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In the field of spatial data analysis, spatially varying coefficients (SVC) models, which allow regression coefficients to vary by region and flexibly capture spatial heterogeneity, have continued to be developed in various directions.…

In regular statistical models, the leave-one-out cross-validation is asymptotically equivalent to the Akaike information criterion. However, since many learning machines are singular statistical models, the asymptotic behavior of the…

Longitudinal data are common in clinical trials and observational studies, where missing outcomes due to dropouts are always encountered. Under such context with the assumption of missing at random, the weighted generalized estimating…

Leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC) are methods for estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model using the log-likelihood evaluated at the…

Learning invariant representations is a critical first step in a number of machine learning tasks. A common approach corresponds to the so-called information bottleneck principle in which an application dependent function of mutual…

The main purpose of incremental learning is to learn new knowledge while not forgetting the knowledge which have been learned before. At present, the main challenge in this area is the catastrophe forgetting, namely the network will lose…

The intraclass correlation coefficient (ICC) is a classical index of measurement reliability. With the advent of new and complex types of data for which the ICC is not defined, there is a need for new ways to assess reliability. To meet…

Generalised Bayesian Inference (GBI) attempts to address model misspecification in a standard Bayesian setup by tempering the likelihood. The likelihood is raised to a fractional power, called the learning rate, which reduces its importance…

This paper introduces and develops a theoretical extension of the widely applicable information criterion (WAIC), called the Covariance-Corrected WAIC (CC-WAIC), that applied for Bayesian sequential data models. The CC-WAIC accounts for…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

This paper introduces the concept of uniform classification, which employs a unified threshold to classify all samples rather than adaptive threshold classifying each individual sample. We also propose the uniform classification accuracy as…

We propose a new method for parameter learning in Bayesian networks with qualitative influences. This method extends our previous work from networks of binary variables to networks of discrete variables with ordered values. The specified…

We are interested in the large-scale learning of Mahalanobis distances, with a particular focus on person re-identification. We propose a metric learning formulation called Weighted Approximate Rank Component Analysis (WARCA). WARCA…

Bayesian model averaging is a practical method for dealing with uncertainty due to model specification. Use of this technique requires the estimation of model probability weights. In this work, we revisit the derivation of estimators for…

In this paper, we propose an information-theoretic approach to design the functional representations to extract the hidden common structure shared by a set of random variables. The main idea is to measure the common information between the…

Bayesian diagnostic classification models (Bayesian DCMs) are effective for diagnosing students' skills. Research on the evaluation of relative model fit indices for DCMs using Bayesian estimation, however, is deficient. This study…

Class-incremental learning (CIL) is a particularly challenging variant of continual learning, where the goal is to learn to discriminate between all classes presented in an incremental fashion. Existing approaches often suffer from…

We go through the process of crafting a robust and numerically stable online algorithm for the computation of the Watanabe-Akaike information criteria (WAIC). We implement this algorithm in the NIMBLE software. The implementation is…

Catastrophic forgetting is a critical challenge in training deep neural networks. Although continual learning has been investigated as a countermeasure to the problem, it often suffers from the requirements of additional network components…

Meta-learning, or "learning to learn", refers to techniques that infer an inductive bias from data corresponding to multiple related tasks with the goal of improving the sample efficiency for new, previously unobserved, tasks. A key…