eqs
April 08, 2021

# Beamer Example

April 08, 2021

## Transcript

1. ### Beamer Example eqs April 8, 2021

both Japanese and English. ▶ 日本語と英語のどっちのプレゼンでも使えます． 2/9
3. ### Commands for brackets in equations ▶ \nbracket: \left( ... \right)

lim x→∞ ( 1 + 1 x ) x = e ▶ \cbracket: \left\{ ... \right\} β 2 N ∑ n=1 { tn − w⊤ϕ(xn) } 2 ▶ \rbracket: \left[ ... \right] ▶ \abracket: \left\langle ... \right\rangle 3/9

6. ### Example 1 (highlight) x2 − 6x + 2 = x2

− 6x + 9 − 7 = (x − 3)2 − 7 6/9
7. ### Example 2 (highlightcap, cbracket) When we consider a Gaussian prior

p(w|α) = N(w|0, α−1I), maximization of the corresponding posterior p(w|t) with respect to w is equivalent to the minimization of β 2 N ∑ n=1 { tn − w⊤ϕ(xn) } 2 + α 2 w⊤w (3.55’) the minimization corresponds to (3.27) with λ = α/β. 7/9
8. ### Example 2 (highlightcap, cbracket) When we consider a Gaussian prior

p(w|α) = N(w|0, α−1I), maximization of the corresponding posterior p(w|t) with respect to w is equivalent to the minimization of β 2 N ∑ n=1 { tn − w⊤ϕ(xn) } 2 an error function + α 2 w⊤w (3.55’) the minimization corresponds to (3.27) with λ = α/β. 7/9
9. ### Example 2 (highlightcap, cbracket) When we consider a Gaussian prior

p(w|α) = N(w|0, α−1I), maximization of the corresponding posterior p(w|t) with respect to w is equivalent to the minimization of β 2 N ∑ n=1 { tn − w⊤ϕ(xn) } 2 an error function + α 2 w⊤w a quadratic regularization (3.55’) the minimization corresponds to (3.27) with λ = α/β. 7/9
10. ### Example 3 (highlightcapoverlay) For the moment, the noise precision β

as a known constant. Where the likelihood function of t is defined as: p(t|w) = N ∏ n=1 N(tn|w⊤ϕ(xn), β−1) (3.10’) 8/9
11. ### Example 3 (highlightcapoverlay) For the moment, the noise precision β

as a known constant. Where the likelihood function of t is defined as: p(t|w) = N ∏ n=1 N(tn|w⊤ϕ(xn), β−1) The exponential of a quadratic func. of w (3.10’) 8/9
12. ### Example 4 (multi-columns) a c b d ▶ Item 1

▶ Item 2 ▶ Item 3 9/9
13. ### Example 4 (multi-columns) a c b d ▶ Item 1

▶ Item 2 ▶ Item 3 9/9