In this paper, we consider the risk assessment problem under multi-levels and multiple mixture subpopulations. Our result is the generalization of the results of [1-5].1 Finite Mixture Normal ModelsIn dose-response s...In this paper, we consider the risk assessment problem under multi-levels and multiple mixture subpopulations. Our result is the generalization of the results of [1-5].1 Finite Mixture Normal ModelsIn dose-response studies, a class of phenomena that frequently occur are that experimental subjects (e.g., mice) may have different responses like ’none, mild, severe’ after a toxicant experiment, or ’getting worse, no change, getting better’ after a medical treatment, etc. These phenomena have attracted the attention of many researchers in recent years. Finite展开更多
Cognitive diagnosis is an important issue of intelligent education systems,which aims to estimate students'proficiency on specific knowledge concepts.Most existing studies rely on the assumption of static student ...Cognitive diagnosis is an important issue of intelligent education systems,which aims to estimate students'proficiency on specific knowledge concepts.Most existing studies rely on the assumption of static student states and ig-nore the dynamics of proficiency in the learning process,which makes them unsuitable for online learning scenarios.In this paper,we propose a unified temporal item response theory(UTIRT)framework,incorporating temporality and random-ness of proficiency evolving to get both accurate and interpretable diagnosis results.Specifically,we hypothesize that stu-dents'proficiency varies as a Wiener process and describe a probabilistic graphical model in UTIRT to consider temporali-ty and randomness factors.Furthermore,based on the relationship between student states and exercising answers,we hy-pothesize that the answering result at time k contributes most to inferring a student's proficiency at time k,which also re-flects the temporality aspect and enables us to get analytical maximization(M-step)in the expectation maximization(EM)algorithm when estimating model parameters.Our UTIRT is a framework containing unified training and inferenc-ing methods,and is general to cover several typical traditional models such as Item Response Theory(IRT),multidimen-sional IRT(MIRT),and temporal IRT(TIRT).Extensive experimental results on real-world datasets show the effective-ness of UTIRT and prove its superiority in leveraging temporality theoretically and practically over TIRT.展开更多
A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment group than others. Finite mixture models have traditionally been used to d...A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment group than others. Finite mixture models have traditionally been used to describe the distribution of responses in treated subjects for such studies. In this paper, we first study the mixture normal model with multi-levels and multiple mixture sub-populations under each level, with particular attention being given to the model in which the proportions of susceptibility are related to dose levels, then we use EM-algorithm to find the maximum likelihood estimators of model parameters. Our results are generalizations of the existing results. Finally, we illustrate realistic significance of the above extension based on a set of real dose-response data.展开更多
文摘In this paper, we consider the risk assessment problem under multi-levels and multiple mixture subpopulations. Our result is the generalization of the results of [1-5].1 Finite Mixture Normal ModelsIn dose-response studies, a class of phenomena that frequently occur are that experimental subjects (e.g., mice) may have different responses like ’none, mild, severe’ after a toxicant experiment, or ’getting worse, no change, getting better’ after a medical treatment, etc. These phenomena have attracted the attention of many researchers in recent years. Finite
基金supported by the National Key Research and Development Program of China under Grant No.2021YFF0901003the National Natural Science Foundation of China under Grant Nos.U20A20229,61922073,and 62106244the Natural Science Foundation of Anhui Province of China under Grant No.2108085QF272.
文摘Cognitive diagnosis is an important issue of intelligent education systems,which aims to estimate students'proficiency on specific knowledge concepts.Most existing studies rely on the assumption of static student states and ig-nore the dynamics of proficiency in the learning process,which makes them unsuitable for online learning scenarios.In this paper,we propose a unified temporal item response theory(UTIRT)framework,incorporating temporality and random-ness of proficiency evolving to get both accurate and interpretable diagnosis results.Specifically,we hypothesize that stu-dents'proficiency varies as a Wiener process and describe a probabilistic graphical model in UTIRT to consider temporali-ty and randomness factors.Furthermore,based on the relationship between student states and exercising answers,we hy-pothesize that the answering result at time k contributes most to inferring a student's proficiency at time k,which also re-flects the temporality aspect and enables us to get analytical maximization(M-step)in the expectation maximization(EM)algorithm when estimating model parameters.Our UTIRT is a framework containing unified training and inferenc-ing methods,and is general to cover several typical traditional models such as Item Response Theory(IRT),multidimen-sional IRT(MIRT),and temporal IRT(TIRT).Extensive experimental results on real-world datasets show the effective-ness of UTIRT and prove its superiority in leveraging temporality theoretically and practically over TIRT.
基金Supported by the National Natural Science Foundation of China (No. 10571073)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20070183023)Program for New Century Excellent Talents in University, Scientific Research Fund of Jilin University (No. 200810024)
文摘A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment group than others. Finite mixture models have traditionally been used to describe the distribution of responses in treated subjects for such studies. In this paper, we first study the mixture normal model with multi-levels and multiple mixture sub-populations under each level, with particular attention being given to the model in which the proportions of susceptibility are related to dose levels, then we use EM-algorithm to find the maximum likelihood estimators of model parameters. Our results are generalizations of the existing results. Finally, we illustrate realistic significance of the above extension based on a set of real dose-response data.
