Related papers: Functional Analysis of Loss-development Patterns i…

Loss functions are error metrics that quantify the difference between a prediction and its corresponding ground truth. Fundamentally, they define a functional landscape for traversal by gradient descent. Although numerous loss functions…

This paper studies high-dimensional curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor…

Interest-rate risk is a key factor for property-casualty insurer capital. P&C companies tend to be highly leveraged, with bond holdings much greater than capital. For GAAP capital, bonds are marked to market but liabilities are not, so…

Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid…

We present observations and discussion of previously unreported phenomena discovered while training residual networks. The goal of this work is to better understand the nature of neural networks through the examination of these new…

Regression learning is classic and fundamental for medical image analysis. It provides the continuous mapping for many critical applications, like the attribute estimation, object detection, segmentation and non-rigid registration. However,…

The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…

In this article, we proposed a partition:wise robust loss function based on the previous robust loss function. The characteristics of this loss function are that it achieves high robustness and a wide range of applicability through…

This paper proposes econometric methods for studying how economic variables respond to function-valued shocks. Our methods are developed based on linear projection estimation of predictive regression models with a function-valued predictor…

The analysis of standardized low cycle fatigue (LCF) experiments shows that the failure times widely scatter. Furthermore, mechanical components often fail before the deterministic failure time is reached. A possibility to overcome these…

Partial least squares regression---or PLS---is a multivariate method in which models are estimated using either the SIMPLS or NIPALS algorithm. PLS regression has been extensively used in applied research because of its effectiveness in…

A full parametric and linear specification may be insufficient to capture complicated patterns in studies exploring complex features, such as those investigating age-related changes in brain functional abilities. Alternatively, a partially…

State of the art Symbolic Regression (SR) methods currently build specialized models, while the application of Large Language Models (LLMs) remains largely unexplored. In this work, we introduce the first comprehensive framework that…

In-context learning (ICL) exhibits dual operating modes: task learning, i.e., acquiring a new skill from in-context samples, and task retrieval, i.e., locating and activating a relevant pretrained skill. Recent theoretical work investigates…

The Lorenz curve is a fundamental tool for analysing income and wealth distribution and inequality at national and regional levels. We utilise a one-way functional analysis of variance to decompose a time series of Lorenz curves and develop…

Monitoring awkward postures is a proactive prevention for Musculoskeletal Disorders (MSDs)in construction. Machine Learning (ML) models have shown promising results for posture recognition from Wearable Sensors. However, further…

We use the Kac-Rice formula and results from random matrix theory to obtain the average number of critical points of a family of high-dimensional empirical loss functions, where the data are correlated $d$-dimensional Gaussian vectors,…

The paper considers functional linear regression, where scalar responses $Y_1,\ldots,Y_n$ are modeled in dependence of i.i.d. random functions $X_1,\ldots,X_n$. We study a generalization of the classical functional linear regression model.…

This study presents machine learning models that forecast and categorize lost circulation severity preemptively using a large class imbalanced drilling dataset. We demonstrate reproducible core techniques involved in tackling a large…

Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…