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Models with unnormalized probability density functions are ubiquitous in statistics, artificial intelligence and many other fields. However, they face significant challenges in model selection if the normalizing constants are intractable.…
We deal with a model selection problem for structural equation modeling (SEM) with latent variables for diffusion processes. Based on the asymptotic expansion of the marginal quasi-log likelihood, we propose two types of quasi-Bayesian…
The linear hazard regression model developed by Aalen is becoming an increasingly popular alternative to the Cox multiplicative hazard regression model. There are no methods in the literature for selecting among different candidate models…
Despite the remarkable performance of Large Language Models (LLMs) in natural language processing tasks, they still struggle with generating logically sound arguments, resulting in potential risks such as spreading misinformation. To…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
Federated learning (FL) is a widely adopted privacy-preserving distributed learning framework, yet its generalization performance remains less explored compared to centralized learning. In FL, the generalization error consists of two…
Variable selection in linear regression has been a central topic in statistical research for decades. Bayesian variable selection methods, which account for uncertainty in both the regression coefficients and the noise variance, have…
Bayesian phylogenetic methods are generating noticeable enthusiasm in the field of molecular systematics. Many phylogenetic models are often at stake and different approaches are used to compare them within a Bayesian framework. The Bayes…
Recent research has demonstrated that Feed-Forward Networks (FFNs) in Large Language Models (LLMs) play a pivotal role in storing diverse linguistic and factual knowledge. Conventional methods frequently face challenges due to knowledge…
The multivariate normal linear model is one of the most widely employed models for statistical inference in applied research. Special cases include (multivariate) t testing, (M)AN(C)OVA, (multivariate) multiple regression, and repeated…
While Multimodal Large Language Models (MLLMs) have demonstrated impressive capabilities in general visual understanding, they frequently falter in fine-grained perception tasks that require identifying tiny objects or discerning subtle…
For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…
Factor models are widely applied to the analysis of multivariate data across disparate fields of research. However, modern scientific data are often incomplete, and estimating a factor model from partially observed data can be very…
Ancestral graph models, introduced by Richardson and Spirtes (2002), generalize both Markov random fields and Bayesian networks to a class of graphs with a global Markov property that is closed under conditioning and marginalization. By…
Feature selection is a crucial step in large-scale industrial machine learning systems, directly affecting model accuracy, efficiency, and maintainability. Traditional feature selection methods rely on labeled data and statistical…
High-dimensional linear and nonlinear models have been extensively used to identify associations between response and explanatory variables. The variable selection problem is commonly of interest in the presence of massive and complex data.…
Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…
In many learning systems, such as activity recognition systems, as new data collection methods continue to emerge in various dynamic environmental applications, the attributes of instances accumulate incrementally, with data being stored in…
Many problems in statistics and machine learning can be formulated as model selection problems, where the goal is to choose an optimal parsimonious model among a set of candidate models. It is typical to conduct model selection by…