Logic and Foundations Commons^™

Occam Software (And Manual) For Reconstructability Analysis, Martin Zwick, Kenneth Willett, Joe Fusion, Heather Alexander

Complex Systems Faculty Publications and Presentations

OCCAM is a Discrete Multivariate Modeling (DMM) tool based on the methodology of Reconstructability Analysis (RA). As an acronym it stands for Organizational Complexity Computation and Modeling, and the name is also a reference (with a non-standard spelling) to Ockham’s Razor. The principal programmers of its current version have been Kenneth Willett, Joe Fusion, and Heather Alexander. Ken Willett totally rewrote earlier versions of OCCAM. His version was originally called “OCCAM3” to distinguish it from these earlier OCCAM incarnations; the “3” has finally been dropped.

OCCAM’s typical use is to analyze data involving a large number of discrete variables, but …

Joint Lattice Of Reconstructability Analysis And Bayesian Network General Graphs, Marcus Harris, Martin Zwick

Complex Systems Faculty Publications and Presentations

This paper integrates the structures considered in Reconstructability Analysis (RA) and those considered in Bayesian Networks (BN) into a joint lattice of probabilistic graphical models. This integration and associated lattice visualizations are done in this paper for four variables, but the approach can easily be expanded to more variables. The work builds on the RA work of Klir (1985), Krippendorff (1986), and Zwick (2001), and the BN work of Pearl (1985, 1987, 1988, 2000), Verma (1990), Heckerman (1994), Chickering (1995), Andersson (1997), and others. The RA four variable lattice and the BN four variable lattice partially overlap: there are ten …

Reconstructability Analysis And Its Occam Implementation, Martin Zwick

Complex Systems Faculty Publications and Presentations

This talk will describe Reconstructability Analysis (RA), a probabilistic graphical modeling methodology deriving from the 1960s work of Ross Ashby and developed in the systems community in the 1980s and afterwards. RA, based on information theory and graph theory, resembles and partially overlaps Bayesian networks (BN) and log-linear techniques, but also has some unique capabilities. (A paper explaining the relationship between RA and BN will be given in this special session.) RA is designed for exploratory modeling although it can also be used for confirmatory hypothesis testing. In RA modeling, one either predicts some DV from a set of IVs …

Predicting Cost Of Care In Total Hip Replacement, Cecily Corrine Froemke, Martin Zwick

Complex Systems Faculty Publications and Presentations

Legislative reforms aimed at slowing growth of US healthcare costs are focused on achieving greater value per dollar. To increase value healthcare providers must not only provide high quality care, but deliver this care at a sustainable cost. Predicting risks that may lead to poor outcomes and higher costs enable providers to augment decision making for optimizing patient care and inform the risk stratification necessary in emerging reimbursement models. Healthcare delivery systems are looking at their high volume service lines and identifying variation in cost and outcomes in order to determine the patient factors that are driving this variation and …

Keyword-Based Patent Citation Prediction Via Information Theory, Farshad Madani, Martin Zwick, Tugrul U. Daim

Engineering and Technology Management Faculty Publications and Presentations

Patent citation shows how a technology impacts other inventions, so the number of patent citations (backward citations) is used in many technology prediction studies. Current prediction methods use patent citations, but since it may take a long time till a patent is cited by other inventors, identifying impactful patents based on their citations is not an effective way. The prediction method offered in this article predicts patent citations based on the content of patents. In this research, Reconstructability Analysis (RA), which is based on information theory and graph theory, is applied to predict patent citations based on keywords extracted from …

Reconstructability And Dynamics Of Elementary Cellular Automata, Martin Zwick

Complex Systems Faculty Publications and Presentations

Reconstructability analysis (RA) is a method to determine whether a multivariate relation, defined set- or information-theoretically, is decomposable with or without loss into lower ordinality relations. Set-theoretic RA (SRA) is used to characterize the mappings of elementary cellular automata. The decomposition possible for each mapping w/o loss is a better predictor than the λ parameter (Walker & Ashby, Langton) of chaos, & non-decomposable mappings tend to produce chaos. SRA yields not only the simplest lossless structure but also a vector of losses for all structures, indexed by parameter τ. These losses are analogous to transmissions in information-theoretic RA (IRA). IRA …

Introduction To Reconstructability Analysis, Martin Zwick

Complex Systems Faculty Publications and Presentations

This talk will introduce Reconstructability Analysis (RA), a data modeling methodology deriving from the 1960s work of Ross Ashby and developed in the systems community in the 1980s and afterwards. RA, based on information theory and graph theory, is a member of the family of methods known as ‘graphical models,’ which also include Bayesian networks and log-linear techniques. It is designed for exploratory modeling, although it can also be used for confirmatory hypothesis testing. RA can discover high ordinality and nonlinear interactions that are not hypothesized in advance. Its conceptual framework illuminates the relationships between wholes and parts, a subject …

Preliminary Results Of Bayesian Networks And Reconstructability Analysis Applied To The Electric Grid, Marcus Harris, Martin Zwick

Complex Systems Faculty Publications and Presentations

Reconstructability Analysis (RA) is an analytical approach developed in the systems community that combines graph theory and information theory. Graph theory provides the structure of relations (model of the data) between variables and information theory characterizes the strength and the nature of the relations. RA has three primary approaches to model data: variable based (VB) models without loops (acyclic graphs), VB models with loops (cyclic graphs) and state-based models (nearly always cyclic, individual states specifying model constraints). These models can either be directed or neutral. Directed models focus on a single response variable whereas neutral models focus on all relations …

Beyond Spatial Autocorrelation: A Novel Approach Using Reconstructability Analysis, David Percy, Martin Zwick

Complex Systems Faculty Publications and Presentations

Raster data are digital representations of spatial phenomena that are organized into rows and columns that typically have the same dimensions in each direction. They are used to represent image data at any scale. Common raster data are medical images, satellite data, and photos generated by modern smartphones.
Satellites capture reflectance data in specific bands of wavelength that correspond to red, green, blue, and often some infrared and thermal bands. These composite vectors can then be classified into actual land use categories such as forest or water using automated techniques. These classifications are verified on the ground using hand-held sensors. …

Statistical Analysis Of Network Change, Teresa D. Schmidt, Martin Zwick

Complex Systems Faculty Publications and Presentations

Networks are rarely subjected to hypothesis tests for difference, but when they are inferred from datasets of independent observations statistical testing is feasible. To demonstrate, a healthcare provider network is tested for significant change after an intervention using Medicaid claims data. First, the network is inferred for each time period with (1) partial least squares (PLS) regression and (2) reconstructability analysis (RA). Second, network distance (i.e., change between time periods) is measured as the mean absolute difference in (1) coefficient matrices for PLS and (2) calculated probability distributions for RA. Third, the network distance is compared against a reference distribution …

Ideas And Graphs, Martin Zwick

Complex Systems Faculty Publications and Presentations

A graph can specify the skeletal structure of an idea, onto which meaning can be added by interpreting the structure.

This paper considers graphs (but not hypergraphs) consisting of four nodes, and suggests meanings that can be associated with several different directed and undirected graphs.

Drawing on Bennett's "systematics," specifically on the Tetrad that systematics offers as a model of 'activity,' the analysis here shows that the Tetrad is versatile model of problem-solving, regulation and control, and other processes.

Slides are available below.

Formalizing The Panarchy Adaptive Cycle With The Cusp Catastrophe [Presentation], Martin Zwick, Joshua Hughes

Complex Systems Faculty Publications and Presentations

The panarchy adaptive cycle, a general model for change in natural and human systems, can be formalized by the cusp catastrophe of René Thom's topological theory. Both the adaptive cycle and the cusp catastrophe have been used to model ecological, economic, and social systems in which slow and small continuous changes in two control variables produce fast and large discontinuous changes in system behavior. The panarchy adaptive cycle, the more recent of the two models, has been used so far only for qualitative descriptions of typical dynamics of such systems. The cusp catastrophe, while also often employed qualitatively, is a …

Predicting Risk Of Adverse Outcomes In Knee Replacement Surgery With Reconstructability Analysis, Cecily Corrine Froemke, Martin Zwick

Complex Systems Faculty Publications and Presentations

Reconstructability Analysis (RA) is a data mining method that searches for relations in data, especially non-linear and higher order relations. This study shows that RA can provide useful predictions of complications in knee replacement surgery.

Secondary Analysis Of Concussion Data, Martin Zwick, Stephanie Kolakowsky-Hayner, Nancy Carney, Maya Balamane, Tracie Nettleton, D. Wright

Complex Systems Faculty Publications and Presentations

Clinical studies are expensive & time-consuming. Typically in these studies specific hypotheses are subjected to confirmatory test. Yet the data may harbor evidence of unanticipated relations between variables. It is thus desirable to subject the data to secondary analyses in the hope of discovering novel & valuable associations. Exploratory analysis, however, is tentative: findings should be replicated in new data. This presentation reports some secondary analyses on concussion data. Data mining on 2 datasets will be discussed, & some unexpected findings reported. The analyses use reconstructability analysis (RA), a probabilistic graphical modeling method implemented in the Occam software package developed …

Exploratory Modeling Of Tbi Data, Martin Zwick, Stephanie Kolakowsky-Hayner, Sadie Carney, Maya Balamane, Tracie Nettleton, D. Wright

Complex Systems Faculty Publications and Presentations

Most data analyses are confirmatory, but exploratory studies can find unexpected non-linear & many-variable interaction effects. The methodology of reconstructability analysis (RA) is explicitly designed for exploratory modeling. It analyzes both nominal and continuous (binned) variables, is easily interpretable, takes standard text input, is web-accessible, and is available for research use. This presentation reports some results of applying RA to data sets from Preece (auto accidents) and Wright (auto/motorcycle/bike accidents, hit pedestrians, and falls).

Modal Logic And Its Applications, Explained Using Puzzles And Examples, Marek Perkowski

Systems Science Friday Noon Seminar Series

The talk introduces Modal Logic as an extension of classical propositional and First Order Logics. We discuss motivations of Lewis to create modal logic system, axioms and rules of proof. Several examples illustrate deriving theorems from axioms. "Muddy Children" puzzle is used to explain the principles of dealing with uncertainty problems where a temporal lack of response is used as additional information. Other examples include "Narrow Bridge" problem/game which relates to the problem of necessary evil in the world, robot planning and law and robot morality problems, especially related to military robots and use of force by police. Kripke semantics …

Application Of Information-Theoretic Data Mining Techniques In A National Ambulatory Practice Outcomes Research Network, Adam Wright, Thomas N. Ricciardi, Martin Zwick

Complex Systems Faculty Publications and Presentations

The Medical Quality Improvement Consortium data warehouse contains de-identified data on more than 3.6 million patients including their problem lists, test results, procedures and medication lists. This study uses reconstructability analysis, an information-theoretic data mining technique, on the MQIC data warehouse to empirically identify risk factors for various complications of diabetes including myocardial infarction and microalbuminuria. The risk factors identified match those risk factors identified in the literature, demonstrating the utility of the MQIC data warehouse for outcomes research, and RA as a technique for mining clinical data warehouses.

Enhancements To Crisp Possibilistic Reconstructability Analysis, Anas Al-Rabadi, Martin Zwick

Complex Systems Faculty Publications and Presentations

Modified Reconstructibility Analysis (MRA), a novel decomposition within the framework of set-theoretic (crisp possibilistic) Reconstructibility Analysis, is presented. It is shown that in some cases while 3-variable NPN-classified Boolean functions are not decomposable using Conventional Reconstructibility Analysis (CRA), they are decomposable using Modified Reconstructibility Analysis (MRA). Also, it is shown that whenever a decomposition of 3-variable NPN-classified Boolean functions exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. A comparison of the corresponding complexities for Ashenhurst-Curtis decompositions, and Modified Reconstructibility Analysis (MRA) is also presented. While both AC and MRA decompose some but …

A Comparison Of Modified Reconstructability Analysis And Ashenhurst‐Curtis Decomposition Of Boolean Functions, Anas Al-Rabadi, Marek Perkowski, Martin Zwick

Complex Systems Faculty Publications and Presentations

Modified reconstructability analysis (MRA), a novel decomposition technique within the framework of set‐theoretic (crisp possibilistic) reconstructability analysis, is applied to three‐variable NPN‐classified Boolean functions. MRA is superior to conventional reconstructability analysis, i.e. it decomposes more NPN functions. MRA is compared to Ashenhurst‐Curtis (AC) decomposition using two different complexity measures: log‐functionality, a measure suitable for machine learning, and the count of the total number of two‐input gates, a measure suitable for circuit design. MRA is superior to AC using the first of these measures, and is comparable to, but different from AC, using the second.

State-Based Reconstructability Analysis, Martin Zwick, Michael S. Johnson

Complex Systems Faculty Publications and Presentations

Reconstructability analysis (RA) is a method for detecting and analyzing the structure of multivariate categorical data. While Jones and his colleagues extended the original variable‐based formulation of RA to encompass models defined in terms of system states, their focus was the analysis and approximation of real‐valued functions. In this paper, we separate two ideas that Jones had merged together: the “g to k” transformation and state‐based modeling. We relate the idea of state‐based modeling to established variable‐based RA concepts and methods, including structure lattices, search strategies, metrics of model quality, and the statistical evaluation of model fit for analyses based …

Reversible Modified Reconstructability Analysis Of Boolean Circuits And Its Quantum Computation, Anas Al-Rabadi, Martin Zwick

Complex Systems Faculty Publications and Presentations

Modified Reconstructability Analysis (MRA) can be realized reversibly by utilizing Boolean reversible (3,3) logic gates that are universal in two arguments. The quantum computation of the reversible MRA circuits is also introduced. The reversible MRA transformations are given a quantum form by using the normal matrix representation of such gates. The MRA-based quantum decomposition may play an important role in the synthesis of logic structures using future technologies that consume less power and occupy less space.

Modified Reconstructability Analysis For Many-Valued Functions And Relations, Anas Al-Rabadi, Martin Zwick

Complex Systems Faculty Publications and Presentations

A novel many-valued decomposition within the framework of lossless Reconstructability Analysis is presented. In previous work, Modified Recontructability Analysis (MRA) was applied to Boolean functions, where it was shown that most Boolean functions not decomposable using conventional Reconstructability Analysis (CRA) are decomposable using MRA. Also, it was previously shown that whenever decomposition exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. In this paper, MRA is extended to many-valued logic functions, and logic structures that correspond to such decomposition are developed. It is shown that many-valued MRA can decompose many-valued functions when CRA fails to do …

Using Reconstructability Analysis To Select Input Variables For Artificial Neural Networks, Stephen Shervais, Martin Zwick

Complex Systems Faculty Publications and Presentations

We demonstrate the use of Reconstructability Analysis to reduce the number of input variables for a neural network. Using the heart disease dataset we reduce the number of independent variables from 13 to two, while providing results that are statistically indistinguishable from those of NNs using the full variable set. We also demonstrate that rule lookup tables obtained directly from the data for the RA models are almost as effective as NNs trained on model variables.

State-Based Reconstructability Modeling For Decision Analysis, Michael S. Johnson, Martin Zwick

Complex Systems Faculty Publications and Presentations

Reconstructability analysis (RA) is a method for detecting and analyzing the structure of multivariate categorical data. Jones and his colleagues extended the original variable-based formulation of RA to encompass models defined in terms of system states (Jones 1982; Jones 1985; Jones 1985; Jones 1986; Jones 1989). In this paper, we demonstrate that Jones’ previous work comprises two separable ideas: the “g to k” transformation and state-based modeling. We relate the concept of state-based modeling to established variable-based RA methods (Klir 1985; Krippendorff 1986), and demonstrate that statebased modeling, when applied to event and decision tree models, is a valuable adjunct …

Prestructuring Neural Networks Via Extended Dependency Analysis With Application To Pattern Classification, George G. Lendaris, Thaddeus T. Shannon, Martin Zwick

Complex Systems Faculty Publications and Presentations

We consider the problem of matching domain-specific statistical structure to neural-network (NN) architecture. In past work we have considered this problem in the function approximation context; here we consider the pattern classification context. General Systems Methodology tools for finding problem-domain structure suffer exponential scaling of computation with respect to the number of variables considered. Therefore we introduce the use of Extended Dependency Analysis (EDA), which scales only polynomially in the number of variables, for the desired analysis. Based on EDA, we demonstrate a number of NN pre-structuring techniques applicable for building neural classifiers. An example is provided in which EDA …

Complexity Reduction In State-Based Modeling, Martin Zwick

Complex Systems Faculty Publications and Presentations

For a system described by a relation among qualitative variables (or quantitative variables "binned" into symbolic states), expressed either set-theoretically or as a multivariate joint probability distribution, complexity reduction (compression of representation) is normally achieved by modeling the system with projections of the overall relation. To illustrate, if ABCD is a four variable relation, then models ABC:BCD or AB:BC:CD:DA, specified by two triadic or four dyadic relations, respectively, represent simplifications of the ABCD relation. Simplifications which are lossless are always preferred over the original full relation, while simplifications which lose constraint are still preferred if the reduction of complexity more …

Complexity And Decomposability Of Relations, Martin Zwick

Complex Systems Faculty Publications and Presentations

A discrete multivariate relation, defined set-theoretically, is a subset of a cartesian product of sets which specify the possible values of a number of variables. Where three or more variables are involved, the highest order relation, namely the relation between all the variables, may or may not be decomposable without loss into sets of lower order relations which involve subsets of the variables. In a completely parallel manner, the highest order relation defined information-theoretically, namely the joint probability distribution involving all the variables, may or may not be decomposed without loss into lower-order distributions involving subsets of the variables. Decomposability …

Resolution Of Local Inconsistency In Identification, Douglas Ray Anderson, Martin Zwick

Complex Systems Faculty Publications and Presentations

This paper reports an algorithm for the resolution of local inconsistency in information-theoretic identification. This problem was first pointed out by Klir as an important research area in reconstructability analysis. Local inconsistency commonly arises when an attempt is made to integrate multiple data sources, i.e., contingency tables, which have differing common margins. For example, if one ha)s an AB table and a BC table, the B margins obtained from the two tables may disagree. If the disagreement can be assigned to sampling error, then one can arrive at a compromise B margin, adjust the original AB and BC tables to …

On Matching Ann Structure To Problem Domain Structure, George G. Lendaris, Martin Zwick, Karl Mathia

Complex Systems Faculty Publications and Presentations

To achieve reduced training time and improved generalization with artificial neural networks (ANN, or NN), it is important to use a reduced complexity NN structure. A "problem" is defined by constraints among the variables describing it. If knowledge about these constraints could be obtained a priori, this could be used to reduce the complexity of the ANN before training it. Systems theory literature contains methods for determining and representing structural aspects of constrained data (these methods are herein called GSM, general systems method). The suggestion here is to use the GSM model of the given data as a pattern for …