Error-Free and Best-Fit Extensions of Partially Defined Boolean Functions

Boros, Endre; Ibaraki, Toshihide; Makino, Kazuhisa

doi:10.1006/inco.1997.2687

Cited by 56 publications

(41 citation statements)

References 19 publications

(45 reference statements)

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“…There may be no such solution, particularly if there are errors in the data leading to logical inconsistencies, or if the class of functions considered is restricted for practical or theoretical reasons. If so, we may then proceed by analogy with statistical modeling, accepting a best-fit solution that minimizes the number of misclassifications within the data, as in Boros, Ibaraki, and Makino (1998). When consistent solutions exist they will almost certainly not be unique.…”

Section: Inference Methods -Logical Consistencymentioning

confidence: 99%

Fitting Boolean Networks from Steady State Perturbation Data

Almudevar¹,

McCall²,

McMurray³

et al. 2011

Statistical Applications in Genetics and Molecular Biology

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Gene perturbation experiments are commonly used for the reconstruction of gene regulatory networks. Typical experimental methodology imposes persistent changes on the network. The resulting data must therefore be interpreted as a steady state from an altered gene regulatory network, rather than a direct observation of the original network. In this article an implicit modeling methodology is proposed in which the unperturbed network of interest is scored by first modeling the persistent perturbation, then predicting the steady state, which may then be compared to the observed data. This results in a many-to-one inverse problem, so a computational Bayesian approach is used to assess model uncertainty.The methodology is first demonstrated on a number of synthetic networks. It is shown that the Bayesian approach correctly assigns high posterior probability to the network structure and steady state behavior. Further, it is demonstrated that where uncertainty of model features is indicated, the uncertainty may be accurately resolved with further perturbation experiments. The methodology is then applied to the modeling of a gene regulatory network using perturbation data from nine genes which have been shown to respond synergistically to known oncogenic mutations. A hypothetical model emerges which conforms to reported regulatory properties of these genes. Furthermore, the Bayesian methodology is shown to be consistent in the sense that multiple randomized applications of the fitting algorithm converge to an approximately common posterior density on the space of models. Such consistency is generally not feasible for algorithms which report only single models. We conclude that fully Bayesian methods, coupled with models which accurately account for experimental constraints, are a suitable tool for the inference of gene regulatory networks, in terms of accuracy, estimation of model uncertainty, and experimental design.

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Section: Inference Methods -Logical Consistencymentioning

confidence: 99%

Fitting Boolean Networks from Steady State Perturbation Data

Almudevar¹,

McCall²,

McMurray³

et al. 2011

Statistical Applications in Genetics and Molecular Biology

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show abstract

“…Proof : The property is a simple extension of binary case (see [6]), and we therefore leave the details to the reader.…”

Section: Positive Functionsmentioning

confidence: 99%

“…The binary case of this problem has been already studied (e.g. in [6]) and it would not be hard to generalize the result in a straightforward way to the ternary case. So let us now look at the case with missing bits and the rules for their feasible replacements.…”

Section: Introductionmentioning

confidence: 99%

Analysing DNA microarray data using Boolean techniques

2010

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Abstract. We address in this manuscript a problem arising in molecular biology, namely a problem of discovering dependencies among gene expression levels. The problem is formulated in mathematical terms as a search for a fully defined three valued function defined on three valued variables which is partially specified by the DNA microarray measurments. This formulation as well as our solution methods are strongly motivated by results in the area of logical analysis of data (LAD) and in the area of partially defined Boolean functions (pdBfs), in particular by procedures for finding fully defined extensions of pdBfs. On one hand we present several algorithms which (under some assumptions) construct the desired three valued functional extension of the input data, and on the other hand we derive several proofs showing that (under different assumptions) finding such an extension is NP-hard.

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“…Early work in this area was targeted at binary domains. Recent work has extended this target to include numeric predictor attributes by using a process known as "binarization" (Boros et al 1997). Consider the example from Boros et al (1997) shown in Table 1.…”

Section: Building Classifiers Using Nonlinearmentioning

confidence: 99%

On the Use of Optimization for Data Mining: Theoretical Interactions and eCRM Opportunities

Padmanabhan

Tuzhilin

2003

Management Science

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P revious work on the solution to analytical electronic customer relationship management (eCRM) problems has used either data-mining (DM) or optimization methods, but has not combined the two approaches. By leveraging the strengths of both approaches, the eCRM problems of customer analysis, customer interactions, and the optimization of performance metrics (such as the lifetime value of a customer on the Web) can be better analyzed. In particular, many eCRM problems have been traditionally addressed using DM methods. There are opportunities for optimization to improve these methods, and this paper describes these opportunities. Further, an online appendix (mansci.pubs.informs.org/ecompanion.html) describes how DM methods can help optimization-based approaches. More generally, this paper argues that the reformulation of eCRM problems within this new framework of analysis can result in more powerful analytical approaches.

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Error-Free and Best-Fit Extensions of Partially Defined Boolean Functions

Cited by 56 publications

References 19 publications

Fitting Boolean Networks from Steady State Perturbation Data

Fitting Boolean Networks from Steady State Perturbation Data

Analysing DNA microarray data using Boolean techniques

On the Use of Optimization for Data Mining: Theoretical Interactions and eCRM Opportunities

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