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Page 1

Personalization Through the Application
of Inverse Bayes to Student Modeling

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Citation Lang, Charles WM. 2015. Personalization Through the Application of
Inverse Bayes to Student Modeling. Doctoral dissertation, Harvard
Graduate School of Education.

Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:16461031

Terms of Use This article was downloaded from Harvard University’s DASH
repository, and is made available under the terms and conditions
applicable to Other Posted Material, as set forth at http://
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use#LAA

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Running head: PERSONALIZATION THROUGH INVERSE BAYES










Personalization through the Application of Inverse Bayes to Student Modeling






Charles William McLeod Lang




Prof. Howard Gardner
Prof. Terrence Tivnan

Prof. Ryan Baker




A Thesis Presented to the Faculty of the
Graduate School of Education of Harvard

University in Partial Fulfillment of the
Requirements for the Degree of Doctor of

Education



2015

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PERSONALIZATION THROUGH INVERSE BAYES


 

60


 

Inverse Bayesian Filter. A model type that is routinely used with partial knowledge

to both define constructs and measure their change is the family of Rational Models.

Rational Models describe and explain human learning, judgment, and inference, often

through the use of Bayes Theorem. They are used to determine whether people’s behavior is

rational (whether it conforms to some optimality constraint) but if their implementation is

inverted (i.e. – run backwards), instead of describing how a task should be completed, they

generate the parameters that describe the way that people did complete a task (whether

rationally or not). This inversion is the basic idea behind the process of the Inverse Bayes

Filter.

IBFi seeks to determine the relative contributions of context and aptitude to student

performance. Aptitude in this framework is whatever cognitive, emotional and conative

resources a student brings to a task. Contexts are the conditions of the task that impact a

student’s performance. For example, a student may be certain about her name, but within a

high stress context she may not be able to report it. Likewise, she may be very uncertain

about the laws of thermodynamics, but if we provide enough context cues she may be able

to choose the correct answer from a selection.

IBFi determines how knowledge and context should be weighted for a student, given

their answer and according to logical probability. Bayes Theorem posits that the conditional

probability of a hypothesis (posterior) is proportional to the product of the probability of

that hypothesis (prior) and the likelihood of the available data conditioned on the hypothesis

(likelihood):


𝑃 ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑠 𝑑𝑎𝑡𝑎 ∝ 𝑃 ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑠  ×  𝑃!𝑑𝑎𝑡𝑎|ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑠) (1)

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PERSONALIZATION THROUGH INVERSE BAYES


 

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Rational Bayes models such as Decision Theory (Schlaifer & Raiffa, 1961) and those

of Griffiths, Kemp, & Tenenbaum (2008) treat the posterior as observed human behavior,

the prior as stored knowledge and the likelihood as how the environment impacts the

application of that knowledge (EG – the impact of the context). Bayes Theorem then gives

the relationship between knowledge and behavior according to context. The following graph

(Figure 1) demonstrates this by showing how, according to Bayes theorem, as aptitude

increases (dot-dashed line), context (solid line) must drop quickly (become very hostile) to

reduce performance (dotted line).

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PERSONALIZATION THROUGH INVERSE BAYES


 

126


 

Yudelson, M. V., Koedinger, K. R., & Gordon, G. J. (2013). Individualized Bayesian

Knowledge Tracing models. In Artificial Intelligence in Education (pp. 171–180).

Springer.

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PERSONALIZATION THROUGH INVERSE BAYES


 

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VITA

Charles William McLeod Lang



2001 – 2007 The University of Melbourne
Victoria, Australia

B.A.
March 2007

B.Sc.
March 2007

2007 – 2008 Harvard Graduate School of
Education
Cambridge, MA

Ed.M.
May 2008

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