A traditional way of introducing the inference facility in operational contexts is through the match box metaphor. You buy your box and wonder how many matches will fire, how many not. You cannot check all them otherwise you will be satisfied with your knowledge but cannot use the obtained information on the current box because it became empty. Thus you are challenged to understand the quality of the box by firing a small number of its matches. We link the metaphor to statistical framework we are building up through the noodles' picture in Fig. 3.1. For a fixed string of bits recording the sample of a random variable X you have a plenty of suffixes along which the population of subsequent X observations may develop. The compatibility requirement stresses the prefix-suffix relation between the strings as observations of the same phenomenon. With the increase of the complexity of the phenomena we study, and of computational power as well, the inference methods augmented their scope. Not only we want to forecast something of the future of X specifications, but we want to understand better what we have really observed. Per se the second goal complies with the noodles picture as well, since, in any case, what you will have understood will be employed to frame future data, as the current one belongs to the past. However the new objective calls for drilling relations between data, an attitude that is particular relevant in learning tasks, as we mentioned above, but is now going up till the most elementary parametric inference problems, when they are afforded in terms of genotypical features (see Section 3.2).

Inferring from samples / B. Apolloni, W. Pedrycz, S. Bassis, D. Malchiodi (STUDIES IN COMPUTATIONAL INTELLIGENCE). - In: The Puzzle of Granular Computing / [a cura di] B. Apolloni, W. Pedrycz, S. Bassis, D. Malchiodi. - [s.l] : Springer, 2008. - ISBN 9783540798637. - pp. 65-123 [10.1007/978-3-540-79864-4_3]

Inferring from samples

B. Apolloni;S. Bassis;D. Malchiodi
2008

Abstract

A traditional way of introducing the inference facility in operational contexts is through the match box metaphor. You buy your box and wonder how many matches will fire, how many not. You cannot check all them otherwise you will be satisfied with your knowledge but cannot use the obtained information on the current box because it became empty. Thus you are challenged to understand the quality of the box by firing a small number of its matches. We link the metaphor to statistical framework we are building up through the noodles' picture in Fig. 3.1. For a fixed string of bits recording the sample of a random variable X you have a plenty of suffixes along which the population of subsequent X observations may develop. The compatibility requirement stresses the prefix-suffix relation between the strings as observations of the same phenomenon. With the increase of the complexity of the phenomena we study, and of computational power as well, the inference methods augmented their scope. Not only we want to forecast something of the future of X specifications, but we want to understand better what we have really observed. Per se the second goal complies with the noodles picture as well, since, in any case, what you will have understood will be employed to frame future data, as the current one belongs to the past. However the new objective calls for drilling relations between data, an attitude that is particular relevant in learning tasks, as we mentioned above, but is now going up till the most elementary parametric inference problems, when they are afforded in terms of genotypical features (see Section 3.2).
Boolean Function; Master Equation; Concept Class; Algorithmic Inference; Propositional Variable
Settore INF/01 - Informatica
2008
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/703655
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