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These instructions give you guidelines for preparing Students were unable to gain exposure to think practically, solve real-world problems, and think critically in recent years following pandemic situations, so design thinking is a rapid change in engineering education strategies to increase students' engagement in imparting knowledge and skills remotely to the students. The traditional approach to teaching-learning strategies has given way to some advanced methods utilizing various modern approaches such as design thinking. The engagement of students actively and learning collaboratively with thinking ability is the major challenge in the learning of courses like metrology. The paper is a report on the author's use of the design thinking approach for the learning and active participation of third-year mechanical engineering students at Rajarambapu Institute of Technology in Rajaramnagar. This paper describes the use of the design thinking approach for the metrology course and summaries of students' active participation and improvement in terms of students' "Learning Coefficient (LC)" based on the responses collected. The learning coefficient is represented by a number ranging from 0 to 1, with 0 indicating fewer interactive sessions and 1 indicating extremely interactive sessions. These coefficients reveal how much learning is taking place. Furthermore, the impact assessment shows that course results and course outcome attainment were significantly improved. The students' feedback indicates that they had a great time and appreciated the opportunity to learn. [ABSTRACT FROM AUTHOR]

Latent Dirichlet allocation (LDA) obtains essential information from data by using Bayesian inference. It is applied to knowledge discovery via dimension reducing and clustering in many fields. However, its generalization error had not been yet clarified since it is a singular statistical model where there is no one-to-one mapping from parameters to probability distributions. In this paper, we give the exact asymptotic form of its generalization error and marginal likelihood, by theoretical analysis of its learning coefficient using algebraic geometry. The theoretical result shows that the Bayesian generalization error in LDA is expressed in terms of that in matrix factorization and a penalty from the simplex restriction of LDA's parameter region. A numerical experiment is consistent with the theoretical result. • Latent Dirichlet Allocation (LDA) is a widely used statistical model in many fields. • The Bayesian generalization error (GE) in LDA has been unknown since it is singular. • We determine the learning coefficient of GE in LDA with resolution of singularity. • The main result shows the behavior of GE in LDA when topics or sample size increases. • The experimental result is consistent with Main Theorem when sample size is finite. [ABSTRACT FROM AUTHOR]

Due to the current pandemic situation all across the world, the education sector is undergoing a transformation. Engineering education is changing its face, too, as it is the need of the hour to impart knowledge and skills remotely to the students. At our Institute, we had not attempted the online teaching-learning methodology before the pandemic because students daily travelled to the Institute, and the need did not arise. Currently, we have adapted to MS Teams as our online platform for the conduction of classes and software laboratories. The major challenge in online teaching is to engage the students actively and ensure that learning is happening. Active learning is defined as "educational methods in which students are involved in higher-order thinking (analysis, synthesis, evaluation)." This work is a report on the methodologies adopted by the authors in the ongoing semester, involving some of the well-documented active learning strategies for two undergraduate courses in Mumbai University curriculum. The paper describes the adopted teaching methodologies with statistics collected during the ongoing semester and summarizes the outcomes of these experiments in terms of students' "Learning Coefficient (LC)" in the undertaken courses based on the feedback collected by the course coordinators. Learning Coefficient is a number between 0 to 1 where 0 indicates non-interactive sessions and 1 indicates the highly interactive and highest level of learning. In this paper, we report a learning coefficient of 0.7 for one course and 0.64 for the other course through active learning techniques. These coefficients are indicative of "learning happening". [ABSTRACT FROM AUTHOR]

Non-negative matrix factorization (NMF) is a knowledge discovery method that is used in many fields. Variational inference and Gibbs sampling methods for it are also well-known. However, the variational approximation error has not been clarified yet, because NMF is not statistically regular and the prior distribution used in variational Bayesian NMF (VBNMF) has zero or divergence points. In this paper, using algebraic geometrical methods, we theoretically analyze the difference in negative log evidence (a.k.a. free energy) between VBNMF and Bayesian NMF, i.e., the Kullback–Leibler divergence between the variational posterior and the true posterior. We derive an upper bound for the learning coefficient (a.k.a. the real log canonical threshold) in Bayesian NMF. By using the upper bound, we find a lower bound for the approximation error, asymptotically. The result quantitatively shows how well the VBNMF algorithm can approximate Bayesian NMF; the lower bound depends on the hyperparameters and the true non-negative rank. A numerical experiment demonstrates the theoretical result. • Variational inference approximates the posterior using mean-field approximation. • We give a lower bound for the approximation error by using algebraic geometry. • The lower bound depends on the true non-negative rank and the hyperparameters. [ABSTRACT FROM AUTHOR]

In recent years, selecting appropriate learning models has become more important with the increased need to analyze learning systems, and many model selection methods have been developed. The learning coefficient in Bayesian estimation, which serves to measure the learning efficiency in singular learning models, has an important role in several information criteria. The learning coefficient in regular models is known as the dimension of the parameter space over two, while that in singular models is smaller and varies in learning models. The learning coefficient is known mathematically as the log canonical threshold. In this paper, we provide a new rational blowing-up method for obtaining these coefficients. In the application to Vandermonde matrix-type singularities, we show the efficiency of such methods.

We consider the learning coefficients in learning theory and give two new methods for obtaining these coefficients in a homogeneous case: a method for finding a deepest singular point and a method to add variables. In application to Vandermonde matrix-type singularities, we show that these methods are effective. The learning coefficient of the generalization error in Bayesian estimation serves to measure the learning efficiency in singular learning models. Mathematically, the learning coefficient corresponds to a real log canonical threshold of singularities for the Kullback functions (relative entropy) in learning theory.

The accurate asymptotic evaluation of marginal likelihood integrals is a fundamental problem in Bayesian statistics. Following the approach introduced by Watanabe, we translate this into a problem of computational algebraic geometry, namely, to determine the real log canonical threshold of a polynomial ideal, and we present effective methods for solving this problem. Our results are based on resolution of singularities. They apply to parametric models where the Kullback-Leibler distance is upper and lower bounded by scalar multiples of some sum of squared real analytic functions. Such models include finite state discrete models. [ABSTRACT FROM AUTHOR]

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We consider the real log canonical threshold for the learning model in Bayesian estimation. This threshold corresponds to a learning coefficient of generalization error in Bayesian estimation, which serves to measure learning efficiency in hierarchical learning models [30, 31, 33]. In this paper, we clarify the ideal which gives the log canonical threshold of the restricted Boltzmann machine and consider the learning coefficients of this model. 2000 Mathematics Subject Classifications: 62D05, 62M20, 32S10, 14Q15 [ABSTRACT FROM AUTHOR]

This study explores the effect of the length of learning period on capture rate of a previously unfamiliar prey by an invasive freshwater crayfish ( Procambarus clarkii). Juvenile crayfish were subjected to different periods of contact (learning period) with a larvae prey ( Chaoborus sp.). The length of the learning period significantly affected the number of prey consumed by the predator. Our results indicate that the naive crayfish require less than 12 h to learn to maximize capture rate of this prey. The learning coefficient, adopted in the present study, may be useful in exploring predation capabilities of alien species in newly invaded habitats. [ABSTRACT FROM AUTHOR]

When considering the algorithm of error back-propagation learning, it is seen that the learning of each layer is not completed independently. This paper proposes a DLBP learning algorithm which uses different learning coefficients for each layer. By changing the ratio of the learning coefficients, the following can be controlled: * the learning progress of the hidden units; * the influence of the hidden units on the network. With DLBP learning, we can construct the corresponding networks to the different requirement such as; * to obtain a network with small number of hidden units; and * to obtain a fault tolerant network. [ABSTRACT FROM AUTHOR]

In recent years, selecting appropriate learning models has become more important with the increased need to analyze learning systems, and many model selection methods have been developed. The learning coefficient in Bayesian estimation, which serves to measure the learning efficiency in singular learning models, has an important role in several information criteria. The learning coefficient in regular models is known as the dimension of the parameter space over two, while that in singular models is smaller and varies in learning models. The learning coefficient is known mathematically as the log canonical threshold. In this paper, we provide a new rational blowing-up method for obtaining these coefficients. In the application to Vandermonde matrix-type singularities, we show the efficiency of such methods. [ABSTRACT FROM AUTHOR]