diff --git a/.nojekyll b/.nojekyll
index fec702f..d7bdd33 100644
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+++ b/.nojekyll
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+a4dd7030
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diff --git a/schedule/slides/17-nonlinear-classifiers.html b/schedule/slides/17-nonlinear-classifiers.html
index b056529..f8a4a0c 100644
--- a/schedule/slides/17-nonlinear-classifiers.html
+++ b/schedule/slides/17-nonlinear-classifiers.html
@@ -397,7 +397,7 @@
17 Nonlinear classifiers
Stat 406
Daniel J. McDonald
-Last modified – 26 October 2023
+Last modified – 30 October 2023
\[
\DeclareMathOperator*{\argmin}{argmin}
\DeclareMathOperator*{\argmax}{argmax}
@@ -716,6 +716,32 @@ knn.cv() (leave one out)I would use the largest (odd) k that is close to the minimum.
+
+Alternative (using deviance loss, I think this is right)
+
+
+Code
+<- function (y, prob, prob_min = 1e-5 ) {<- as.numeric (as.factor (y)) - 1 # 0/1 valued <- mean (y)<- 1 - prob_min<- pmin (pmax (prob, prob_min), prob_max)<- (1 - y) * log (1 - prob) + y * log (prob)<- (1 - y) * log (1 - m) + y * log (m)2 * (ly - lp)<- function (train, cl, k = 1 ) {<- knn.cv (train, cl, k = k, prob = TRUE )<- attr (o, "prob" )<- as.numeric (as.factor (o)) - 1 == 0 ] <- 1 - p[o == 0 ]<- map_dbl (1 : kmax, ~ mean (dev (dat1$ y, knn.cv_probs (dat1[, - 1 ], dat1$ y, k = .x))))
+
Final version
@@ -723,26 +749,26 @@
Final version
Code
-<- max (which (err == min (err)))<- kopt + 1 * (kopt %% 2 == 0 )$ opt <- knn (dat1[, - 1 ], gr[, 1 : 2 ], dat1$ y, k = kopt)<- table (knn (dat1[, - 1 ], dat1[, - 1 ], dat1$ y, k = kopt), dat1$ y, dnn = c ("predicted" , "truth" ))ggplot (dat1, aes (x1, x2)) + theme_bw (base_size = 24 ) + scale_shape_manual (values = c ("0" , "1" ), guide = "none" ) + geom_raster (data = gr, aes (x1, x2, fill = opt), alpha = .6 ) + geom_point (aes (shape = y), size = 4 ) + coord_cartesian (c (- 2.5 , 3 ), c (- 2.5 , 3 )) + scale_fill_manual (values = c (orange, green), labels = c ("0" , "1" )) + theme (legend.position = "bottom" , legend.title = element_blank (),legend.key.width = unit (2 , "cm" )<- max (which (err == min (err)))<- kopt + 1 * (kopt %% 2 == 0 )$ opt <- knn (dat1[, - 1 ], gr[, 1 : 2 ], dat1$ y, k = kopt)<- table (knn (dat1[, - 1 ], dat1[, - 1 ], dat1$ y, k = kopt), dat1$ y, dnn = c ("predicted" , "truth" ))ggplot (dat1, aes (x1, x2)) + theme_bw (base_size = 24 ) + scale_shape_manual (values = c ("0" , "1" ), guide = "none" ) + geom_raster (data = gr, aes (x1, x2, fill = opt), alpha = .6 ) + geom_point (aes (shape = y), size = 4 ) + coord_cartesian (c (- 2.5 , 3 ), c (- 2.5 , 3 )) + scale_fill_manual (values = c (orange, green), labels = c ("0" , "1" )) + theme (legend.position = "bottom" , legend.title = element_blank (),legend.key.width = unit (2 , "cm" )
diff --git a/schedule/slides/17-nonlinear-classifiers_files/figure-revealjs/unnamed-chunk-6-1.svg b/schedule/slides/17-nonlinear-classifiers_files/figure-revealjs/unnamed-chunk-6-1.svg
index 22a006e..a6c8754 100644
--- a/schedule/slides/17-nonlinear-classifiers_files/figure-revealjs/unnamed-chunk-6-1.svg
+++ b/schedule/slides/17-nonlinear-classifiers_files/figure-revealjs/unnamed-chunk-6-1.svg
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diff --git a/schedule/slides/17-nonlinear-classifiers_files/figure-revealjs/unnamed-chunk-8-1.svg b/schedule/slides/17-nonlinear-classifiers_files/figure-revealjs/unnamed-chunk-8-1.svg
new file mode 100644
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--- /dev/null
+++ b/schedule/slides/17-nonlinear-classifiers_files/figure-revealjs/unnamed-chunk-8-1.svg
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diff --git a/schedule/slides/17-nonlinear-classifiers_files/figure-revealjs/unnamed-chunk-9-1.svg b/schedule/slides/17-nonlinear-classifiers_files/figure-revealjs/unnamed-chunk-9-1.svg
new file mode 100644
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diff --git a/schedule/slides/18-the-bootstrap.html b/schedule/slides/18-the-bootstrap.html
index dec905f..38f8b18 100644
--- a/schedule/slides/18-the-bootstrap.html
+++ b/schedule/slides/18-the-bootstrap.html
@@ -397,7 +397,7 @@
18 The bootstrap
Stat 406
Daniel J. McDonald
-
Last modified – 11 October 2023
+
Last modified – 30 October 2023
\[
\DeclareMathOperator*{\argmin}{argmin}
\DeclareMathOperator*{\argmax}{argmax}
@@ -493,10 +493,29 @@ Bootstrap procedure
\(\hat{F}\) is the “empirical” distribution of the bootstraps.
+
+Empirical distribution
+
+
+Code
+<- rexp (50 , 1 / 5 )ggplot (tibble (r = r), aes (r)) + stat_ecdf (colour = orange) + geom_vline (xintercept = quantile (r, probs = c (.05 , .95 ))) + geom_hline (yintercept = c (.05 , .95 ), linetype = "dashed" ) + annotate ("label" , x = c (5 , 12 ), y = c (.25 , .75 ), label = c ("hat(F)[boot](.05)" , "hat(F)[boot](.95)" ), parse = TRUE
+
+
Very basic example
-Let \(X_i\sim Exponential(1/5)\) . The pdf is \(f(x) = \frac{1}{5}e^{-x/5}\)
Let \(X_i\sim \textrm{Exponential}(1/5)\) . The pdf is \(f(x) = \frac{1}{5}e^{-x/5}\)
I know if I estimate the mean with \(\bar{X}\) , then by the CLT (if \(n\) is big),
\[\frac{\sqrt{n}(\bar{X}-E[X])}{s} \approx N(0, 1).\]
@@ -510,19 +529,19 @@
Code
-ggplot (data.frame (x = c (0 , 12 )), aes (x)) + stat_function (fun = function (x) dexp (x, 1 / 5 ), color = orange) + geom_vline (xintercept = 5 , color = blue) + # mean geom_vline (xintercept = qexp (.5 , 1 / 5 ), color = red) + # median annotate ("label" ,x = c (2.5 , 5.5 , 10 ), y = c (.15 , .15 , .05 ),label = c ("median" , "bar(x)" , "pdf" ), parse = TRUE ,color = c (red, blue, orange), size = 6 ggplot (data.frame (x = c (0 , 12 )), aes (x)) + stat_function (fun = function (x) dexp (x, 1 / 5 ), color = orange) + geom_vline (xintercept = 5 , color = blue) + # mean geom_vline (xintercept = qexp (.5 , 1 / 5 ), color = red) + # median annotate ("label" ,x = c (2.5 , 5.5 , 10 ), y = c (.15 , .15 , .05 ),label = c ("median" , "bar(x)" , "pdf" ), parse = TRUE ,color = c (red, blue, orange), size = 6
-
+
Now what…
-
set.seed (406406406 )<- rexp (n, 1 / 5 )<- median (x)) # sample median
+
set.seed (406406406 )<- rexp (n, 1 / 5 )<- median (x)) # sample median
-
<- 100 <- 0.05 <- map_dbl (1 : B, ~ median (sample (x, replace = TRUE ))) # repeat B times, "empirical distribution" <- 2 * med - quantile (Fhat, probs = c (1 - alpha / 2 , alpha / 2 ))
+
<- 100 <- 0.05 <- map_dbl (1 : B, ~ median (sample (x, replace = TRUE ))) # repeat B times, "empirical distribution" <- 2 * med - quantile (Fhat, probs = c (1 - alpha / 2 , alpha / 2 ))
@@ -548,23 +567,23 @@
Code
-ggplot (data.frame (Fhat), aes (Fhat)) + geom_density (color = orange) + geom_vline (xintercept = CI, color = orange, linetype = 2 ) + geom_vline (xintercept = med, col = blue) + geom_vline (xintercept = qexp (.5 , 1 / 5 ), col = red) + annotate ("label" ,x = c (3.15 , 3.5 , 3.75 ), y = c (.5 , .5 , 1 ),color = c (orange, red, blue),label = c ("widehat(F)" , "true~median" , "widehat(median)" ),parse = TRUE + xlab ("x" ) + geom_rug (aes (2 * med - Fhat))ggplot (data.frame (Fhat), aes (Fhat)) + geom_density (color = orange) + geom_vline (xintercept = CI, color = orange, linetype = 2 ) + geom_vline (xintercept = med, col = blue) + geom_vline (xintercept = qexp (.5 , 1 / 5 ), col = red) + annotate ("label" ,x = c (3.15 , 3.5 , 3.75 ), y = c (.5 , .5 , 1 ),color = c (orange, red, blue),label = c ("widehat(F)" , "true~median" , "widehat(median)" ),parse = TRUE + xlab ("x" ) + geom_rug (aes (2 * med - Fhat))
-
+
How does this work?
@@ -578,14 +597,14 @@ Slightly harder example
-
ggplot (fatcats, aes (Bwt, Hwt)) + geom_point (color = blue) + xlab ("Cat body weight (Kg)" ) + ylab ("Cat heart weight (g)" )
+
ggplot (fatcats, aes (Bwt, Hwt)) + geom_point (color = blue) + xlab ("Cat body weight (Kg)" ) + ylab ("Cat heart weight (g)" )
@@ -593,8 +612,8 @@
Slightly harder example
-
<- lm (Hwt ~ 0 + Bwt, data = fatcats)summary (cats.lm)
+
<- lm (Hwt ~ 0 + Bwt, data = fatcats)summary (cats.lm)
Call:
@@ -614,7 +633,7 @@ Slightly harder example
Multiple R-squared: 0.965, Adjusted R-squared: 0.9648
F-statistic: 3947 on 1 and 143 DF, p-value: < 2.2e-16
-
+
2.5 % 97.5 %
Bwt 3.829836 4.078652
@@ -628,12 +647,12 @@
When we fit models, we examine diagnostics
-
qqnorm (residuals (cats.lm), pch = 16 , col = blue)qqline (residuals (cats.lm), col = orange, lwd = 2 )
+
qqnorm (residuals (cats.lm), pch = 16 , col = blue)qqline (residuals (cats.lm), col = orange, lwd = 2 )
@@ -643,21 +662,21 @@
When we fit models, we examine diagnostics
We bootstrap
-
<- 500 <- .05 <- map_dbl (1 : B, ~ {<- fatcats |> slice_sample (prop = 1 , replace = TRUE )coef (lm (Hwt ~ 0 + Bwt, data = newcats))2 * coef (cats.lm) - # Bootstrap CI quantile (bhats, probs = c (1 - alpha / 2 , alpha / 2 ))
+
<- 500 <- .05 <- map_dbl (1 : B, ~ {<- fatcats |> slice_sample (prop = 1 , replace = TRUE )coef (lm (Hwt ~ 0 + Bwt, data = newcats))2 * coef (cats.lm) - # Bootstrap CI quantile (bhats, probs = c (1 - alpha / 2 , alpha / 2 ))
97.5% 2.5%
3.826735 4.084322
-
confint (cats.lm) # Original CI
+
confint (cats.lm) # Original CI
2.5 % 97.5 %
Bwt 3.829836 4.078652
@@ -688,21 +707,21 @@
Same data
Non-parametric bootstrap
Same as before
-
<- 500 <- .05 <- map_dbl (1 : B, ~ {<- fatcats |> slice_sample (prop = 1 , replace = TRUE )coef (lm (Hwt ~ 0 + Bwt, data = newcats))2 * coef (cats.lm) - # NP Bootstrap CI quantile (bhats, probs = c (1 - alpha / 2 , alpha / 2 ))
+
<- 500 <- .05 <- map_dbl (1 : B, ~ {<- fatcats |> slice_sample (prop = 1 , replace = TRUE )coef (lm (Hwt ~ 0 + Bwt, data = newcats))2 * coef (cats.lm) - # NP Bootstrap CI quantile (bhats, probs = c (1 - alpha / 2 , alpha / 2 ))
97.5% 2.5%
3.832907 4.070232
-
confint (cats.lm) # Original CI
+
confint (cats.lm) # Original CI
2.5 % 97.5 %
Bwt 3.829836 4.078652
@@ -717,20 +736,20 @@
Same data
The \(\epsilon_i\) is random \(\longrightarrow\) just resample \(\widehat{e}_i\) .
-
<- 500 <- double (B)<- lm (Hwt ~ 0 + Bwt, data = fatcats)<- residuals (cats.lm)<- map_dbl (1 : B, ~ {<- fatcats |> mutate (Hwt = predict (cats.lm) + sample (r, n (), replace = TRUE )coef (lm (Hwt ~ 0 + Bwt, data = newcats))2 * coef (cats.lm) - # Parametric Bootstrap CI quantile (bhats, probs = c (1 - alpha / 2 , alpha / 2 ))
+
<- 500 <- double (B)<- lm (Hwt ~ 0 + Bwt, data = fatcats)<- residuals (cats.lm)<- map_dbl (1 : B, ~ {<- fatcats |> mutate (Hwt = predict (cats.lm) + sample (r, n (), replace = TRUE )coef (lm (Hwt ~ 0 + Bwt, data = newcats))2 * coef (cats.lm) - # Parametric Bootstrap CI quantile (bhats, probs = c (1 - alpha / 2 , alpha / 2 ))
97.5% 2.5%
3.815162 4.065045
@@ -775,7 +794,7 @@
Types of intervals
Types of intervals
Let \(\hat{\theta}\) be our sample statistic, \(\hat{\Theta}\) be the resamples
\[
-[\hat{\theta} - t_{\alpha/2}\hat{s},\ \hat{\theta} - t_{\alpha/2}\hat{s}]
+[\hat{\theta} - t_{\alpha/2}s,\ \hat{\theta} - t_{\alpha/2}s]
\]
where \(\hat{s} = \sqrt{\Var{\hat{\Theta}}}\)
diff --git a/schedule/slides/18-the-bootstrap_files/figure-revealjs/unnamed-chunk-1-1.svg b/schedule/slides/18-the-bootstrap_files/figure-revealjs/unnamed-chunk-1-1.svg
index efa4791..d5b0a50 100644
--- a/schedule/slides/18-the-bootstrap_files/figure-revealjs/unnamed-chunk-1-1.svg
+++ b/schedule/slides/18-the-bootstrap_files/figure-revealjs/unnamed-chunk-1-1.svg
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diff --git a/schedule/slides/18-the-bootstrap_files/figure-revealjs/unnamed-chunk-2-1.svg b/schedule/slides/18-the-bootstrap_files/figure-revealjs/unnamed-chunk-2-1.svg
new file mode 100644
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diff --git a/schedule/slides/18-the-bootstrap_files/figure-revealjs/unnamed-chunk-5-1.svg b/schedule/slides/18-the-bootstrap_files/figure-revealjs/unnamed-chunk-5-1.svg
new file mode 100644
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diff --git a/schedule/slides/18-the-bootstrap_files/figure-revealjs/unnamed-chunk-7-1.svg b/schedule/slides/18-the-bootstrap_files/figure-revealjs/unnamed-chunk-7-1.svg
new file mode 100644
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--- /dev/null
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diff --git a/schedule/slides/18-the-bootstrap_files/figure-revealjs/unnamed-chunk-9-1.svg b/schedule/slides/18-the-bootstrap_files/figure-revealjs/unnamed-chunk-9-1.svg
new file mode 100644
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--- /dev/null
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@@ -0,0 +1,412 @@
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diff --git a/search.json b/search.json
index 42d04c1..85a422d 100644
--- a/search.json
+++ b/search.json
@@ -186,7 +186,7 @@
"href": "schedule/slides/18-the-bootstrap.html#meta-lecture",
"title": "UBC Stat406 2023W",
"section": "18 The bootstrap",
- "text": "18 The bootstrap\nStat 406\nDaniel J. McDonald\nLast modified – 11 October 2023\n\\[\n\\DeclareMathOperator*{\\argmin}{argmin}\n\\DeclareMathOperator*{\\argmax}{argmax}\n\\DeclareMathOperator*{\\minimize}{minimize}\n\\DeclareMathOperator*{\\maximize}{maximize}\n\\DeclareMathOperator*{\\find}{find}\n\\DeclareMathOperator{\\st}{subject\\,\\,to}\n\\newcommand{\\E}{E}\n\\newcommand{\\Expect}[1]{\\E\\left[ #1 \\right]}\n\\newcommand{\\Var}[1]{\\mathrm{Var}\\left[ #1 \\right]}\n\\newcommand{\\Cov}[2]{\\mathrm{Cov}\\left[#1,\\ #2\\right]}\n\\newcommand{\\given}{\\ \\vert\\ }\n\\newcommand{\\X}{\\mathbf{X}}\n\\newcommand{\\x}{\\mathbf{x}}\n\\newcommand{\\y}{\\mathbf{y}}\n\\newcommand{\\P}{\\mathcal{P}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\norm}[1]{\\left\\lVert #1 \\right\\rVert}\n\\newcommand{\\snorm}[1]{\\lVert #1 \\rVert}\n\\newcommand{\\tr}[1]{\\mbox{tr}(#1)}\n\\newcommand{\\brt}{\\widehat{\\beta}^R_{s}}\n\\newcommand{\\brl}{\\widehat{\\beta}^R_{\\lambda}}\n\\newcommand{\\bls}{\\widehat{\\beta}_{ols}}\n\\newcommand{\\blt}{\\widehat{\\beta}^L_{s}}\n\\newcommand{\\bll}{\\widehat{\\beta}^L_{\\lambda}}\n\\]"
+ "text": "18 The bootstrap\nStat 406\nDaniel J. McDonald\nLast modified – 30 October 2023\n\\[\n\\DeclareMathOperator*{\\argmin}{argmin}\n\\DeclareMathOperator*{\\argmax}{argmax}\n\\DeclareMathOperator*{\\minimize}{minimize}\n\\DeclareMathOperator*{\\maximize}{maximize}\n\\DeclareMathOperator*{\\find}{find}\n\\DeclareMathOperator{\\st}{subject\\,\\,to}\n\\newcommand{\\E}{E}\n\\newcommand{\\Expect}[1]{\\E\\left[ #1 \\right]}\n\\newcommand{\\Var}[1]{\\mathrm{Var}\\left[ #1 \\right]}\n\\newcommand{\\Cov}[2]{\\mathrm{Cov}\\left[#1,\\ #2\\right]}\n\\newcommand{\\given}{\\ \\vert\\ }\n\\newcommand{\\X}{\\mathbf{X}}\n\\newcommand{\\x}{\\mathbf{x}}\n\\newcommand{\\y}{\\mathbf{y}}\n\\newcommand{\\P}{\\mathcal{P}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\norm}[1]{\\left\\lVert #1 \\right\\rVert}\n\\newcommand{\\snorm}[1]{\\lVert #1 \\rVert}\n\\newcommand{\\tr}[1]{\\mbox{tr}(#1)}\n\\newcommand{\\brt}{\\widehat{\\beta}^R_{s}}\n\\newcommand{\\brl}{\\widehat{\\beta}^R_{\\lambda}}\n\\newcommand{\\bls}{\\widehat{\\beta}_{ols}}\n\\newcommand{\\blt}{\\widehat{\\beta}^L_{s}}\n\\newcommand{\\bll}{\\widehat{\\beta}^L_{\\lambda}}\n\\]"
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"objectID": "schedule/slides/18-the-bootstrap.html#a-small-detour",
@@ -230,12 +230,19 @@
"section": "Bootstrap procedure",
"text": "Bootstrap procedure\n\nResample your training data w/ replacement.\nCalculate LDA on this sample.\nProduce a new prediction, call it \\(\\widehat{Pr}_b(y_0 =1 \\given x_0)\\).\nRepeat 1-3 \\(b = 1,\\ldots,B\\) times.\nCI: \\(\\left[2\\widehat{Pr}(y_0 =1 \\given x_0) - \\widehat{F}_{boot}(1-\\alpha/2),\\ 2\\widehat{Pr}(y_0 =1 \\given x_0) - \\widehat{F}_{boot}(\\alpha/2)\\right]\\)\n\n\n\\(\\hat{F}\\) is the “empirical” distribution of the bootstraps."
},
+ {
+ "objectID": "schedule/slides/18-the-bootstrap.html#empirical-distribution",
+ "href": "schedule/slides/18-the-bootstrap.html#empirical-distribution",
+ "title": "UBC Stat406 2023W",
+ "section": "Empirical distribution",
+ "text": "Empirical distribution\n\n\nCode\nr <- rexp(50, 1 / 5)\nggplot(tibble(r = r), aes(r)) + \n stat_ecdf(colour = orange) +\n geom_vline(xintercept = quantile(r, probs = c(.05, .95))) +\n geom_hline(yintercept = c(.05, .95), linetype = \"dashed\") +\n annotate(\n \"label\", x = c(5, 12), y = c(.25, .75), \n label = c(\"hat(F)[boot](.05)\", \"hat(F)[boot](.95)\"), \n parse = TRUE\n )"
+ },
{
"objectID": "schedule/slides/18-the-bootstrap.html#very-basic-example",
"href": "schedule/slides/18-the-bootstrap.html#very-basic-example",
"title": "UBC Stat406 2023W",
"section": "Very basic example",
- "text": "Very basic example\n\nLet \\(X_i\\sim Exponential(1/5)\\). The pdf is \\(f(x) = \\frac{1}{5}e^{-x/5}\\)\nI know if I estimate the mean with \\(\\bar{X}\\), then by the CLT (if \\(n\\) is big),\n\n\\[\\frac{\\sqrt{n}(\\bar{X}-E[X])}{s} \\approx N(0, 1).\\]\n\nThis gives me a 95% confidence interval like \\[\\bar{X} \\pm 2s/\\sqrt{n}\\]\nBut I don’t want to estimate the mean, I want to estimate the median."
+ "text": "Very basic example\n\nLet \\(X_i\\sim \\textrm{Exponential}(1/5)\\). The pdf is \\(f(x) = \\frac{1}{5}e^{-x/5}\\)\nI know if I estimate the mean with \\(\\bar{X}\\), then by the CLT (if \\(n\\) is big),\n\n\\[\\frac{\\sqrt{n}(\\bar{X}-E[X])}{s} \\approx N(0, 1).\\]\n\nThis gives me a 95% confidence interval like \\[\\bar{X} \\pm 2s/\\sqrt{n}\\]\nBut I don’t want to estimate the mean, I want to estimate the median."
},
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@@ -319,7 +326,7 @@
"href": "schedule/slides/18-the-bootstrap.html#types-of-intervals-1",
"title": "UBC Stat406 2023W",
"section": "Types of intervals",
- "text": "Types of intervals\nLet \\(\\hat{\\theta}\\) be our sample statistic, \\(\\hat{\\Theta}\\) be the resamples\n\\[\n[\\hat{\\theta} - t_{\\alpha/2}\\hat{s},\\ \\hat{\\theta} - t_{\\alpha/2}\\hat{s}]\n\\]\nwhere \\(\\hat{s} = \\sqrt{\\Var{\\hat{\\Theta}}}\\)\n\n\nCalled the “Normal Interval”\nOnly works if the distribution of \\(\\hat{\\Theta}\\) is approximately Normal.\nUnlikely to work well\nDon’t do this"
+ "text": "Types of intervals\nLet \\(\\hat{\\theta}\\) be our sample statistic, \\(\\hat{\\Theta}\\) be the resamples\n\\[\n[\\hat{\\theta} - t_{\\alpha/2}s,\\ \\hat{\\theta} - t_{\\alpha/2}s]\n\\]\nwhere \\(\\hat{s} = \\sqrt{\\Var{\\hat{\\Theta}}}\\)\n\n\nCalled the “Normal Interval”\nOnly works if the distribution of \\(\\hat{\\Theta}\\) is approximately Normal.\nUnlikely to work well\nDon’t do this"
},
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"objectID": "schedule/slides/18-the-bootstrap.html#types-of-intervals-2",
@@ -3546,7 +3553,7 @@
"href": "schedule/slides/17-nonlinear-classifiers.html#meta-lecture",
"title": "UBC Stat406 2023W",
"section": "17 Nonlinear classifiers",
- "text": "17 Nonlinear classifiers\nStat 406\nDaniel J. McDonald\nLast modified – 26 October 2023\n\\[\n\\DeclareMathOperator*{\\argmin}{argmin}\n\\DeclareMathOperator*{\\argmax}{argmax}\n\\DeclareMathOperator*{\\minimize}{minimize}\n\\DeclareMathOperator*{\\maximize}{maximize}\n\\DeclareMathOperator*{\\find}{find}\n\\DeclareMathOperator{\\st}{subject\\,\\,to}\n\\newcommand{\\E}{E}\n\\newcommand{\\Expect}[1]{\\E\\left[ #1 \\right]}\n\\newcommand{\\Var}[1]{\\mathrm{Var}\\left[ #1 \\right]}\n\\newcommand{\\Cov}[2]{\\mathrm{Cov}\\left[#1,\\ #2\\right]}\n\\newcommand{\\given}{\\ \\vert\\ }\n\\newcommand{\\X}{\\mathbf{X}}\n\\newcommand{\\x}{\\mathbf{x}}\n\\newcommand{\\y}{\\mathbf{y}}\n\\newcommand{\\P}{\\mathcal{P}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\norm}[1]{\\left\\lVert #1 \\right\\rVert}\n\\newcommand{\\snorm}[1]{\\lVert #1 \\rVert}\n\\newcommand{\\tr}[1]{\\mbox{tr}(#1)}\n\\newcommand{\\brt}{\\widehat{\\beta}^R_{s}}\n\\newcommand{\\brl}{\\widehat{\\beta}^R_{\\lambda}}\n\\newcommand{\\bls}{\\widehat{\\beta}_{ols}}\n\\newcommand{\\blt}{\\widehat{\\beta}^L_{s}}\n\\newcommand{\\bll}{\\widehat{\\beta}^L_{\\lambda}}\n\\]"
+ "text": "17 Nonlinear classifiers\nStat 406\nDaniel J. McDonald\nLast modified – 30 October 2023\n\\[\n\\DeclareMathOperator*{\\argmin}{argmin}\n\\DeclareMathOperator*{\\argmax}{argmax}\n\\DeclareMathOperator*{\\minimize}{minimize}\n\\DeclareMathOperator*{\\maximize}{maximize}\n\\DeclareMathOperator*{\\find}{find}\n\\DeclareMathOperator{\\st}{subject\\,\\,to}\n\\newcommand{\\E}{E}\n\\newcommand{\\Expect}[1]{\\E\\left[ #1 \\right]}\n\\newcommand{\\Var}[1]{\\mathrm{Var}\\left[ #1 \\right]}\n\\newcommand{\\Cov}[2]{\\mathrm{Cov}\\left[#1,\\ #2\\right]}\n\\newcommand{\\given}{\\ \\vert\\ }\n\\newcommand{\\X}{\\mathbf{X}}\n\\newcommand{\\x}{\\mathbf{x}}\n\\newcommand{\\y}{\\mathbf{y}}\n\\newcommand{\\P}{\\mathcal{P}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\norm}[1]{\\left\\lVert #1 \\right\\rVert}\n\\newcommand{\\snorm}[1]{\\lVert #1 \\rVert}\n\\newcommand{\\tr}[1]{\\mbox{tr}(#1)}\n\\newcommand{\\brt}{\\widehat{\\beta}^R_{s}}\n\\newcommand{\\brl}{\\widehat{\\beta}^R_{\\lambda}}\n\\newcommand{\\bls}{\\widehat{\\beta}_{ols}}\n\\newcommand{\\blt}{\\widehat{\\beta}^L_{s}}\n\\newcommand{\\bll}{\\widehat{\\beta}^L_{\\lambda}}\n\\]"
},
{
"objectID": "schedule/slides/17-nonlinear-classifiers.html#last-time",
@@ -3639,6 +3646,13 @@
"section": "knn.cv() (leave one out)",
"text": "knn.cv() (leave one out)\n\nkmax <- 20\nerr <- map_dbl(1:kmax, ~ mean(knn.cv(dat1[, -1], dat1$y, k = .x) != dat1$y))\n\n\nI would use the largest (odd) k that is close to the minimum.\nThis produces simpler, smoother, decision boundaries."
},
+ {
+ "objectID": "schedule/slides/17-nonlinear-classifiers.html#alternative-using-deviance-loss-i-think-this-is-right",
+ "href": "schedule/slides/17-nonlinear-classifiers.html#alternative-using-deviance-loss-i-think-this-is-right",
+ "title": "UBC Stat406 2023W",
+ "section": "Alternative (using deviance loss, I think this is right)",
+ "text": "Alternative (using deviance loss, I think this is right)\n\n\nCode\ndev <- function(y, prob, prob_min = 1e-5) {\n y <- as.numeric(as.factor(y)) - 1 # 0/1 valued\n m <- mean(y)\n prob_max <- 1 - prob_min\n prob <- pmin(pmax(prob, prob_min), prob_max)\n lp <- (1 - y) * log(1 - prob) + y * log(prob)\n ly <- (1 - y) * log(1 - m) + y * log(m)\n 2 * (ly - lp)\n}\nknn.cv_probs <- function(train, cl, k = 1) {\n o <- knn.cv(train, cl, k = k, prob = TRUE)\n p <- attr(o, \"prob\")\n o <- as.numeric(as.factor(o)) - 1\n p[o == 0] <- 1 - p[o == 0]\n p\n}\ndev_err <- map_dbl(1:kmax, ~ mean(dev(dat1$y, knn.cv_probs(dat1[, -1], dat1$y, k = .x))))"
+ },
{
"objectID": "schedule/slides/17-nonlinear-classifiers.html#final-version",
"href": "schedule/slides/17-nonlinear-classifiers.html#final-version",
diff --git a/sitemap.xml b/sitemap.xml
index 45346a0..bbe3039 100644
--- a/sitemap.xml
+++ b/sitemap.xml
@@ -2,166 +2,166 @@
https://github.com/UBC-STAT/stat-406/schedule/handouts/lab00-git.html
- 2023-10-26T13:27:09.096Z
+ 2023-10-30T17:41:01.448Z
https://github.com/UBC-STAT/stat-406/schedule/slides/22-nnets-estimation.html
- 2023-10-26T13:27:06.196Z
+ 2023-10-30T17:40:59.100Z
https://github.com/UBC-STAT/stat-406/schedule/slides/20-boosting.html
- 2023-10-26T13:27:04.808Z
+ 2023-10-30T17:40:57.956Z
https://github.com/UBC-STAT/stat-406/schedule/slides/18-the-bootstrap.html
- 2023-10-26T13:27:02.872Z
+ 2023-10-30T17:40:56.436Z
https://github.com/UBC-STAT/stat-406/schedule/slides/16-logistic-regression.html
- 2023-10-26T13:27:00.820Z
+ 2023-10-30T17:40:54.748Z
https://github.com/UBC-STAT/stat-406/schedule/slides/14-classification-intro.html
- 2023-10-26T13:26:59.144Z
+ 2023-10-30T17:40:53.376Z
https://github.com/UBC-STAT/stat-406/schedule/slides/12-why-smooth.html
- 2023-10-26T13:26:57.276Z
+ 2023-10-30T17:40:51.824Z
https://github.com/UBC-STAT/stat-406/schedule/slides/10-basis-expansions.html
- 2023-10-26T13:26:55.764Z
+ 2023-10-30T17:40:50.640Z
https://github.com/UBC-STAT/stat-406/schedule/slides/08-ridge-regression.html
- 2023-10-26T13:26:53.932Z
+ 2023-10-30T17:40:49.084Z
https://github.com/UBC-STAT/stat-406/schedule/slides/06-information-criteria.html
- 2023-10-26T13:26:51.908Z
+ 2023-10-30T17:40:47.432Z
https://github.com/UBC-STAT/stat-406/schedule/slides/04-bias-variance.html
- 2023-10-26T13:26:50.024Z
+ 2023-10-30T17:40:45.832Z
https://github.com/UBC-STAT/stat-406/schedule/slides/02-lm-example.html
- 2023-10-26T13:26:48.152Z
+ 2023-10-30T17:40:44.224Z
https://github.com/UBC-STAT/stat-406/schedule/slides/00-version-control.html
- 2023-10-26T13:26:46.524Z
+ 2023-10-30T17:40:42.920Z
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- 2023-10-26T13:26:43.216Z
+ 2023-10-30T17:40:40.188Z
https://github.com/UBC-STAT/stat-406/schedule/slides/00-gradient-descent.html
- 2023-10-26T13:26:41.532Z
+ 2023-10-30T17:40:38.876Z
https://github.com/UBC-STAT/stat-406/schedule/slides/00-classification-losses.html
- 2023-10-26T13:26:39.768Z
+ 2023-10-30T17:40:36.448Z
https://github.com/UBC-STAT/stat-406/course-setup.html
- 2023-10-26T13:26:37.540Z
+ 2023-10-30T17:40:33.627Z
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- 2023-10-26T13:26:35.148Z
+ 2023-10-30T17:40:31.655Z
https://github.com/UBC-STAT/stat-406/computing/mac_x86.html
- 2023-10-26T13:26:33.136Z
+ 2023-10-30T17:40:29.975Z
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- 2023-10-26T13:26:31.268Z
+ 2023-10-30T17:40:28.383Z
https://github.com/UBC-STAT/stat-406/index.html
- 2023-10-26T13:26:29.064Z
+ 2023-10-30T17:40:26.495Z
https://github.com/UBC-STAT/stat-406/faq.html
- 2023-10-26T13:26:30.768Z
+ 2023-10-30T17:40:27.951Z
https://github.com/UBC-STAT/stat-406/computing/mac_arm.html
- 2023-10-26T13:26:32.252Z
+ 2023-10-30T17:40:29.183Z
https://github.com/UBC-STAT/stat-406/computing/ubuntu.html
- 2023-10-26T13:26:34.068Z
+ 2023-10-30T17:40:30.731Z
https://github.com/UBC-STAT/stat-406/syllabus.html
- 2023-10-26T13:26:36.716Z
+ 2023-10-30T17:40:32.963Z
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- 2023-10-26T13:26:38.776Z
+ 2023-10-30T17:40:34.655Z
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- 2023-10-26T13:26:40.520Z
+ 2023-10-30T17:40:38.072Z
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- 2023-10-26T13:26:42.448Z
+ 2023-10-30T17:40:39.568Z
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- 2023-10-26T13:26:45.136Z
+ 2023-10-30T17:40:41.760Z
https://github.com/UBC-STAT/stat-406/schedule/slides/01-lm-review.html
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https://github.com/UBC-STAT/stat-406/schedule/slides/03-regression-function.html
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https://github.com/UBC-STAT/stat-406/schedule/slides/05-estimating-test-mse.html
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https://github.com/UBC-STAT/stat-406/schedule/slides/07-greedy-selection.html
- 2023-10-26T13:26:52.864Z
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https://github.com/UBC-STAT/stat-406/schedule/slides/09-l1-penalties.html
- 2023-10-26T13:26:54.924Z
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https://github.com/UBC-STAT/stat-406/schedule/slides/11-kernel-smoothers.html
- 2023-10-26T13:26:56.700Z
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https://github.com/UBC-STAT/stat-406/schedule/slides/13-gams-trees.html
- 2023-10-26T13:26:58.084Z
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https://github.com/UBC-STAT/stat-406/schedule/slides/15-LDA-and-QDA.html
- 2023-10-26T13:27:00.000Z
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https://github.com/UBC-STAT/stat-406/schedule/slides/17-nonlinear-classifiers.html
- 2023-10-26T13:27:01.840Z
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https://github.com/UBC-STAT/stat-406/schedule/slides/19-bagging-and-rf.html
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https://github.com/UBC-STAT/stat-406/schedule/slides/21-nnets-intro.html
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https://github.com/UBC-STAT/stat-406/schedule/slides/23-nnets-other.html
- 2023-10-26T13:27:07.276Z
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