p. 50, algorithm 3.3, line 15 and 16, the term "+\sum_{i}\log(...)"
has the wrong sign, the correct term is "-\sum__{i}\log(...)" in both line 15 and 16. (thanks to Chris Mansley)

p. 51, algorithm 3.4, line 11, two occurrences of "R" should be "R_c". A
simpler expression is "**c** := E_c(M^{T}\(M\**b**))". (thanks
to Yang Song and Chris Mansley)

p. 56, above eq. (3.61) "the role of W" should be "the role of W^{-1}".

p. 97, the eigenfunction given in eq. (4.40) is not normalized. It can be shown using eq 7.374.1 in Gradshteyn and Ryzhik (1980) that "\phi_k(x) = h_k \exp(-(c-a)x^2) H_k(\sqrt{2c}x)" is normalized wrt p(x) by setting "h_k^{-2} = \sqrt{a/c} 2^k k!". (thanks to Christian Walder)

p. 11, eq (2.9), the third expression is incorrect. The first, second and fourth expressions are equal. (thanks to Kevin S. Van Horn)

p. 12, line 16, typo: "setting Z^{-1}=\Sigma_p^2", should be "setting Z^{-1}=\Sigma_p". (thanks to Mikhail Parakhin)

p. 28, eq (2.41), top line, typo: the term "K_*K_y^{-1}(y - H \bar\beta)"
should be "K^{T}_*K_y^{-1}(y - H^{T} \bar\beta)", ie transposes
on both "K_*" and "H" are missing. (thanks to Mikhail Parakhin)

p. 50, algorithm 3.3, line 15 and 16, the term "+\sum_{i}\log(...)"
has the wrong sign, the correct term is "-\sum__{i}\log(...)" in both line 15 and 16. (thanks to Chris Mansley)

p. 51, algorithm 3.4, line 11, two occurrences of "R" should be "R_c". A
simpler expression is "**c** := E_c(M^{T}\(M\**b**))". (thanks
to Yang Song and Chris Mansley)

p. 56, above eq. (3.61) "the role of W" should be "the role of W^{-1}".

p. 59, penultimate line, replace "In eq.(3.65) we have factored" with "In eq.(3.73) we have factored". (thanks to Baback Moghaddam)

p. 61, figure caption, the final two lines should read "The maximum value attained is 0.84, and the minimium is 0.19."

p. 68, Figure 3.9, caption, third line: Figure 3.7(a) should read Figure 3.8(a).(thanks to Baback Moghaddam)

p. 95, line 14 just under eq. (4.35) typo: "k(**x**,**x**')" should be
"\tilde k(**x**,**x**')", ie there is a tilde missing over the "k".

p. 97, the eigenfunction given in eq. (4.40) is not normalized. It can be shown using eq 7.374.1 in Gradshteyn and Ryzhik (1980) that "\phi_k(x) = h_k \exp(-(c-a)x^2) H_k(\sqrt{2c}x)" is normalized wrt p(x) by setting "h_k^{-2} = \sqrt{a/c} 2^k k!". (thanks to Christian Walder)

p. 102, eq (4.46), \phi_{\theta}(x) should be
\phi^{T}_{\theta}(x). (thanks to Baback Moghaddam)

p. 121, eq (5.18), the Kronecker delta, \delta_{xx'} should really
be on the *indexes* (not the *values* of x), i.e
\delta_{pq} as in eq (2.20). (thanks to Aki Vehtari)

p. 125, eq (5.24), the matrix "B^{-1}" in the right-hand side is incorrect. Instead of "B^{-1}" it should be "(I+KW)^{-1}".

p. 126, caption for Algorithm 5.1, 4th line: "line 11" should be "line 12". (thanks to Baback Moghaddam)

p. 126, line -6: "B^{-1}=(I+W^\frac{1}{2}KW^\frac{1}{2})^{-1}" is incorrect. It should be "(I+KW)^{-1}".

p. 127, eq (5.26) and (5.27), in both equations, the left hand side
should be the "partial derivative of the *log of*
Z_{EP}, not Z_{EP} itself. (thanks to Baback Moghaddam
and Jurgen Van Gael)

p. 127, eq (5.26), first line, first term in rhs, \Sigma should be \tilde{\Sigma}. (thanks to Baback Moghaddam)

p. 137, both occurrences of 4 \pi should be 4 \pi^2. (thanks to Baback Moghaddam)

p. 139, eq (6.30), Z(u) should be Z(u) du. (thanks to Baback Moghaddam)

p. 144, eqs (6.37) and (6.38), both equations are missing a
transpose on the first term's first **f** vector.
(thanks to Baback Moghaddam)

p. 148, eq (6.43), replace both occurrences of
p(y_i|X, **y**, \theta) with p(y_i|X, **y**_{-i}, \theta).
(thanks to Baback Moghaddam)

p. 153, eq (7.9), rhs final denominator should be
1 + S^{-1}_f (**s**) \sigma^2_n/ \rho.
(thanks to Baback Moghaddam)

p. 158, third line, replace J < \infty with KL_{sym} < \infty. (thanks to Baback Moghaddam)

p. 160, eq. (7.23), third line, last term
**k**_{1}(**x**)^{T} should read
**k**_{1}(**x**_{*})^{T}.
(thanks to Baback Moghaddam)

p. 160, above eq. (7.26): eq. (7.26) is a **lower** bound on the
generalization error, not (as stated) an upper bound. (thanks to
Benjamin Sobotta)

p. 165, eq (7.34), first term is missing a trailing | (for det) and the third term is missing a tr(). (thanks to Baback Moghaddam)

p. 182 and 184, sec. 8.3.7: Unfortunately there was an error in the scripts
that meant that the noise variance was added in twice when computing the
predictive variance for the PP runs; this affected the PP results for
MSLL (but not SMSE) in Table 8.1 and Figure 8.1(b). This
pdf file gives corrected versions of the Table and plot. Notice now that
there is not much difference in performance between the SR, PP and BCM methods
for various sizes of *m* on this problem, and that they all outperform
the SD method.

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