Related papers: Multi-Dimensional Item Response Theory and the For…
We propose MIRA, a new benchmark designed to evaluate models in scenarios where generating intermediate visual images is essential for successful reasoning. Unlike traditional CoT methods that rely solely on text, tasks in MIRA require…
We have performed a detailed analysis of the fast multipole method (FMM) in the adaptive case, in which the depth of the FMM tree is non-uniform. Previous works in this area have focused mostly on special types of adaptive distributions,…
Marginal maximum likelihood (MML) estimation is the preferred approach to fitting item response theory models in psychometrics due to the MML estimator's consistency, normality, and efficiency as the sample size tends to infinity. However,…
In this second part of our series on the recently proposed many-body expanded full configuration interaction (MBE-FCI) method, we introduce the concept of multideterminantal expansion references. Through theoretical arguments and numerical…
The superiority and inferiority ranking (SIR) method is a generation of the well-known PROMETHEE method, which can be more efficient to deal with multi-criterion decision making (MCDM) problem. Intuitionistic fuzzy sets (IFSs), as an…
In this paper, we show that the central limit theorem (CLT) satisfied by the data-driven Multidimensional Increment Ratio (MIR) estimator of the memory parameter d established in Bardet and Dola (2012) for d $\in$ (--0.5, 0.5) can be…
Item parameter estimation in pharmacometric item response theory (IRT) models is predominantly performed using the Laplace estimation algorithm as implemented in NONMEM. In psychometrics a wide range of different software tools, including…
Mixtures of factor analysers (MFA) models represent a popular tool for finding structure in data, particularly high-dimensional data. While in most applications the number of clusters, and especially the number of latent factors within…
Fractured metal fragments with rough and irregular surfaces are often found at crime scenes. Current forensic practice visually inspects the complex jagged trajectory of fractured surfaces to recognize a ``match'' using comparative…
Item response theory (IRT) models are widely used in psychometrics and educational measurement, being deployed in many high stakes tests such as the GRE aptitude test. IRT has largely focused on estimation of a single latent trait (e.g.…
We suggest one redefinition of common clusters of questions used to analyze student responses on the Force and Motion Conceptual Evaluation (FMCE). Our goal is to move beyond the expert/novice analysis of student learning based on…
Vector Fitting (VF) is a popular method of constructing rational approximants that provides a least squares fit to frequency response measurements. In an earlier work, we provided an analysis of VF for scalar-valued rational functions and…
Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to…
Modeling the creative mathematical sensemaking that characterizes expert thinking in physics is typically a struggle for new learners. To help students learn to reason this way, we created a set of supplemental activities called Physics…
Recent advances in large Vision-Language Models (VLMs) have exhibited strong reasoning capabilities on complex visual tasks by thinking with images in their Chain-of-Thought (CoT), which is achieved by actively invoking tools to analyze…
This paper proposes a new method for differentiating through optimal trajectories arising from non-convex, constrained discrete-time optimal control (COC) problems using the implicit function theorem (IFT). Previous works solve a…
Frequent Item-set Mining (FIM), sometimes called Market Basket Analysis (MBA) or Association Rule Learning (ARL), are Machine Learning (ML) methods for creating rules from datasets of transactions of items. Most methods identify items…
Ever since its publication, the Griffith theory is the most widely used criterion for estimating the ideal strength and fracture strength of materials depending on whether the materials contain cracks or not. A Griffith strength limit of…
Ensuring factuality is essential for the safe use of Large Language Models (LLMs) in high-stakes domains such as medicine and law. Conformal inference provides distribution-free guarantees, but existing approaches are either overly…
The minimum aberration criterion has been frequently used in the selection of fractional factorial designs with nominal factors. For designs with quantitative factors, however, level permutation of factors could alter their geometrical…