Plague of dimension
Plague of dimension or Malédiction of dimension ( Curse off dimensionality ) is a term invented by Richard Bellman to qualify the problem of the explosive increase in volumes of data associated with the addition of additional size in a mathematical space.
Leo Breiman gives the example of 100 observations covering the unidimensional interval in realities: it is possible to draw up a Histogramme results and to draw some from the Inférence S. On the other hand, in space corresponding to 10 dimensions 10, the 100 observations are points isolated in a vast empty space, and do not allow the statistical analysis. To carry out in 10 a cover equivalent to that of the 100 point in, one does not need less 1020 observations - gigantic and often impracticable company.
The plague of dimension is a major hurdle in the machine learning, which often amounts drawing from the inférences of a reduced number of experiments in a space of possibilities of high size. It then becomes often necessary to inject information A priori so as to force the system of training to obtain inférences. It must be prepared with the type of information to extract. One speaks then about Inférence bayésienne.
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