Related papers: Vector Quantization with Error Uniformly Distribut…
Cranley and Patterson put forward the following randomization as the basis for the estimation of the error of a lattice rule for an integral of a one-periodic function over the unit cube in s dimensions. The lattice rule is randomized using…
Error models for quantum computing processors describe their deviation from ideal behavior and predict the consequences in applications. But those processors' experimental behavior -- the observed outcome statistics of quantum circuits --…
Distributed graph signal processing algorithms require the network nodes to communicate by exchanging messages in order to achieve a common objective. These messages have a finite precision in realistic networks, which may necessitate to…
We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly…
Quantization can be used to form new vectors/matrices with shared values close to the original. In recent years, the popularity of scalar quantization for value-sharing applications has been soaring as it has been found huge utilities in…
Consensus is a common method for computing a function of the data distributed among the nodes of a network. Of particular interest is distributed average consensus, whereby the nodes iteratively compute the sample average of the data stored…
The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…
We study relativistic scattering when one only has access to a subset of the particles, using the language of quantum measurement theory. We give an exact, non-perturbative formula for the von Neumann entanglement entropy of an apparatus…
Theoretical expressions for the distribution of the ratio of consecutive level spacings for quantum systems with transiting dynamics remain unknown. We propose a family of one-parameter distributions $P(r)\equiv P(r;\beta)$, where…
As quantum computers and simulators begin to produce results that cannot be verified classically, it becomes imperative to develop a variety of tools to detect and diagnose experimental errors on these devices. While state or process…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
In this paper, we give a general formula to determine the quantization coefficients for uniform distributions defined on the boundaries of different regular $m$-sided polygons inscribed in a circle. The result shows that the quantization…
For a voting ensemble that selects an odd-sized subset of the ensemble classifiers at random for each example, applies them to the example, and returns the majority vote, we show that any number of voters may minimize the error rate over an…
Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require…
Distributed learning facilitates the scaling-up of data processing by distributing the computational burden over several nodes. Despite the vast interest in distributed learning, generalization performance of such approaches is not well…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We define the identification set of quantiles of random sets in a way that extends the definition of quantiles for…
Quantum random walks, - coined, lattice ones, - exhibit ballistic behavior with fascinating asymptotic patterns of the amplitudes. We show that averaging over the coins (using the Haar measure), these patterns blend into a spline. Also, we…
An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem…
Rigorous guarantees about the performance of predictive algorithms are necessary in order to ensure their responsible use. Previous work has largely focused on bounding the expected loss of a predictor, but this is not sufficient in many…