相关论文: On a connection between Stein characterizations an…

We propose a new approach to apply the chaining technique in conjunction with information-theoretic measures to bound the generalization error of machine learning algorithms. Different from the deterministic chaining approach based on…

Data compression has become one of the cornerstones of modern astronomical data analysis, with the vast majority of analyses compressing large raw datasets down to a manageable number of informative summaries. In this paper we provide a…

In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-parts formula (IBPF), we derive a Stein operator whose…

We develop a fractional extension of the classical binomial distribution and the associated Bernstein operator, formulated within the framework of the generalized binomial theorem (Hara and Hino [Bull.\ London Math.\ Soc. \textbf{42}…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…

Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the…

We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated,…

Quantum synchronization has emerged as a crucial phenomenon in quantum nonlinear dynamics with potential applications in quantum information processing. Multiple measures for quantifying quantum synchronization exist. However, there is…

We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…

Shared information is a measure of mutual dependence among multiple jointly distributed random variables with finite alphabets. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit…

We extend Stein's method to include dependence with respect to an auxiliary random variable, for conditional laws for which Stein's characterizations do exist.

Mat\'ern's hard-core processes are valuable point process models in spatial statistics. In order to extend their field of application, Mat\'ern's original models are generalized here, both as point processes and particle processes. The…

We extend classical analytic tools for finite-state statistical models to allow zero probabilities. Using methods from algebraic statistics and information geometry, we develop a framework in which a smooth statistical model could hit the…

Wasserstein distributionally robust optimization (DRO) has gained prominence in operations research and machine learning as a powerful method for achieving solutions with favorable out-of-sample performance. Two compelling explanations for…

We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine…

In many fields, data appears in the form of direction (unit vector) and usual statistical procedures are not applicable to such directional data. In this study, we propose non-parametric goodness-of-fit testing procedures for general…

The problem of estimating the shift (or, equivalently, the center of symmetry) of an unknown symmetric and periodic function $f$ observed in Gaussian white noise is considered. Using the blockwise Stein method, a penalized profile…

In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central…

In this era of Big Data, proficient use of data mining is the key to capture useful information from any dataset. As numerous data mining techniques make use of information theory concepts, in this paper, we discuss how Fisher information…

The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and…