Related papers: A Study of Functional Depths
Discrete convex functions are used in many areas, including operations research, discrete-event systems, game theory, and economics. The objective of this paper is to offer a survey on fundamental operations for various kinds of discrete…
Subgraph matching in logic circuits is foundational for numerous Electronic Design Automation (EDA) applications, including datapath optimization, arithmetic verification, and hardware trojan detection. However, existing techniques rely…
We provide several new depth-based separation results for feed-forward neural networks, proving that various types of simple and natural functions can be better approximated using deeper networks than shallower ones, even if the shallower…
Model diagnostics is an indispensable component of regression analysis, yet it is not well addressed in standard textbooks on generalized linear models. The lack of exposition is attributed to the fact that when outcome data are discrete,…
In the functional linear regression model, many methods have been proposed and studied to estimate the slope function while the functional predictor was observed in the entire domain. However, works on functional linear regression models…
Statistical depths have been well studied for multivariate and functional data over the past few decades, but remain under-explored for point processes. A first attempt on the notion of point process depth was conducted recently where the…
Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…
The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…
Parameter-Efficient Fine-Tuning (PEFT) methods achieve performance comparable to Full Fine-Tuning (FFT) while requiring significantly fewer computing resources, making it the go-to choice for researchers. We find that although PEFT can…
Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
In this article, we use L$_p$ depth for classification of multivariate data, where the value of $p$ is chosen adaptively using observations from the training sample. While many depth based classifiers are constructed assuming elliptic…
The relative performance of competing point forecasts is usually measured in terms of loss or scoring functions. It is widely accepted that these scoring function should be strictly consistent in the sense that the expected score is…
This research explores the role and representation of network structure for LTI Systems. We demonstrate that transfer functions contain no structural information without more assumptions being made about the system, assumptions that we…
Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The…
Classical latent-score ranking models often fail to distinguish objects' intrinsic scores from contextual effects, which are typically nonlinear and can dominate the observed outcomes. To address this, we introduce a semiparametric ranking…
Bands of vector-valued functions $f:T\mapsto\mathbb{R}^d$ are defined by considering convex hulls generated by their values concatenated at $m$ different values of the argument. The obtained $m$-bands are families of functions, ranging from…
This article presents an empirical validation of the functional multidimensional scaling model, a novel approach that improves the smoothness of time-varying dissimilarities in a low-dimensional space, embedding a modified Adam stochastic…
Functional brain imaging allows measuring dynamic functionality in all brain regions. It is broadly used in clinical cognitive neuroscience as, well as in research. It will allow the observation of neural activities in the brain…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…