A. Takemura, "Modern Mathematical Statistics," Sobunsya, Tokyo, 1991. (in Japanese) Home/Search Document Not in Database Summary Related Articles Check |
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Pseudo Orthogonal Bases Give the Optimal Solution to Active.. - Sugiyama, Ogawa (1999) (Correct)
....f 0 measured by . 9) Eq. 9) can be decomposed as follows: For any fixed g in a Hilbert space H 1 and any fixed f in a Hilbert space H 2 , the Neumann Schatten product g) is an operator from H 1 to H 2 defined by using any h H 1 as (see [25] g)h = #h, g#f. 7) Proposition 1 [26] It holds that #E n f 0 E n f 0 . 10) The first and second terms of the right hand side of Eq. 10) is called the bias and variance of f 0 , respectively. In this paper, we adopt the projection learning criterion. Let A # , # ) and PR(A # ) be the adjoint operator of A, the ....
A. Takemura, "Modern Mathematical Statistics," Sobunsya, Tokyo, 1991. (in Japanese)
Bias Estimation and Model Selection - Sugiyama, al. (2000) (Correct)
....u z = f. 8) A detailed discussion about Assumption 3 is given in Section 5. The unbiased learning result f u and the learning operator X u are used for estimating the generalization error of f # . It is well known that the generalization error of f # is decomposed into the bias and variance [26]: En# f # f# 2 = #En f # f# 2 En# f # En f # # 2 . 9) It follows from Eqs. 4) and (3) that Eq. 9) yields En # f # f# 2 = #X # z f# 2 En #X # n# 2 = #X # z f# 2 tr (X # QX # # ) 10) where tr ( denotes the trace of an ....
Takemura, A. (1991). Modern mathematical statistics. Tokyo: Sobunsya. (In Japanese)
Incremental Active Learning in. . . - Sugiyama, al. (Correct)
....learning result fm obtained by eqs. 7) and (10) belongs to R(A # m ) R(A # m ) is called the approximation space. Let us measure the generalization error of fm by JG = En#fm f# 2 . 14) Then, it is well known that eq. 14) can be decomposed into the bias and variance (Takemura [22]) JG = #En fm f# 2 En#fm En fm # 2 . 15) Substituting eqs. 7) 6) and (9) into eq. 15) we have JG = #PR(A # m ) f f# 2 En#Xmn (m) # 2 . 16) Eq. 16) implies that the projection learning criterion reduces the bias of fm to a certain level and minimizes the ....
Takemura, A. (1991). Modern mathematical statistics. Tokyo: Sobunsya. (in Japanese)
Active Learning for Optimal Generalization - Sugiyama, Ogawa (Correct)
....any fixed g in a Hilbert space H1 and any fixed f in a Hilbert space H2 , the Neumann Schatten product (f# g) is an operator from H1 to H2 defined by using any h # H1 as (Schatten [12] f# g)h = #h, g#f. It is well known that eq. 7) can be decomposed into the bias and variance (Takemura [15]) JG = #E n f 0 f# 2 E n #f 0 E n f 0 # 2 . 10) Substituting eqs. 6) 5) and (9) into eq. 10) we have JG = #P R(A # ) f f# 2 E n #Xn# 2 . 11) Eq. 11) implies that the projection learning criterion reduces the bias to a certain level and minimizes the variance. ....
A. Takemura. Modern Mathematical Statistics. Sobunsya, Tokyo, 1991.
Pseudo Orthogonal Bases Give the Optimal Solution to Active.. - Sugiyama, Ogawa (1999) (Correct)
.... f# 2 . 9) Eq. 9) can be decomposed as follows: 1 For any fixed g in a Hilbert space H 1 and any fixed f in a Hilbert space H 2 , the Neumann Schatten product (f# g) is an operator from H 1 to H 2 defined by using any h # H 1 as (see [25] f# g)h = #h, g#f. 7) 4 Proposition 1 [26] It holds that JG = #E n f 0 f# 2 E n #f 0 E n f 0 # 2 . 10) The first and second terms of the right hand side of Eq. 10) is called the bias and variance of f 0 , respectively. In this paper, we adopt the projection learning criterion. Let A # , R(A # ) and PR(A # ) be the ....
A. Takemura, "Modern Mathematical Statistics," Sobunsya, Tokyo, 1991. (in Japanese)
Properties of Incremental Projection Learning - Sugiyama, Ogawa (2001) (Correct)
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Takemura, A. (1991). Modern mathematical statistics. Tokyo: Sobunsya. (in Japanese)
Properties of Incremental Projection Learning - Sugiyama, Ogawa (2000) (Correct)
No context found.
Takemura, A. (1991). Modern mathematical statistics. Tokyo: Sobunsya. (in Japanese)
Pseudo Orthogonal Bases Give the Optimal Generalization.. - Sugiyama, Ogawa (Correct)
No context found.
A. Takemura, Modern Mathematical Statistics, Sobunsya, Tokyo, 1991.
Subspace Information Criterion for Model Selection - Sugiyama, Ogawa (1999) (1 citation) (Correct)
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Takemura, A. (1991). Modern Mathematical Statistics. Tokyo: Sobunsya. (in Japanese)
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