相关论文: On the definition of a concentration function rele…
In the present paper, the concept of contraction has been extended in a refined manner by introducing $\mathfrak{D}$-Contraction defined on a family $\mathfrak{F}$ of bounded functions. Also, a new notion of fixed function has been…
The ROC curve is the gold standard for measuring the performance of a test/scoring statistic regarding its capacity to discriminate between two statistical populations in a wide variety of applications, ranging from anomaly detection in…
Concentration of measure is studied, and obtained, for stable and related random vectors.
Stochastic optimal control (SOC) aims to direct the behavior of noisy systems and has widespread applications in science, engineering, and artificial intelligence. In particular, reward fine-tuning of diffusion and flow matching models and…
The aim of this paper is to present an alternative formulation of the attention scoring function in translation tasks. Generally speaking, language is deeply structured, and this is reflected in the attention scoring matrix. We exploit this…
The ROC curve is a statistical tool that analyses the accuracy of a diagnostic test in which a variable is used to decide whether an individual is healthy or not. Along with that diagnostic variable it is usual to have information of some…
The area under the ROC curve is widely used as a measure of performance of classification rules. However, it has recently been shown that the measure is fundamentally incoherent, in the sense that it treats the relative severities of…
Functional markers become a more frequent tool in medical diagnosis. In this paper, we aim to define an index allowing to discriminate between populations when the observations are functional data belonging to a Hilbert space. We discuss…
As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality…
Classification is one of the most popular and widely used supervised learning tasks, which categorizes objects into predefined classes based on known knowledge. Classification has been an important research topic in machine learning and…
Attention is an operation that selects some largest element from some set, where the notion of largest is defined elsewhere. Applying this operation to sequence to sequence mapping results in significant improvements to the task at hand. In…
Let $\boldsymbol{X}$ be a $d$-dimensional random array on $[n]$ whose entries take values in a finite set $\mathcal{X}$, that is, $\boldsymbol{X}=\langle X_s:s\in \binom{[n]}{d}\rangle$ is an $\mathcal{X}$-valued stochastic process indexed…
The FOCUS constraint expresses the notion that solutions are concentrated. In practice, this constraint suffers from the rigidity of its semantics. To tackle this issue, we propose three generalizations of the FOCUS constraint. We provide…
The purpose of this paper is to introduce into consideration an analogue of the concentration index in the class of subharmonic functions of infinite order. The one in the case of finite order is used in the interpolation theory.
Evaluating and comparing the academic performance of a journal, a researcher or a single paper has long remained a critical, necessary but also controversial issue. Most of existing metrics invalidate comparison across different fields of…
Background: Understanding the distinction between function and role is vexing and difficult. While it appears to be useful, in practice this distinction is hard to apply, particularly within biology. Results: I take an evolutionary…
We estimate the concentration functions of $n$-fold convolutions of one-dimensional probability measures. The main result is a supplement to the results of G\"otze and Zaitsev (1998). We show that the estimation of concentration functions…
We study concentration of measure in Lie group actions. We define the notion of concentration locus of a flag sequence of Lie groups. Some examples of infinite group action on an infinite dimensional compact and non compact manifold show…
Sentence function is an important linguistic feature referring to a user's purpose in uttering a specific sentence. The use of sentence function has shown promising results to improve the performance of conversation models. However, there…
When evaluating medical tests or biomarkers for disease classification, the area under the receiver-operating characteristic (ROC) curve is a widely used performance metric that does not require us to commit to a specific decision…