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統計的機械学習は単純な最適化問題ではない

It might seem that minimization of  K_n(w) is equivalent to minimization of  K(w). If these two minimization problems were equivalent, then maximization of  L_n(w) would be the best method in statistical estimation. However, minimization and expectation cannot be commutative.

 E[\min_w K_n(w) ] \neq \min_w E[K_n(w)] = \min_w K(w)

Hence maximization of  L_n(w) does not mean minimization of  K(w). This is the basic reason why statistical learning does not result in a simple optimization problem.

p.7

Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics)

Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics)

Jeffreys' prior

In statistical estimation, the pair  (p(x|w), \varphi(w)) is statistical model which is optimized for given random samples. Hence, if  p(x|w) is fixed and  \varphi(w) is made coordinate-free, such a pair  (p(x|w), \varphi(w)) is not appropriate for statistical estimation in general.

p.222

Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics)

Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics)

MAP推定とベイズ推定

Although the MAP employs an a priori distribution, its generalization error is quite different from that of Bayes estimation.

p.204

Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics)

Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics)

言葉

言葉

孤独には二種類ある。対話のある孤独と、対話のない孤独だ

数学ガール/乱択アルゴリズム (数学ガールシリーズ 4)

数学ガール/乱択アルゴリズム (数学ガールシリーズ 4)

中心極限定理と特異学習理論

As the central limit theory is characterized by the mean and the variance of the random variables, the stastical learning theory is characterized by the largest pole of zeta function and the singular fluctuation.

p.47

Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics)

Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics)

ティンバーゲンの4つのなぜ

ティンバーゲンの4つのなぜ - Wikipedia