arXiv research

Surveying nonparametric inference with shape constraints, past and future.

Explains isometric immersions and their applications.

This paper reviews Douglas curvature in Finsler geometry.

Study on spectral asymptotics in elasticity on smooth manifolds.

In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the other. On the way we show how this problem has profited from the d…

We give a brief historical overview of the Tait conjectures, made 120 years ago in the course of his pioneering work in tabulating the simplest knots, and solved a century later using the Jones polynomial. We announce the solution, again based on a substantial study of the Jones polynomial, of one (possibly his last re…

Machine learning automates digitization of historical data.

Classical (Itô diffusions) stochastic volatility models are not able to capture the steepness of small-maturity implied volatility smiles. Jumps, in particular exponential Lévy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see \cite{Tank} for an overvi…

A pedagogical but concise overview of fiber bundles and their connections is provided, in the context of gauge theories in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems…

The paper explores Wiener-Granger causality and its computational enhancements.

This report first provides a brief overview of a number of supervised learning algorithms for regression tasks. Among those are neural networks, regression trees, and the recently introduced Nexting. Nexting has been presented in the context of reinforcement learning where it was used to predict a large number of signa…

In machine learning we often try to optimise a decision rule that would have worked well over a historical dataset; this is the so called empirical risk minimisation principle. In the context of learning from recommender system logs, applying this principle becomes a problem because we do not have available the reward …

We discuss deep reinforcement learning in an overview style. We draw a big picture, filled with details. We discuss six core elements, six important mechanisms, and twelve applications, focusing on contemporary work, and in historical contexts. We start with background of artificial intelligence, machine learning, deep…

A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is gi…

Marketing analytics is a diverse field, with both academic researchers and practitioners coming from a range of backgrounds including marketing, expert systems, statistics, and operations research. This paper provides an integrative review at the boundary of these areas. The aim is to give researchers in the intelligen…

In this paper we provide a conceptual overview of latent variable models within a probabilistic modeling framework, an overview that emphasizes the compositional nature and the interconnectedness of the seemingly disparate models commonly encountered in statistical practice.

Genealogy research is the study of family history using available resources such as historical records. Ancestry provides its customers with one of the world's largest online genealogical index with billions of records from a wide range of sources, including vital records such as birth and death certificates, census re…

This paper applies Heath-Jarrow-Morton framework to energy markets for practical use.

A quick overview is provided on the current development of the WP metric geometry.

Markov models lie at the interface between statistical independence in a probability distribution and graph separation properties. We review model selection and estimation in directed and undirected Markov models with Gaussian parametrization, emphasizing the main similarities and differences. These two model classes a…

Among the machine learning applications to business, recommender systems would take one of the top places when it comes to success and adoption. They help the user in accelerating the process of search while helping businesses maximize sales. Post phenomenal success in computer vision and speech recognition, deep learn…

This review deals with several microscopic (``agent-based'') models of financial markets which have been studied by economists and physicists over the last decade: Kim-Markowitz, Levy-Levy-Solomon, Cont-Bouchaud, Solomon-Weisbuch, Lux-Marchesi, Donangelo-Sneppen and Solomon-Levy-Huang. After an overview of simulation a…

Overview of affine surface area and its history.

Overview of infinite surface mapping class groups.

ARIMA model outperforms advanced forecasting models in predicting Walmart sales.

We give a quite detailed overview on the proof of the Cheeger-Colding-Gromoll splitting theorem in the abstract framework of spaces with Riemannian Ricci curvature bounded from below.

This Chapter, "Overview of Approximate Bayesian Computation", is to appear as the first chapter in the forthcoming Handbook of Approximate Bayesian Computation (2018). It details the main ideas and concepts behind ABC methods with many examples and illustrations.

Recent research on Bitcoin Transaction Networks reveals a growing, sparse, and core-periphery structure.

This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary differential equations, these algebras, or infinitesimal groups, are a recurring theme in 20th-century research on Lie algebras. I will…

Multi-task learning (MTL) has led to successes in many applications of machine learning, from natural language processing and speech recognition to computer vision and drug discovery. This article aims to give a general overview of MTL, particularly in deep neural networks. It introduces the two most common methods for…

Multi-view learning (MVL) is a strategy for fusing data from different sources or subsets. Canonical correlation analysis (CCA) is very important in MVL, whose main idea is to map data from different views onto a common space with maximum correlation. Traditional CCA can only be used to calculate the linear correlation…

This paper provides an overview of activation functions in neural networks.

This paper offers an overview of neural network compression techniques.

Overview of Thurston's work in math.

Unified HS and related methods with explicit modeling assumptions.

We present a brief overview of the Korányi-Reimann theory of quasiconformal mappings on the Heisenberg group stressing on the analogies as well as on the differences between the Heisenberg group case and the classical two-dimensional case. We examine the extensions of the theory to more general spaces and we state some…

Data mining is about obtaining new knowledge from existing datasets. However, the data in the existing datasets can be scattered, noisy, and even incomplete. Although lots of effort is spent on developing or fine-tuning data mining models to make them more robust to the noise of the input data, their qualities still st…

Provides an overview of Bartnik's quasi-local mass.

Quantifying and managing uncertainties that occur when data-driven models such as those provided by AI and machine learning methods are applied is crucial. This whitepaper provides a brief motivation and first overview of the state of the art in identifying and quantifying sources of uncertainty for data-driven compone…

The link between different psychophysiological measures during emotion episodes is not well understood. To analyse the functional relationship between electroencephalography (EEG) and facial electromyography (EMG), we apply historical function-on-function regression models to EEG and EMG data that were simultaneously r…

Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory. We target at a broad audience, not necessarily machine learning researchers. Thi…

Overview of risk-sensitive Markov decision processes with Optimized Certainty Equivalent.

Overview of SML techniques with banking applications.

ArtificialReplay improves data efficiency in bandits using historical data.

ADR helps LLMs find and use historical analogies for foresight analysis.

In the overview, a generic mathematical object (mapping) is introduced, and its relation to model physics parameterization is explained. Machine learning (ML) tools that can be used to emulate and/or approximate mappings are introduced. Applications of ML to emulate existing parameterizations, to develop new parameteri…

In math.GT/0106017 it was shown that thin position on Heegaard spines can be a useful tool for analyzing the topology of knots in 3-space. The proof there (specifically, of the Goda-Teragaito conjecture) requires masses of technical detail; it is easy to lose track of the underlying ideas. The present paper gives an ov…

Proposes dynamic borrowing method for historical data in clinical trials.