A Midpoint–Radius approach to regression with interval data

Boukezzoula, Reda; Galichet, Sylvie; Bisserier, Amory

doi:10.1016/j.ijar.2011.07.002

Cited by 33 publications

(19 citation statements)

References 38 publications

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“…Continuing example 2, the UCSOP has two possible instances such that the parameter constraint λ 2 = λ 1 + 3 holds, given that λ 1 ∈ U 1 , λ 2 ∈ U 2 . The valid tuples (λ 1 , λ 2 ) are (2, 5), and (3,6). The CSOP instances we generate are:…”

Section: Methodology and Algorithmmentioning

confidence: 99%

“…Regression analysis is one of the most widely used statistical techniques to model and represent the relationship among variables. Recently, models derived from fuzzy regression have been defined to represent incomplete and imprecise measurements in a contextual manner, using intervals [6]. Such models apply to problems in finance or complex systems analysis in engineering whereby a relationship between crisp or fuzzy measurements is sought.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

El MUNDO: Embedding Measurement Uncertainty in Decision Making and Optimization

Gervet

Galichet

2015

European Project Space on Intelligent Systems, Pattern Recognition and Biomedical Systems

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In this project we address the problem of modelling and solving constraint based problems permeated with data uncertainty, due to imprecise measurements or incomplete knowledge. It is commonly specified as bounded interval parameters in a constraint problem. For tractability reasons, existing approaches assume independence of the data, also called parameters. This assumption is safe as no solutions are lost, but can lead to large solution spaces, and a loss of the problem structure. In this paper we present two approaches we have investigated in the El MUNDO project, to handle data parameter dependencies effectively. The first one is generic whereas the second one focuses on a specific problem structure. The first approach combines two complementary paradigms, namely constraint programming and regression analysis, and identifies the relationships between potential solutions and parameter variations. The second approach identifies the context of matrix models and shows how dependency constraints over the data columns of such matrices can be modeled and handled very efficiently. Illustrations of both approaches and their benefits are shown.

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Section: Methodology and Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

El MUNDO: Embedding Measurement Uncertainty in Decision Making and Optimization

Gervet

Galichet

2015

European Project Space on Intelligent Systems, Pattern Recognition and Biomedical Systems

Self Cite

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“…: 4 The definition of independence between two random sets can be easily extended to the general case where either the initial space Ω, or the final universes, S 1 and S 2 , are necessarily finite. We just need to consider appropriate σ -fields, σ ⊆ ℘ (Ω), σ 1 ⊆ ℘ (℘ (S 1 )) and σ 2 ⊆ ℘ (℘ (S 2 )) and assume that the two-dimensional vector (X, Y ) : Ω → ℘ (S 1 ) × ℘ (S 2 ) (whose images are pairs of subsets of S 1 and S 2 , respectively) is σ − σ 1 ⊗ σ 2 measurable, so that it induces a probability measure on the product σ -field.…”

Section: Independencementioning

confidence: 99%

“…This is similar with the difference between the independence between variables and the independence between sources of information. In an ontic reading, one may wish to interpolate the interval data in a more sophisticated way than assuming linearity of the boundaries of the evolving interval (see Boukezzoula et al [4] for improvements of Tanaka's methods that cope with such defects).…”

Section: Possibilistic Regressionmentioning

confidence: 99%

Statistical reasoning with set-valued information: Ontic vs. epistemic views

Couso

Dubois

2014

International Journal of Approximate Reasoning

160

107

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. In information processing tasks, sets may have a conjunctive or a disjunctive reading. In the conjunctive reading, a set represents an object of interest and its elements are subparts of the object, forming a composite description. In the disjunctive reading, a set contains mutually exclusive elements and refers to the representation of incomplete knowledge. It does not model an actual object or quantity, but partial information about an underlying object or a precise quantity. This distinction between what we call ontic vs. epistemic sets remains valid for fuzzy sets, whose membership functions, in the disjunctive reading are possibility distributions, over deterministic or random values. This paper examines the impact of this distinction in statistics. We show its importance because there is a risk of misusing basic notions and tools, such as conditioning, distance between sets, variance, regression, etc. when data are set-valued. We discuss several examples where the ontic and epistemic points of view yield different approaches to these concepts.

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“…Regression analysis is one of the most widely used statistical techniques to model and represent the relationship among variables to describe or predict phenomena for a given context. Recently, models derived from fuzzy regression have been defined to represent incomplete and imprecise measurements in a contextual manner, using intervals [2]. Such models apply to problems in finance or complex systems analysis in engineering whereby a relationship between crisp or fuzzy measurements is sought.…”

Section: Introductionmentioning

confidence: 99%

On Combining Regression Analysis and Constraint Programming

Gervet¹,

Galichet²

2014

Information Processing and Management of Uncertainty in Knowledge-Based Systems

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Abstract. Uncertain data due to imprecise measurements is commonly specified as bounded interval parameters in a constraint problem. For tractability reasons, existing approaches assume independence of the parameters. This assumption is safe, but can lead to large solution spaces, and a loss of the problem structure. In this paper we propose to combine the strengths of two frameworks to tackle parameter dependency effectively, namely constraint programming and regression analysis. Our methodology is an iterative process. The core intuitive idea is to account for data dependency by solving a set of constraint models such that each model uses data parameter instances that satisfy the dependency constraints. Then we apply a regression between the parameter instances and the corresponding solutions found to yield a possible relationship function. Our findings show that this methodology exploits the strengths of both paradigms effectively, and provides valuable insights to the decision maker by accounting for parameter dependencies.

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A Midpoint–Radius approach to regression with interval data

Cited by 33 publications

References 38 publications

El MUNDO: Embedding Measurement Uncertainty in Decision Making and Optimization

El MUNDO: Embedding Measurement Uncertainty in Decision Making and Optimization

Statistical reasoning with set-valued information: Ontic vs. epistemic views

On Combining Regression Analysis and Constraint Programming

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