Related papers: Maximum likelihood estimation in the sparse Rasch …
The Rasch model, a classical model in the item response theory, is widely used in psychometrics to model the relationship between individuals' latent traits and their binary responses to assessments or questionnaires. In this paper, we…
The Rasch model is one of the most fundamental models in \emph{item response theory} and has wide-ranging applications from education testing to recommendation systems. In a universe with $n$ users and $m$ items, the Rasch model assumes…
The Rasch model is widely used for item response analysis in applications ranging from recommender systems to psychology, education, and finance. While a number of estimators have been proposed for the Rasch model over the last decades, the…
Statistical inference using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this paper, we propose a general framework to model the mutual interactions in a network, which enjoys ample…
A strong tool for the selection of items that share a common trait from a set of given items is proposed. The selection method is based on marginal estimates and exploits that the estimates of the standard deviation of the mixing…
Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim…
Marginal maximum likelihood estimation (MMLE) in item response theory (IRT) is highly sensitive to aberrant responses, such as careless answering and random guessing, which can reduce estimation accuracy. To address this issue, this study…
Ranking problems based on pairwise comparisons, such as those arising in online gaming, often involve a large pool of items to order. In these situations, the gap in performance between any two items can be significant, and the smallest and…
The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or…
Estimating the matrix of connections probabilities is one of the key questions when studying sparse networks. In this work, we consider networks generated under the sparse graphon model and the in-homogeneous random graph model with missing…
Modeling sparse data such as microbiome and transcriptomics (RNA-seq) data is very challenging due to the exceeded number of zeros and skewness of the distribution. Many probabilistic models have been used for modeling sparse data,…
Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there…
This paper considers the sample-efficiency of preference learning, which models and predicts human choices based on comparative judgments. The minimax optimal estimation error rate $\Theta(d/n)$ in classical estimation theory requires that…
In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator…
A number of applications (e.g., AI bot tournaments, sports, peer grading, crowdsourcing) use pairwise comparison data and the Bradley-Terry-Luce (BTL) model to evaluate a given collection of items (e.g., bots, teams, students, search…
Joint maximum likelihood (JML) estimation is one of the earliest approaches to fitting item response theory (IRT) models. This procedure treats both the item and person parameters as unknown but fixed model parameters and estimates them…
We consider a linear model which can have a large number of explanatory variables, the errors with an asymmetric distribution or some values of the explained variable are missing at random. In order to take in account these several…
The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to…
This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…
The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the…