Context-Dependent Criteria for Dirichlet Process in Sequential Decision-Making Problems
In models with insufficient initial information, parameter estimation can be subject to statistical uncertainty, potentially resulting in suboptimal decision-making; however, delaying implementation to gather more information can also incur costs. This paper examines an extension of information-theo...
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MDPI AG
2024-10-01
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| author | Ksenia Kasianova Mark Kelbert |
| author_facet | Ksenia Kasianova Mark Kelbert |
| author_sort | Ksenia Kasianova |
| collection | DOAJ |
| description | In models with insufficient initial information, parameter estimation can be subject to statistical uncertainty, potentially resulting in suboptimal decision-making; however, delaying implementation to gather more information can also incur costs. This paper examines an extension of information-theoretic approaches designed to address this classical dilemma, focusing on balancing the expected profits and the information needed to be obtained about all of the possible outcomes. Initially utilized in binary outcome scenarios, these methods leverage information measures to harmonize competing objectives efficiently. Building upon the foundations laid by existing research, this methodology is expanded to encompass experiments with multiple outcome categories using Dirichlet processes. The core of our approach is centered around weighted entropy measures, particularly in scenarios dictated by Dirichlet distributions, which have not been extensively explored previously. We innovatively adapt the technique initially applied to binary case to Dirichlet distributions/processes. The primary contribution of our work is the formulation of a sequential minimization strategy for the main term of an asymptotic expansion of differential entropy, which scales with sample size, for non-binary outcomes. This paper provides a theoretical grounding, extended empirical applications, and comprehensive proofs, setting a robust framework for further interdisciplinary applications of information-theoretic paradigms in sequential decision-making. |
| format | Article |
| id | doaj-art-cee3e2398a7e4a369db048dd5b7935f6 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-cee3e2398a7e4a369db048dd5b7935f62024-11-08T14:37:32ZengMDPI AGMathematics2227-73902024-10-011221332110.3390/math12213321Context-Dependent Criteria for Dirichlet Process in Sequential Decision-Making ProblemsKsenia Kasianova0Mark Kelbert1Faculty of Economic Sciences, National Research University Higher School of Economics, Myasnitskaya St. 20, 101000 Moscow, RussiaFaculty of Economic Sciences, National Research University Higher School of Economics, Myasnitskaya St. 20, 101000 Moscow, RussiaIn models with insufficient initial information, parameter estimation can be subject to statistical uncertainty, potentially resulting in suboptimal decision-making; however, delaying implementation to gather more information can also incur costs. This paper examines an extension of information-theoretic approaches designed to address this classical dilemma, focusing on balancing the expected profits and the information needed to be obtained about all of the possible outcomes. Initially utilized in binary outcome scenarios, these methods leverage information measures to harmonize competing objectives efficiently. Building upon the foundations laid by existing research, this methodology is expanded to encompass experiments with multiple outcome categories using Dirichlet processes. The core of our approach is centered around weighted entropy measures, particularly in scenarios dictated by Dirichlet distributions, which have not been extensively explored previously. We innovatively adapt the technique initially applied to binary case to Dirichlet distributions/processes. The primary contribution of our work is the formulation of a sequential minimization strategy for the main term of an asymptotic expansion of differential entropy, which scales with sample size, for non-binary outcomes. This paper provides a theoretical grounding, extended empirical applications, and comprehensive proofs, setting a robust framework for further interdisciplinary applications of information-theoretic paradigms in sequential decision-making.https://www.mdpi.com/2227-7390/12/21/3321experimental designBayesian analysisinformation gainDirichlet processweighted information |
| spellingShingle | Ksenia Kasianova Mark Kelbert Context-Dependent Criteria for Dirichlet Process in Sequential Decision-Making Problems Mathematics experimental design Bayesian analysis information gain Dirichlet process weighted information |
| title | Context-Dependent Criteria for Dirichlet Process in Sequential Decision-Making Problems |
| title_full | Context-Dependent Criteria for Dirichlet Process in Sequential Decision-Making Problems |
| title_fullStr | Context-Dependent Criteria for Dirichlet Process in Sequential Decision-Making Problems |
| title_full_unstemmed | Context-Dependent Criteria for Dirichlet Process in Sequential Decision-Making Problems |
| title_short | Context-Dependent Criteria for Dirichlet Process in Sequential Decision-Making Problems |
| title_sort | context dependent criteria for dirichlet process in sequential decision making problems |
| topic | experimental design Bayesian analysis information gain Dirichlet process weighted information |
| url | https://www.mdpi.com/2227-7390/12/21/3321 |
| work_keys_str_mv | AT kseniakasianova contextdependentcriteriafordirichletprocessinsequentialdecisionmakingproblems AT markkelbert contextdependentcriteriafordirichletprocessinsequentialdecisionmakingproblems |