Computational commutative algebra in discrete statistics

Pistone, Giovanni; Riccomagno, Eva; Wynn, Henry P.

doi:10.1090/conm/287/04791

Cited by 70 publications

(134 citation statements)

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“…, 3 in a supervised learning experiment. It is easy to show that there is a unique quadratic curve through these points [57]. Let us define the polynomial…”

Section: Interpolationmentioning

confidence: 99%

“…However, a word of caution must be given should we use this argument in high dimensions (>2) since the division operation and the remainder themselves are not unique [57]. For this reason, we need to move into the field of Algebraic Geometry in order to guarantee unique representations.…”

Section: Interpolationmentioning

confidence: 99%

“…These parametrizations become even harder because statistical models or submodels are obtained by imposing restrictions on the parameters. In this thesis we will define an Algebraic Statistical Model (ASM) as one which adopts one of these parametrizations and for which the restrictions on the parameters themselves are also polynomial [57]. A more formal definition of these ASM shall be given below.…”

Section: Polynomial Representation Of a Univariate Gaussian Variablementioning

confidence: 99%

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Intelligent Management of Sepsis in the Intensive Care Unit

Ripoll

Rodríguez

Vellido

2012

Medical Applications of Intelligent Data Analysis

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Sepsis is a transversal pathology and one of the main causes of death in the Intensive Care Unit (ICU). It has in fact become the tenth most common cause of death in western societies. Its mortality rates can reach up to 60% for Septic Shock, its most acute manifestation. For these reasons, the prediction of the mortality caused by Sepsis is an open and relevant medical research challenge. This problem requires prediction methods that are robust and accurate, but also readily interpretable. This is paramount if they are to be used in the demanding context of real-time decision making at the ICU. In this brief contribution, three different methods are presented. One is based on a variant of the well-known support vector machine (SVM) model and provides and automated ranking of relevance of the mortality predictors while the other two are based on logistic-regression and logistic regression over latent Factors. The reported results show that the methods presented outperform in terms of accuracy alternative techniques currently in use in clinical settings, while simultaneously assessing the relative impact of individual pathology indicators.

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“…, 3 in a supervised learning experiment. It is easy to show that there is a unique quadratic curve through these points [57]. Let us define the polynomial…”

Section: Interpolationmentioning

confidence: 99%

Section: Interpolationmentioning

confidence: 99%

Section: Polynomial Representation Of a Univariate Gaussian Variablementioning

confidence: 99%

See 1 more Smart Citation

Intelligent Management of Sepsis in the Intensive Care Unit

Ripoll

Rodríguez

Vellido

2012

Medical Applications of Intelligent Data Analysis

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“…More precisely let V be Proof. For the first part see for example Cox et al (1996) and for the second and third parts see Pistone, Riccomagno and Wynn (2000).…”

Section: A Polynomial Algebraic Representation Of £(D)mentioning

confidence: 99%

“…See Pistone and Wynn (1996), Pistone, Riccomagno and Wynn (2000) and Riccomagno (1997). They are particularly useful in the analysis of complex experiments where there is a large number of factors and runs and the structure of the design is not regular, for example there are missing observations from a standard full factorial experiment.…”

Section: Introductionmentioning

confidence: 99%

Replications with Gröbner Bases

Cohen

Bucchianico²,

Riccomagno³

2001

mODa 6 — Advances in Model-Oriented Design and Analysis

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Advances in Robust Parameter Design: From Taguchi's Inner‐Outer Arrays to Combined Arrays

Evangelaras

Koukouvinos

Koutras

2005

Encyclopedia of Statistical Sciences

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Robust parameter design, originally proposed by Taguchi, is an off‐line technique for maintaining variance reduction and improving quality. According to Taguchi, product variation from the desirable target is affected by two types of factors: control factors and noise factors. The basic idea in robust parameter design is to identify the levels of the control factors so that the product's quality characteristic becomes insensitive to changes in the levels of the noise factors. As a consequence, the effect of uncontrollable variations on the response will be reduced. Taguchi suggested the use of inner‐outer arrays with the control factors being assigned to an inner array and the noise factors assigned to an outer array. After the collection of the data, a performance measure called signal‐to‐noise ratio is calculated and analyzed in order to identify the optimal levels of the control factors. After the introduction of Taguchi's philosophy in the field of experimental design and data analysis, several new designs and techniques have been explored and adopted in this field. This chapter overviews well established approaches and analysis techniques that have been exploited to the robust parameter design field.

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Computational commutative algebra in discrete statistics

Cited by 70 publications

References 0 publications

Intelligent Management of Sepsis in the Intensive Care Unit

Intelligent Management of Sepsis in the Intensive Care Unit

Replications with Gröbner Bases

Advances in Robust Parameter Design: From Taguchi's Inner‐Outer Arrays to Combined Arrays

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