13,402 research outputs found
Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond
There is a hidden intrigue in the title. CT is one of the most abstract
mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a
recent trend in software development, industrially supported by standards,
tools, and the status of a new "silver bullet". Surprisingly, categorical
patterns turn out to be directly applicable to mathematical modeling of
structures appearing in everyday MDE practice. Model merging, transformation,
synchronization, and other important model management scenarios can be seen as
executions of categorical specifications.
Moreover, the paper aims to elucidate a claim that relationships between CT
and MDE are more complex and richer than is normally assumed for "applied
mathematics". CT provides a toolbox of design patterns and structural
principles of real practical value for MDE. We will present examples of how an
elementary categorical arrangement of a model management scenario reveals
deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430
Bayesian Item Response Modeling in R with brms and Stan
Item Response Theory (IRT) is widely applied in the human sciences to model
persons' responses on a set of items measuring one or more latent constructs.
While several R packages have been developed that implement IRT models, they
tend to be restricted to respective prespecified classes of models. Further,
most implementations are frequentist while the availability of Bayesian methods
remains comparably limited. We demonstrate how to use the R package brms
together with the probabilistic programming language Stan to specify and fit a
wide range of Bayesian IRT models using flexible and intuitive multilevel
formula syntax. Further, item and person parameters can be related in both a
linear or non-linear manner. Various distributions for categorical, ordinal,
and continuous responses are supported. Users may even define their own custom
response distribution for use in the presented framework. Common IRT model
classes that can be specified natively in the presented framework include 1PL
and 2PL logistic models optionally also containing guessing parameters, graded
response and partial credit ordinal models, as well as drift diffusion models
of response times coupled with binary decisions. Posterior distributions of
item and person parameters can be conveniently extracted and post-processed.
Model fit can be evaluated and compared using Bayes factors and efficient
cross-validation procedures.Comment: 54 pages, 16 figures, 3 table
Towards Translating Graph Transformation Approaches by Model Transformations
Recently, many researchers are working on semantics preserving model transformation. In the field of graph transformation one can think of translating graph grammars written in one approach to a behaviourally equivalent graph grammar in another approach. In this paper we translate graph grammars developed with the GROOVE tool to AGG graph grammars by first investigating the set of core graph transformation concepts supported by both tools. Then, we define what it means for two graph grammars to be behaviourally equivalent, and for the regarded approaches we actually show how to handle different definitions of both - application conditions and graph structures. The translation itself is explained by means of intuitive examples
rTisane: Externalizing conceptual models for data analysis increases engagement with domain knowledge and improves statistical model quality
Statistical models should accurately reflect analysts' domain knowledge about
variables and their relationships. While recent tools let analysts express
these assumptions and use them to produce a resulting statistical model, it
remains unclear what analysts want to express and how externalization impacts
statistical model quality. This paper addresses these gaps. We first conduct an
exploratory study of analysts using a domain-specific language (DSL) to express
conceptual models. We observe a preference for detailing how variables relate
and a desire to allow, and then later resolve, ambiguity in their conceptual
models. We leverage these findings to develop rTisane, a DSL for expressing
conceptual models augmented with an interactive disambiguation process. In a
controlled evaluation, we find that rTisane's DSL helps analysts engage more
deeply with and accurately externalize their assumptions. rTisane also leads to
statistical models that match analysts' assumptions, maintain analysis intent,
and better fit the data
A Factor Graph Approach to Automated Design of Bayesian Signal Processing Algorithms
The benefits of automating design cycles for Bayesian inference-based
algorithms are becoming increasingly recognized by the machine learning
community. As a result, interest in probabilistic programming frameworks has
much increased over the past few years. This paper explores a specific
probabilistic programming paradigm, namely message passing in Forney-style
factor graphs (FFGs), in the context of automated design of efficient Bayesian
signal processing algorithms. To this end, we developed "ForneyLab"
(https://github.com/biaslab/ForneyLab.jl) as a Julia toolbox for message
passing-based inference in FFGs. We show by example how ForneyLab enables
automatic derivation of Bayesian signal processing algorithms, including
algorithms for parameter estimation and model comparison. Crucially, due to the
modular makeup of the FFG framework, both the model specification and inference
methods are readily extensible in ForneyLab. In order to test this framework,
we compared variational message passing as implemented by ForneyLab with
automatic differentiation variational inference (ADVI) and Monte Carlo methods
as implemented by state-of-the-art tools "Edward" and "Stan". In terms of
performance, extensibility and stability issues, ForneyLab appears to enjoy an
edge relative to its competitors for automated inference in state-space models.Comment: Accepted for publication in the International Journal of Approximate
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BayesX: Analyzing Bayesian Structural Additive Regression Models
There has been much recent interest in Bayesian inference for generalized additive and related models. The increasing popularity of Bayesian methods for these and other model classes is mainly caused by the introduction of Markov chain Monte Carlo (MCMC) simulation techniques which allow realistic modeling of complex problems. This paper describes the capabilities of the free software package BayesX for estimating regression models with structured additive predictor based on MCMC inference. The program extends the capabilities of existing software for semiparametric regression included in S-PLUS, SAS, R or Stata. Many model classes well known from the literature are special cases of the models supported by BayesX. Examples are generalized additive (mixed) models, dynamic models, varying coefficient models, geoadditive models, geographically weighted regression and models for space-time regression. BayesX supports the most common distributions for the response variable. For univariate responses these are Gaussian, Binomial, Poisson, Gamma, negative Binomial, zero inflated Poisson and zero inflated negative binomial. For multicategorical responses, both multinomial logit and probit models for unordered categories of the response as well as cumulative threshold models for ordered categories can be estimated. Moreover, BayesX allows the estimation of complex continuous time survival and hazard rate models.
Software and systems traceability for safety-critical projects: report from Dagstuhl Seminar 15162
This report documents the program and the outcomes of Dagstuhl Seminar 15162 on “Software and Systems Traceability for Safety-Critical Projects”. The event brought together researchers and industrial practitioners working in the field of safety critical software to explore the needs, challenges, and solutions for Software and Systems Traceability in this domain. The goal was to explore the gap between the traceability prescribed by guidelines and that delivered by manufacturers, and starting from a clean slate, to clearly articulate traceability needs for safety-critical software systems, to identify challenges, explore solutions, and to propose a set of principles and
domain-specific exemplars for achieving traceability in safety critical systems
Towards Specifying Swarm-based Systems Using Categorical Modeling Language: A Case Study
One of the solutions to the software complexity crisis of this era is the proposition of self-managing systems like autonomous and autonomic systems. The idea has gained wide acceptance in the IT industry but it has also introduced the challenge of specification and development of such systems. Swarm intelligence is finding its applications in research and design of self-managing systems because of the coincidental resemblance between the two domains. However, specification of a swarm-based self-managing system is faced with the difficulty of specifying the complex evolving behavior.
This thesis presents an adaptation of a mathematical technique known as Category Theory to serve as a ‘reasoning and modeling’ paradigm for specifying high-level behavioral patterns of a swarm-based self-managing systems. The crux of this paradigm is the formal categorical modeling language (CML). CML syntax and semantics have been defined using an EBNF-based context-free grammar. The language helps to generate a formal specification of different scenarios/behavioral patterns of a swarm-based system. Moreover, a prototype tool has been implemented as part of this research work to serve as a modeling tool based on CML. In this thesis, NASA’s ANTS-based Prospecting Asteroid Mission (PAM) serves as a case study to analyze the applicability and usability of CML as a formal method of choice
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