Related papers: New iterative algorithms for estimation of item fu…
Accurate estimates of item difficulty are essential for valid assessment and effective adaptive learning. However, for newly created tasks, response data are typically unavailable. Pretesting and expert judgement can be costly and slow,…
Recent advancements in testing differential item functioning (DIF) have greatly relaxed restrictions made by the conventional multiple group item response theory (IRT) model with respect to the number of grouping variables and the…
The stochastic approximation EM algorithm (SAEM) is described for the estimation of item and person parameters given test data coded as dichotomous or ordinal variables. The method hinges upon the eigenanalysis of missing variables sampled…
Expectation maximisation (EM) is an unsupervised learning method for estimating the parameters of a finite mixture distribution. It works by introducing "hidden" or "latent" variables via Baum's auxiliary function $Q$ that allow the joint…
(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…
Traditional methods for determining assessment item parameters, such as difficulty and discrimination, rely heavily on expensive field testing to collect student performance data for Item Response Theory (IRT) calibration. This study…
We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semi-parametric models, the unknown monotone transformation function is approximated via monotone splines. A…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing maximum likelihood estimate when dealing with Gaussian Mixture Model (GMM). When the sample size is smaller than the data dimension, this could lead…
The crossed random effects model is widely used, finding applications in various fields such as longitudinal studies, e-commerce, and recommender systems, among others. However, these models encounter scalability challenges, as the…
Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for…
Evaluating mathematical reasoning in LLMs is constrained by limited benchmark sizes and inherent model stochasticity, yielding high-variance accuracy estimates and unstable rankings across platforms. On difficult problems, an LLM may fail…
Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…
Ordinal user-provided ratings across multiple items are frequently encountered in both scientific and commercial applications. Whilst recommender systems are known to do well on these type of data from a predictive point of view, their…
Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…
Inferring dynamics from time series is an important objective in data analysis. In particular, it is challenging to infer stochastic dynamics given incomplete data. We propose an expectation maximization (EM) algorithm that iterates between…
We extend the linear mixed-effects state model to accommodate the correlated individuals and investigate its parameter and state estimation based on disturbance smoothing in this paper. For parameter estimation, EM and score based…
Item recommendation (the task of predicting if a user may interact with new items from the catalogue in a recommendation system) and link prediction (the task of identifying missing links in a knowledge graph) have long been regarded as…
We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or…