Related papers: Sum-Based Scoring for Dichotomous and Likert-scale…
In this paper, We use the Fourier series expansion of real variables function, We give a formula to calculate the Dirichlet character sum, and four special examples are given.
We give a sharpened form of Siegel Lemma's w. r. t. the maximum norm. This implies a new lower bound on the greatest element of a sum-distinct set of positive integers (Erd\"os-Moser problem). The main tools are Minkowski's theorem on…
Staged trees are a recently-developed, powerful family of probabilistic graphical models. An equivalence class of staged trees has now been characterised, and two fundamental statistical operators have been defined to traverse the…
Answer selection is a task to choose the positive answers from a pool of candidate answers for a given question. In this paper, we propose a novel strategy for answer selection, called hierarchical ranking. We introduce three levels of…
In this paper, we study the multiple $L$-values and the multiple zeta values of level $N$. We set up the algebraic framework for the double shuffle relations of the multiple zeta values of level $N$. Using the regularized double shuffle…
We outline a new algorithm to solve coupled systems of differential equations in one continuous variable $x$ (resp. coupled difference equations in one discrete variable $N$) depending on a small parameter $\epsilon$: given such a system…
In some areas of computing, natural language processing and information science, progress is made by sharing datasets and challenging the community to design the best algorithm for an associated task. This article introduces a shared…
Reasoning with fuzzy sets can be achieved through measures such as similarity and distance. However, these measures can often give misleading results when considered independently, for example giving the same value for two different pairs…
Enumeration problems aim at outputting, without repetition, the set of solutions to a given problem instance. However, outputting the entire solution set may be prohibitively expensive if it is too big. In this case, outputting a small,…
In ranking problems, the goal is to learn a ranking function from labeled pairs of input points. In this paper, we consider the related comparison problem, where the label indicates which element of the pair is better, or if there is no…
How reliable are single-response LLM-as-a-judge ratings without references, and can we obtain fine-grained, deterministic scores in this setting? We study the common practice of asking a judge model to assign Likert-scale scores to…
IRT models are being increasingly used worldwide for test construction and scoring. The study examines the practical implications of estimating individual scores in a paper-and-pencil high-stakes test using 2PL and 3PL models, specifically…
Traditional methods for matching in causal inference are impractical for high-dimensional datasets. They suffer from the curse of dimensionality: exact matching and coarsened exact matching find exponentially fewer matches as the input…
Many probabilistic models that have an intractable normalizing constant may be extended to contain covariates. Since the evaluation of the exact likelihood is difficult or even impossible for these models, score matching was proposed to…
The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…
To obtain reliable results of expertise, which usually use individual and group expert pairwise comparisons, it is important to summarize (aggregate) expert estimates provided that they are sufficiently consistent. There are several ways to…
Automated scoring of student responses to open-ended questions, including short-answer questions, has great potential to scale to a large number of responses. Recent approaches for automated scoring rely on supervised learning, i.e.,…
It is suggested to insert into test matrix 1s for correct responses, 0s for response refusals, and negative corrective elements for incorrect responses. With the classical test theory approach test scores of examinees and items are…
Compositional data and multivariate count data with known totals are challenging to analyse due to the non-negativity and sum-to-one constraints on the sample space. It is often the case that many of the compositional components are highly…
The maximum segment sum problem is to compute, given a list of integers, the largest of the sums of the contiguous segments of that list. This problem specification maps directly onto a cubic-time algorithm; however, there is a very elegant…