Learning coefficients for hierarchical learning models in Bayesian Estimation

Recently, singular learning theory has been analyzed using algebraic geometry as its basis. It is essential to determine the normal crossing divisors of learning machine singularities through a blowing-up process to observe the behaviors of state probability functions in learning theory. In this paper, we investigate learning coefficients for multi-layered neural networks with linear units, especially when dealing with a large number of layers in Bayesian estimation. We make use of the valuable results obtained by Aoyagi(2023), which provide the main terms for Bayesian generalization error and the average stochastic complexity (free energy). These terms are widely employed in numerical experiments, such as in information criteria

Norming a VALUE Rubric to Assess Graduate Information Literacy Skills

OBJECTIVE: The study evaluated whether a modified version of the information literacy Valid Assessment of Learning in Undergraduate Education (VALUE) rubric would be useful for assessing the information literacy skills of graduate health sciences students. METHODS: Through facilitated calibration workshops, an interdepartmental six-person team of librarians and faculty engaged in guided discussion about the meaning of the rubric criteria. They applied the rubric to score student work for a peer-review essay assignment in the Information Literacy for Evidence-Based Practice course. To determine inter-rater reliability, the raters participated in a follow-up exercise in which they independently applied the rubric to ten samples of work from a research project in the doctor of physical therapy program: the patient case report assignment. RESULTS: For the peer-review essay, a high level of consistency in scoring was achieved for the second workshop, with statistically significant intra-class correlation coefficients above 0.8 for 3 criteria: Determine the extent of evidence needed, Use evidence effectively to accomplish a specific purpose, and Access the needed evidence. Participants concurred that the essay prompt and rubric criteria adequately discriminated the quality of student work for the peer-review essay assignment. When raters independently scored the patient case report assignment, inter-rater agreement was low and statistically insignificant for all rubric criteria (kappa=-0.16, p\u3e0.05-kappa=0.12, p\u3e0.05). CONCLUSIONS: While the peer-review essay assignment lent itself well to rubric calibration, scorers had a difficult time with the patient case report. Lack of familiarity among some raters with the specifics of the patient case report assignment and subject matter might have accounted for low inter-rater reliability. When norming, it is important to hold conversations about search strategies and expectations of performance. Overall, the authors found the rubric to be appropriate for assessing information literacy skills of graduate health sciences students

A Bayesian information criterion for singular models

We consider approximate Bayesian model choice for model selection problems that involve models whose Fisher-information matrices may fail to be invertible along other competing submodels. Such singular models do not obey the regularity conditions underlying the derivation of Schwarz's Bayesian information criterion (BIC) and the penalty structure in BIC generally does not reflect the frequentist large-sample behavior of their marginal likelihood. While large-sample theory for the marginal likelihood of singular models has been developed recently, the resulting approximations depend on the true parameter value and lead to a paradox of circular reasoning. Guided by examples such as determining the number of components of mixture models, the number of factors in latent factor models or the rank in reduced-rank regression, we propose a resolution to this paradox and give a practical extension of BIC for singular model selection problems

A Multi-objective Exploratory Procedure for Regression Model Selection

Variable selection is recognized as one of the most critical steps in statistical modeling. The problems encountered in engineering and social sciences are commonly characterized by over-abundance of explanatory variables, non-linearities and unknown interdependencies between the regressors. An added difficulty is that the analysts may have little or no prior knowledge on the relative importance of the variables. To provide a robust method for model selection, this paper introduces the Multi-objective Genetic Algorithm for Variable Selection (MOGA-VS) that provides the user with an optimal set of regression models for a given data-set. The algorithm considers the regression problem as a two objective task, and explores the Pareto-optimal (best subset) models by preferring those models over the other which have less number of regression coefficients and better goodness of fit. The model exploration can be performed based on in-sample or generalization error minimization. The model selection is proposed to be performed in two steps. First, we generate the frontier of Pareto-optimal regression models by eliminating the dominated models without any user intervention. Second, a decision making process is executed which allows the user to choose the most preferred model using visualisations and simple metrics. The method has been evaluated on a recently published real dataset on Communities and Crime within United States.Comment: in Journal of Computational and Graphical Statistics, Vol. 24, Iss. 1, 201

Wavelet Features for Recognition of First Episode of Schizophrenia from MRI Brain Images

Machine learning methods are increasingly used in various fields of medicine, contributing to early diagnosis and better quality of care. These outputs are particularly desirable in case of neuropsychiatric disorders, such as schizophrenia, due to the inherent potential for creating a new gold standard in the diagnosis and differentiation of particular disorders. This paper presents a scheme for automated classification from magnetic resonance images based on multiresolution representation in the wavelet domain. Implementation of the proposed algorithm, utilizing support vector machines classifier, is introduced and tested on a dataset containing 104 patients with first episode schizophrenia and healthy volunteers. Optimal parameters of different phases of the algorithm are sought and the quality of classification is estimated by robust cross validation techniques. Values of accuracy, sensitivity and specificity over 71% are achieved

A Relationship Between Problem Solving Ability and Students' Mathematical Thinking

This research have a purpose to know is there an influence of problem solving abilty to students mathematical thinking, and to know how strong problem solving ability affect students mathematical thinking. This research used descriptive quantitative method, which a population is all of students that taking discrete mathematics courses both in department of Information Systems and department of mathematics education. Based on the results of data analysis showed that there are an influence of problem solving ability to students mathematical thinking either at department of mathematics education or at department of information systems. In this study, it was found that the influence of problem solving ability to students mathematical thinking which take place at mathematics education department is stonger than at information system department. This is because, at mathematics education department, problem-solving activities more often performed in courses than at department of information system. Almost 75% of existing courses in department of mathematics education involve problem solving to the objective of courses, meanwhile, in the department of information systems, there are only 10% of these courses. As a result, mathematics education department student's are better trained in problem solving than information system department students. So, to improve students' mathematical thinking, its would be better, at fisrtly enhance the problem solving ability