Logic and Foundations Commons^™

Occam Manual, Martin Zwick

Systems Science Faculty Publications and Presentations

Occam is a Discrete Multivariate Modeling (DMM) tool based on the methodology of Reconstructability Analysis (RA). Its typical usage is for analysis of problems involving large numbers of discrete variables. Models are developed which consist of one or more components, which are then evaluated for their fit and statistical significance. Occam can search the lattice of all possible models, or can do detailed analysis on a specific model.

In Variable-Based Modeling (VBM), model components are collections of variables. In State-Based Modeling (SBM), components identify one or more specific states or substates.

Occam provides a web-based interface, which …

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

Systems Science 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 & Its Occam Implementation, Martin Zwick

Systems Science 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 …

Enhancing Value-Based Healthcare With Reconstructability Analysis: Predicting Cost Of Care In Total Hip Replacement, Cecily Corrine Froemke, Martin Zwick

Systems Science 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 …

Introduction To Reconstructability Analysis, Martin Zwick

Systems Science 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

Systems Science 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 …

Reconstructability & Dynamics Of Elementary Cellular Automata, Martin Zwick

Systems Science 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 …

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

Systems Science 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 …

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

Systems Science 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

Systems Science 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

Systems Science 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).

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

Systems Science 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

Systems Science 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

Systems Science 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.

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

Systems Science 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 …

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

Systems Science 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

Systems Science 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.

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

Systems Science 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.