Related papers: Scalable Bayesian Approach for the DINA Q-matrix E…
The purpose of this research is to develop an MCMC algorithm for estimating the Q-matrix. Based on the DINA model, the algorithm starts with estimating correlated attributes. Using a saturated model and a binary decimal conversion, the…
This paper establishes fundamental results for statistical inference of diagnostic classification models (DCM). The results are developed at a high level of generality, applicable to essentially all diagnostic classification models. In…
Diagnostic classification models (DCMs) are psychometric models for evaluating a student's mastery of the essential skills in a content domain based upon their responses to a set of test items. Currently, diagnostic model and/or Q-matrix…
Quadratic discriminant analysis (QDA) is a standard tool for classification due to its simplicity and flexibility. Because the number of its parameters scales quadratically with the number of the variables, QDA is not practical, however,…
Cognitive diagnosis is an essential task in many educational applications. Many solutions have been designed in the literature. The deterministic input, noisy "and" gate (DINA) model is a classical cognitive diagnosis model and can provide…
Fueled by the call for formative assessments, diagnostic classification models (DCMs) have recently gained popularity in psychometrics. Despite their potential for providing diagnostic information that aids in classroom instruction and…
Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…
Large language models (LLMs) have achieved remarkable performance on diverse benchmarks, yet existing evaluation practices largely rely on coarse summary metrics that obscure underlying reasoning abilities. In this work, we propose novel…
If the probability model is correctly specified, then we can estimate the covariance matrix of the asymptotic maximum likelihood estimate distribution using either the first or second derivatives of the likelihood function. Therefore, if…
The design of informatively rich input signals is essential for accurate system identification, yet classical Fisher-information-based methods are inherently local and often inadequate in the presence of significant model uncertainty and…
This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…
Cognitive Diagnosis Models (CDMs) are useful statistical tools in cognitive diagnosis assessment. However, as many other latent variable models, the CDMs often suffer from the non-identifiability issue. This work gives the sufficient and…
Bayesian inference promises to ground and improve the performance of deep neural networks. It promises to be robust to overfitting, to simplify the training procedure and the space of hyperparameters, and to provide a calibrated measure of…
We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous…
We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
Matrix decomposition is one of the fundamental tools to discover knowledge from big data generated by modern applications. However, it is still inefficient or infeasible to process very big data using such a method in a single machine.…
As a statistical tool to assist formative assessments in educational settings, diagnostic classification models (DCMs) have been increasingly used to provide diagnostic information regarding examinees' attributes. DCMs often adopt a…
Due to the importance of uncertainty quantification (UQ), Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. However, traditional Bayesian inference methods based on Markov…
We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest.…