Outside The Rectangle

In our last post on Explainable Models: Asset Allocation Example , we separated our asset allocation problem into two parts: A) Estimating future asset performance and correlation, based on model assumptions and available data B) Choosing best portfolio allocation, based on investor preferences and the estimates from A We define these challenges as being entirely separate, when facilitated by our careful design of the data flowing out of estimation process A.   This clear separation provides practical benefits   to teams and systems undertaking either challenge.   We consider A to be primarily a scientific endeavor, albeit one involving some prognosticator's discretion and potential for folly.  Generally this estimation will rely in large part on commonly available data, and be comparable with  estimates provided by alternative sources.  Improvement of these estimates may be pursued in an objective manner.   Meanwhile B involves idi...

  Here we build on the approach outlined in the last 3 blog posts: General Background in knowledge graphs and mathematical type theory Informal Survey of open satisfaction solvers and provers Infrastructure Options for typed knowledge graphs Now we outline a practical modeling approach in an example knowledge domain:        Asset Portfolios and the Allocation Decision Problem We develop a flexible, minimalist theory for describing collections of assets, and estimated knowledge about the assets and collections. These descriptions may be aligned with FIBO ontology concepts, for commercial integration purposes.  Here we are concerned only with  abstract mathematical description sufficient to analyze portfolio allocation decisions, in the context of available knowledge about the constituent assets, and given investor objectives.    Here is a first simple problem, to motivate our thinking: Given a list of 10 available equity ti...

In this post we explore infrastructure required for our emerging synthetic field: Infrastructure for Typed Knowledge Graphs TGKT = Typed Graph Knowledge Theory    is a mathematical definition space (purely functional), in which we obtain proofs as knowledge.    TGKT is an open-world compile-time artifact, used to produce closed-world runtime artifacts    deployed into TGKB below. TGKB = Typed Graph Knowledge Base    is a stateful space of applied effects, in which we reason using compiled artifacts from TGKT above.    Data  received  (effect) in TGKB serves as explicit axioms in a queryable form until purged (effect).    TGKB is closed, predicative, replacable, and equivalent at any moment to a simple set of data files.    One TGKB is always grounded in a single, permanently fixed immutable TGKT.    We derive explainable results from such a TGKB.       Complex behavior is ...

Satisfied? Declarative Mathematical Programming Explicit math models may be harnessed in current (2020)  software applications in several broad ways. Suppose we start from a paper sketch from some application domain, such as finance or planetary science. Our sketch describes some relationships, including mathematical equalities and inequalities, and objective functions to be minimized or maximized.   Any group of such relationships may be treated as a model for use in computer analysis. Our equalities, inequalities and objective functions are defined over some named terms, which are typed.   Typing of each term is fixed by our model.  One practical way to study this model is to encode these relationships in a model language for constrained optimization , such as MiniZinc.  From the MiniZinc Handbook introduction:  "MiniZinc is a language for specifying constrained optimization and decision problems over integers and real numbers. A MiniZinc model ...