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TODOs

  • translate

    • BPS/ltms/ltms.lisp to BPS/ltms/ltms.rkt
    • BPS/ltms/ltms-ex.lisp to BPS/ltms/ltms-ex.rkt

  • (DONE) translate

    • BPS/ltms/jtms.lisp to BPS/ltms/jtms.rkt
    • BPS/ltms/jtms-ex.lisp to BPS/ltms/jtms-ex.rkt

  • Done(namin): show how to run the racket code.

JTMS in mediKanren

  • high level inference rules to reduce hopping

    • gene 1 uprelates another gene 2
      • then can infer that any drug which uprelates gene 1 also uprelates gene 2, and maybe does more...
    • different ontologies
      • traverse two ontologies simultaenously
      • that are at different levels of resolution
        • needs to understand the relationship between the two
        • e.g. create a mapping between the two
          • map between concepts or predicates
        • two ontologies having to do with diseases
        • in one ontology, 1 type of diabetes vs 10 types of diabetes
        • clustering? these drugs are in the same class
        • can we use a galois connection?
    • need the schemas of the ontologies
      • predicates
      • concepts
      • mapping between ontologies

  • problem statement 1 (real!)

    • given two ontologies
    • given the synonyms
    • automatically infer a mapping between the ontologies
      • that is find the closest cross links
    • perhaps propose multiple mappings and need to choose among them
    • can use concrete/abstract data to do so
    • simple question:
      • here is a concept from one ontology
      • what is the closest concept in another ontology?

  • problem statement 2 (problem statement 1 is an instance!)

    • we have pages of racket code intermingly query and logic
    • we have some high level problems that are too high level for a query graph
    • could you build an expert system in mediKanren?
    • can we encode higher level inference rules that serve as the logic glue where we now use ad-hoc racket code

  • problem statement 3

    • abductive reasoning (need LTMS, probably)
    • evidence on a patient (genes, medication, symptoms, past diagnoses)
    • find explanations for their symptoms
    • require a probabilistic graphical model
      • the model encodes all medical knowledge (challenge)
      • with conditional probabilities
      • we fill in the things that we know
      • by bayesian reasoning, figure out the most likely
        • causes of symptoms
        • treatments of symptoms
    • to address challenge?
      • how do we get the probabilities?
        • we will have new clinical data with probabilities
    • pull neigborhoods around the focus to allow reasoning

mediKanren

Random Ideas

  • pattern-directed chess
  • reflection that uses a tms to guide its reasoning

References to Dempster-Shafer Theory

Dempster-Shafer Theory Glenn Shafer http://www.glennshafer.com/assets/downloads/articles/article48.pdf

Dempster-Shafer Theory chapter (see 4.3 for Dempster's Combination Rule) http://www.blutner.de/uncert/DSTh.pdf

Dempster-Shafer Theory slides http://www.blutner.de/uncert/Dempster-Shafer.pdf

Combination of Evidence in Dempster-Shafer Theory, 2002 Kari Sentz, Scott Ferson https://www.researchgate.net/publication/235419085_Combination_of_Evidence_in_Dempster-Shafer_Theory

Dempster's Rule of Combination DEVELOPMENT OF A COMMON EDUCATIONAL AND TRAINING INFRASTRUCTURE for the Integration of Remote Sensing, Digital Processing of Satellite Imagery, Photointerpretation and GIS Methods, Techniques and Applications' CO-ORDINATOR NATIONAL TECHNICAL UNIVERSITY OF ATHENS, LABORATORY OF REMOTE SENSING Scientist in charge: Prof. D. ROKOS http://portal.survey.ntua.gr/main/labs/rsens/DeCETI/IRIT/MSI-FUSION/node183.html

On the behavior of Dempster’s rule of combination, 2011 Jean Dezert, Albena Tchamova. hal-00577983v1 https://hal.archives-ouvertes.fr/file/index/docid/577983/filename/OnBehaviorOfDSRule.pdf

A Simple View of the Dempster-Shafer Theory of Evidence and its Implication for the Rule of Combination, 1986 Lotfi A. Zadeh http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.98.6349

The Unnormalized Dempster’s Rule of Combination: a New Justification from the Least Commitment Principleand some Extensions, May 7, 2010 Frederic Pichon, Thierry Denoeux https://www.lgi2a.univ-artois.fr/~pichon/pdf/jar_final.pdf

Overview of Dempster-Shafer and Belief Function Tracking Method Erik Blasch, Jean Dezert, B Pannetier Advances and Applications of DSmT for Information Fusion. Collected Works. Volume 4 http://fs.unm.edu/OverviewDempsterShafer.pdf

An Introduction to Bayesian and Dempster-Shafer Data Fusion, 2005 Don Koks, Subhash Challa http://robotics.caltech.edu/~jerma/research_papers/BayesChapmanKolmogorov.pdf

A Mathematical Theory of Evidence turns 40. International Journal of Approximate Reasoning 79 7-25. December 2016. Glenn Shafer http://www.glennshafer.com/assets/downloads/MathTheoryofEvidence-turns-40.pdf

http://www.glennshafer.com/books/amte.html

Perform Dempster's Rule of Combination Code Golf https://codegolf.stackexchange.com/questions/94719/perform-dempsters-rule-of-combination

Dempster's Rule As Seen By Little Colored Balls https://dl.acm.org/doi/10.1111/j.1467-8640.2012.00421.x

Notes on Dempster-Shafer and Appliation to JTMS

  • monotonically tightening

  • rule of combination: serial constraining, commutative, each operand acts as a filter

  • so overall necessarily constraining the possibility space

  • not like bayesian reasoning on counterintuitive reasons, but lots of similarity still

  • unsmooth vs smooth?

  • Should we keep both truth/false and DS?

    • DS is compatible with this is true, this is false.
    • You can reprensent true [1 0] and false [0 1].
    • Default belief is [0 0] (completely undecided).
    • A contradiction is an explicit marked contradory node that is almost true (no room for it to be false). Something should only be flagged a contradiction if it's absolutely true. Though interesting to examine our belief in a contradiction at any point.

  • in a JBMS, who drives the inference?

    • the beliefs can do it

  • What is the propagation algorithm?

  • we either say we have a fixed belief for a note

  • or we leave the node to be decided by what implies it

  • Inference in JTMS

    • enable-assumption called propagate-inness

2.5.1 Queries of https://arxiv.org/pdf/1304.3084.pdf

  • true? = belief+(node) > belief-threshold

  • false? = belief-(node) > *belief-threshold•

  • unknown? = belief+(node) < belief-threshold and belief-(node) < belief-threshold

  • absolutely-true? = belief+(node) = 1.0

  • absolutely-false? = belief-(node) = 1.0

  • absolutely-unknown? = belief+(node) = 0.0 and belief-(node) = 0.0

  • support-for = belief+(node)

  • support-against = belief-( node)

  • possible-true = 1 - belief-(node) ;; flipped from paper with next

  • possible-false = 1 - belief+(node)

  • belief-uncertainty = 1 - belief-(node) - belief+(node)

  • If we have A & B -> C and D -> A, when adding the latter, we can influence the former.

  • This suggests we need to propagate every time.

  • In order to avoid cycles from being problematic, what's the solution?

  • We need to recognize when we have reached a fixed point so we can stop the circular propagation, even then it might not make sense. (stretch goal)

  • Are we going to assign beliefs to our implications?

    • If not, we can use oplus for justifications.

  • In mediKanren, an implication would be a multi-hop chain of reasoning.

  • With a BMS, we could do these ad-hoc rules more formally, and perhaps help triaging.

  • TODO: rename interval to belief, since not interval.

  • These are two coarse grains:

    • (assume-node node) (shortcut)
    • (enable-assumption node)
    • (retract-assumption node)

  • Instead we want to have

    • (fix-belief node belief) ;; this is like a manual intervention
    • (unfix-belief node) ;; turning off the manual intervention
    • (update-belief node belief) ;; this is an internal update based on propagation

  • We have

    • (make-contradiction node)

  • Instead

    • (make-contradiction node treshhold)
    • we also want to change thresshold

  • We have

    • (in-node? node)
    • (out-node? node)

  • Instead covered by true? and false? above.

  • We have

    • (justify-node informant consequent antecedents)
    • (supporting-justification-for-node node)
    • (assumptions-of-node node)