相关论文: A data-based notion of quantiles on Hadamard space…

In this paper, we review some features of quantum annealing and related topics from viewpoints of statistical physics, condensed matter physics, and computational physics. We can obtain a better solution of optimization problems in many…

This paper takes a different approach for the distributed linear parameter estimation over a multi-agent network. The parameter vector is considered to be stochastic with a Gaussian distribution. The sensor measurements at each agent are…

Dirac talked about q-numbers versus c-numbers. Quantum observables are q-number variables that generally do not commute among themselves. He was proposing to have a generalized form of numbers as elements of a noncommutative algebra. That…

This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…

A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…

Measurement involves the determination of quantitative estimates of physical quantities from experiment, along with estimates of their associated uncertainties. Herewith an experimental system model is the key to extracting information from…

The traditional concept of space in geography is based on the notion of distance. Where there is a spatial analysis, there is a distance measurement. However, the precondition for effective distance-based space is that the geographical…

The advent of modern technology, permitting the measurement of thousands of characteristics simultaneously, has given rise to floods of data characterized by many large or even huge datasets. This new paradigm presents extraordinary…

Diffusion Maps framework is a kernel based method for manifold learning and data analysis that defines diffusion similarities by imposing a Markovian process on the given dataset. Analysis by this process uncovers the intrinsic geometric…

Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values…

Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its…

We present an innovative approach to dimensional analysis, based on a general representation theorem for complete quantity functions admitting a covariant scalar representation; this theorem is in turn grounded in a purely algebraic theory…

Data-driven algorithm design automates hyperparameter tuning, but its statistical foundations remain limited because model performance can depend on hyperparameters in implicit and highly non-smooth ways. Existing guarantees focus on the…

We present canonical quantiles and depths for directional data following a distribution which is elliptically symmetric about a direction $\mu$ on the sphere $\mathcal{S}^{d-1}$. Our approach extends the concept of Ley et al. [1], which…

The concepts of similarity and distance are crucial in data mining. We consider the problem of defining the distance between two data sets by comparing summary statistics computed from the data sets. The initial definition of our distance…

We can, and should, do statistical inference on simulation models by adjusting the parameters in the simulation so that the values of {\em randomly chosen} functions of the simulation output match the values of those same functions…

A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…

Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common…

When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…