system, Alice and Bob each…

We study the power of uniform sampling for $k$-Median in various metric spaces. We relate the query complexity for approximating $k$-Median, to a key parameter of the dataset, called the balancedness $\beta \in (0, 1]$ (with $1$ being…

Quantum resources may provide advantage over their classical counterparts. We say this as quantum advantage. Here we consider a single communication task to study different approaches of observing quantum advantage. We say this setting as a…

The uncertainty principle sets lower bound on the uncertainties of two incompatible observables measured on a particle. The uncertainty lower bound can be reduced by considering a particle as a quantum memory entangled with the measured…

In this paper, we study the problem of estimating uniformly well the mean values of several distributions given a finite budget of samples. If the variance of the distributions were known, one could design an optimal sampling strategy by…

Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…

Models of economic decision makers often include idealized assumptions, such as rationality, perfect foresight, and access to all relevant pieces of information. These assumptions often assure the models' internal validity, but, at the same…

The outcomes of a series of measurements, made on a quantum system, form a sequence of random events which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network…

We revisit the problem of Gaussian mean testing in a distributed, communication constrained setting, where each of $n$ users independently observes samples from an unknown $d$-dimensional spherical Gaussian distribution…

The method of model averaging has become an important tool to deal with model uncertainty, for example in situations where a large amount of different theories exist, as are common in economics. Model averaging is a natural and formal…

A dynamic mean field theory is developed for finite state and action Bayesian reinforcement learning in the large state space limit. In an analogy with statistical physics, the Bellman equation is studied as a disordered dynamical system;…

Empirical Bayes methods are widely used for large-scale inference, yet most classical approaches assume homoscedastic observations and focus primarily on posterior mean estimation. We develop a nonparametric empirical Bayes framework for…

The ever-growing size of the datasets renders well-studied learning techniques, such as Kernel Ridge Regression, inapplicable, posing a serious computational challenge. Divide-and-conquer is a common remedy, suggesting to split the dataset…

We present unambiguous experimental evidence for (quantum-like) probabilistic contextuality in psychology. All previous attempts to find contextuality in a psychological experiment were unsuccessful because of the gross violations of…

The purpose of this work is to introduce a notion of weak solution to the master equation of a potential mean field game and to prove that existence and uniqueness hold under quite general assumptions. Remarkably, this is achieved without…