相关论文: Changes from Classical Statistics to Modern Statis…

The aim of this work is to show how Einstein's quantum hypothesis leads immediately and necessarily to a departure from classical mechanics. First we note that the classical description and predictions are in terms of idealized measurements…

This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…

With increased access to data and the advent of computers, the use of statistical tools and numerical simulations is becoming commonplace for ecologists. These approaches help improve our understanding of ecological phenomena and their…

Many fundamental statistical methods have become critical tools for scientific data analysis yet do not scale tractably to modern large datasets. This paper will describe very recent algorithms based on computational geometry which have…

Why do we not profit from our long-existing classical robotics knowledge and look for some alternative way for data collection? The situation ignoring all existing methods might be such a waste. This article argues that a dataset created…

Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…

The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…

In the last decade, the scientific community has devolved its attention to the deployment of data-driven approaches in scientific research to provide accurate and reliable analysis of a plethora of phenomena. Most notably, Physics-informed…

Conventional statistical wisdom established a well-understood relationship between model complexity and prediction error, typically presented as a U-shaped curve reflecting a transition between under- and overfitting regimes. However,…

The taxonomic composition and abundance of phytoplankton, having direct impact on marine ecosystem dynamic and global environment change, are listed as essential ocean variables. Phytoplankton classification is very crucial for…

A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…

Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is…

In the modern Bayesian view classical probability theory is simply an extension of conventional logic, i.e., a quantitative tool that allows for consistent reasoning in the presence of uncertainty. Classical theory presupposes, however,…

However, the observations encompassed by classical physics excludes the observer from the physical reality, yet the deep-down understandung of nature --{\it the quantum theory}-- can not avoid the intrusion of observer into the measurement…

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on…

Modern Artificial Intelligence achieves remarkable predictive power by optimizing statistical risk functionals over vast corpora. Yet a gap separates this from genuine intelligence: the inability to distinguish correlation from causation.…

These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…

Correlation clustering is a widely-used approach for clustering large data sets based only on pairwise similarity information. In recent years, there has been a steady stream of better and better classical algorithms for approximating this…

This research explores the integration of quantum data embedding techniques into classical machine learning (ML) algorithms, aiming to assess the performance enhancements and computational implications across a spectrum of models. We…