Knowledge Space Map for Organic Reactions

1
Knowledge Space Map for Organic Reactions

• Knowledge Space Theory
• Existing Rule Set Basis for Chemistry Knowledge
  Space Model
• Data Model Proposal
• Constructing and Learning the Map

2
Knowledge Space Map

• Isolate atomic knowledge units / nodes / elements
• Determine dependency graph of knowledge units
  (defines a learning order by topological sort)
• Enables targeted and purposeful lesson plans
  based on the fringes of students current
  knowledge state

Multiplication
Division
Fractions
Logarithms
Exponents
3
Chemistry Knowledge Space?

• Current system has user driven selection of which
  chapter(s) to work on, then system randomly
  generates problem
• Idealized approach Assess students current
  knowledge state and auto-generate next problem to
  target next most useful subject
• Existing tutorial based on predictive power of
  80 reagents, which are based on 1500 elemental
  rules. These could be interpreted as 1500
  knowledge units

4
Rule Clustering

• Many rules are just variants of the same concept
  / knowledge unit
• Alkene, Protic Acid Addition, Alkoxy
• Alkene, Protic Acid Addition, Benzyl
• Alkene, Protic Acid Addition, Allyl
• Alkene, Protic Acid Addition, Tertiary
• Alkene, Protic Acid Addition, Secondary
• Alkene, Protic Acid Addition, Generic
• Some rules will always be used in conjunction
  with another (like qu)
• Not really a learning dependency order between
  these rules then, you essentially know one of the
  rules IFF (if and only if) you know the others

5
Data Model Proposal

• Want general framework for representing
  relationships
• Each reaction rule represents an elementary
  knowledge unit node
• Weighted, directed edge between each node
  represents learning dependency relationship
• A ? B (90)
• Given that a student knows rule B, there is a
  90 probability that they know rule A
• Conversely, if do NOT know rule A, 90
  probability that do NOT know rule B.
• Define know Student should consistently answer
  correct any problem that is based only on rules
  that they know
• Define rule similarity measure as average of
  reciprocal dependency relationships

6
Major Relationship Cases

• Strong learning dependency
• A ? B (99)
• A ? B (50)
• Strong similarity / mutual dependency
• A ? B (99)
• A ? B (99)
• No relation (random correlation)
• A ? B (50)
• A ? B (50)

7
Additional Enhancements

• Add baseline probability of knowing each node,
  instead of assuming uniform 50
• Analogous to using background weights for amino
  acid distribution in protein sequence
• Add a confidence number for each of these
  probability weights to reflect how trustworthy
  our prior data is
• Analogous (maybe equal) to n, the number of data
  points that were used to arrive at the current
  estimate

8
Learning Relationship Map

• Give students assessment exams based on the rule
  sets with criteria to distinguish problems that
  students get right vs. wrong
• Defines sets of rules
• R All rules used in problems students got right
• W All rules used in problems students got wrong
  (that are not in R)
• Adjust rule relation values
• Decrease Ri ? Wj relations
• Increase Ri ? Rk relations
• Scale adjustment based on confidence in prior

9
Learning Propagation

• Each assessment exam may only cover a handful of
  specific rules in R and W
• When updating relation for rule R1 ? R2, look for
  all rules similar to R1 and all similar to R2
• Assume respective updates for all relations
  between similar rule pairs, scaled by the
  magnitude of similarity to R1 and R2
• Technically, all rules are similar to all others
  by some degree, but dont want to update 15002
  relations every time. Set similarity threshold,
  which effectively defines clusters around rules.

10
Constructing Relationship Map

• Initial pass should be able to automatically find
  a lot of similarity relationships just based on
  existing structured data
• Rule names
• Combined usage in test examples
• Included in common reagents, chapters, etc.
• Use book chapters order as initial guess for
  dependency orders
• Similarity analysis could reduce 1500 rules to
  100? rule clusters which is more tractable to
  manually assign major dependencies not
  automatically addressed by book chapter order

11
Open Questions

• Student knowledge evolves over time, maybe even
  with one exam. How to hit moving target of
  their current knowledge state?
• Baseline probabilities of knowing a rule. Random
  sample of all students? Will differ greatly
  based on population sample chosen.

12
SMILES Extensions

• Atom Mapping
• Necessary to map reactant to product atoms
• Proper transform requires balanced stoichiometry
• Hydrogens generally must be explicitly specified

Carboxylic acid O1C2(9)O3H7. Pr
imary amine ? H8N4(10)H5gtgt Amide
O1C2(9)N4(10)H5. Water
H7O3H8
13
Transformation Rules

• Chemical state machine modeling at mechanistic
  level of detail
• State information Molecular structure
• State transition Transformation rules

carbocationhalide addition
p-bond protic acid addition