diff --git a/.nojekyll b/.nojekyll index 33bbd3b..fec702f 100644 --- a/.nojekyll +++ b/.nojekyll @@ -1 +1 @@ -38a419c5 \ No newline at end of file +50e3d627 \ No newline at end of file diff --git a/schedule/index.html b/schedule/index.html index 4d3cc72..922d2fa 100644 --- a/schedule/index.html +++ b/schedule/index.html @@ -512,20 +512,14 @@

5 Unsupervised learn

F Final exam

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Date and time TBD.

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-
-
- -
-
-Important -
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-
-

Do not make any plans to leave Vancouver before the final exam date is announced.

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+

Monday, December 18 at 12-2pm, location TBA

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Why does this work?

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Heuristic interpretation:

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Heuristic interpretation:

Decay on a schedule

-

\(\gamma_{k+1} = \frac{\gamma_k}{1+ck}\) or \(\gamma_{k} = \gamma_0 b^k\)

+

\(\gamma_{n+1} = \frac{\gamma_n}{1+cn}\) or \(\gamma_{n} = \gamma_0 b^n\)

Exact line search

diff --git a/schedule/slides/16-logistic-regression.html b/schedule/slides/16-logistic-regression.html index b79b38e..178de4a 100644 --- a/schedule/slides/16-logistic-regression.html +++ b/schedule/slides/16-logistic-regression.html @@ -397,7 +397,7 @@

16 Logistic regression

Stat 406

Daniel J. McDonald

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Last modified – 09 October 2023

+

Last modified – 25 October 2023

\[ \DeclareMathOperator*{\argmin}{argmin} \DeclareMathOperator*{\argmax}{argmax} @@ -446,7 +446,7 @@

Direct model

\[ \begin{aligned} Pr(Y = 1 \given X=x) & = \frac{\exp\{\beta_0 + \beta^{\top}x\}}{1 + \exp\{\beta_0 + \beta^{\top}x\}} \\ -\P(Y = 0 | X=x) & = \frac{1}{1 + \exp\{\beta_0 + \beta^{\top}x\}}=1-\frac{\exp\{\beta_0 + \beta^{\top}x\}}{1 + \exp\{\beta_0 + \beta^{\top}x\}} +Pr(Y = 0 | X=x) & = \frac{1}{1 + \exp\{\beta_0 + \beta^{\top}x\}}=1-\frac{\exp\{\beta_0 + \beta^{\top}x\}}{1 + \exp\{\beta_0 + \beta^{\top}x\}} \end{aligned} \]

This is logistic regression.

diff --git a/schedule/slides/17-nonlinear-classifiers.html b/schedule/slides/17-nonlinear-classifiers.html index 4b3ba71..b056529 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 – 09 October 2023

+

Last modified – 26 October 2023

\[ \DeclareMathOperator*{\argmin}{argmin} \DeclareMathOperator*{\argmax}{argmax} @@ -429,8 +429,8 @@

17 Nonlinear classifiers

Last time

We reviewed logistic regression

\[\begin{aligned} -\P(Y = 1 \given X=x) & = \frac{\exp\{\beta_0 + \beta^{\top}x\}}{1 + \exp\{\beta_0 + \beta^{\top}x\}} \\ -\P(Y = 0 \given X=x) & = \frac{1}{1 + \exp\{\beta_0 + \beta^{\top}x\}}=1-\frac{\exp\{\beta_0 + \beta^{\top}x\}}{1 + \exp\{\beta_0 + \beta^{\top}x\}}\end{aligned}\]

+Pr(Y = 1 \given X=x) & = \frac{\exp\{\beta_0 + \beta^{\top}x\}}{1 + \exp\{\beta_0 + \beta^{\top}x\}} \\ +Pr(Y = 0 \given X=x) & = \frac{1}{1 + \exp\{\beta_0 + \beta^{\top}x\}}=1-\frac{\exp\{\beta_0 + \beta^{\top}x\}}{1 + \exp\{\beta_0 + \beta^{\top}x\}}\end{aligned}\]

Make it nonlinear

diff --git a/search.json b/search.json index 53001d1..42d04c1 100644 --- a/search.json +++ b/search.json @@ -340,7 +340,7 @@ "href": "schedule/slides/16-logistic-regression.html#meta-lecture", "title": "UBC Stat406 2023W", "section": "16 Logistic regression", - "text": "16 Logistic regression\nStat 406\nDaniel J. McDonald\nLast modified – 09 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": "16 Logistic regression\nStat 406\nDaniel J. McDonald\nLast modified – 25 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/16-logistic-regression.html#last-time", @@ -354,7 +354,7 @@ "href": "schedule/slides/16-logistic-regression.html#direct-model", "title": "UBC Stat406 2023W", "section": "Direct model", - "text": "Direct model\nInstead, let’s directly model the posterior\n\\[\n\\begin{aligned}\nPr(Y = 1 \\given X=x) & = \\frac{\\exp\\{\\beta_0 + \\beta^{\\top}x\\}}{1 + \\exp\\{\\beta_0 + \\beta^{\\top}x\\}} \\\\\n\\P(Y = 0 | X=x) & = \\frac{1}{1 + \\exp\\{\\beta_0 + \\beta^{\\top}x\\}}=1-\\frac{\\exp\\{\\beta_0 + \\beta^{\\top}x\\}}{1 + \\exp\\{\\beta_0 + \\beta^{\\top}x\\}}\n\\end{aligned}\n\\]\nThis is logistic regression." + "text": "Direct model\nInstead, let’s directly model the posterior\n\\[\n\\begin{aligned}\nPr(Y = 1 \\given X=x) & = \\frac{\\exp\\{\\beta_0 + \\beta^{\\top}x\\}}{1 + \\exp\\{\\beta_0 + \\beta^{\\top}x\\}} \\\\\nPr(Y = 0 | X=x) & = \\frac{1}{1 + \\exp\\{\\beta_0 + \\beta^{\\top}x\\}}=1-\\frac{\\exp\\{\\beta_0 + \\beta^{\\top}x\\}}{1 + \\exp\\{\\beta_0 + \\beta^{\\top}x\\}}\n\\end{aligned}\n\\]\nThis is logistic regression." }, { "objectID": "schedule/slides/16-logistic-regression.html#why-this", @@ -1432,7 +1432,7 @@ "href": "schedule/slides/00-gradient-descent.html#meta-lecture", "title": "UBC Stat406 2023W", "section": "00 Gradient descent", - "text": "00 Gradient descent\nStat 406\nDaniel J. McDonald\nLast modified – 16 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": "00 Gradient descent\nStat 406\nDaniel J. McDonald\nLast modified – 25 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/00-gradient-descent.html#simple-optimization-techniques", @@ -1481,7 +1481,7 @@ "href": "schedule/slides/00-gradient-descent.html#what-gamma-more-details-than-we-have-time-for", "title": "UBC Stat406 2023W", "section": "What \\(\\gamma\\)? (more details than we have time for)", - "text": "What \\(\\gamma\\)? (more details than we have time for)\nWhat to use for \\(\\gamma_k\\)?\nFixed\n\nOnly works if \\(\\gamma\\) is exactly right\nUsually does not work\n\nDecay on a schedule\n\\(\\gamma_{k+1} = \\frac{\\gamma_k}{1+ck}\\) or \\(\\gamma_{k} = \\gamma_0 b^k\\)\nExact line search\n\nTells you exactly how far to go.\nAt each \\(k\\), solve \\(\\gamma_k = \\arg\\min_{s \\geq 0} f( x^{(k)} - s f(x^{(k-1)}))\\)\nUsually can’t solve this." + "text": "What \\(\\gamma\\)? (more details than we have time for)\nWhat to use for \\(\\gamma_k\\)?\nFixed\n\nOnly works if \\(\\gamma\\) is exactly right\nUsually does not work\n\nDecay on a schedule\n\\(\\gamma_{n+1} = \\frac{\\gamma_n}{1+cn}\\) or \\(\\gamma_{n} = \\gamma_0 b^n\\)\nExact line search\n\nTells you exactly how far to go.\nAt each iteration \\(n\\), solve \\(\\gamma_n = \\arg\\min_{s \\geq 0} f( x^{(n)} - s f(x^{(n-1)}))\\)\nUsually can’t solve this." }, { "objectID": "schedule/slides/00-gradient-descent.html#section", @@ -2160,7 +2160,7 @@ "href": "schedule/index.html#f-final-exam", "title": " Schedule", "section": "F Final exam", - "text": "F Final exam\nDate and time TBD.\n\n\n\n\n\n\nImportant\n\n\n\nDo not make any plans to leave Vancouver before the final exam date is announced.\n\n\n\nIn person attendance is required (per Faculty of Science guidelines)\nYou must bring your computer as the exam will be given through Canvas\nPlease arrange to borrow one from the library if you do not have your own. Let me know ASAP if this may pose a problem.\nYou may bring 2 sheets of front/back 8.5x11 paper with any notes you want to use. No other materials will be allowed.\nThere will be no required coding, but I may show code or output and ask questions about it.\nIt will be entirely multiple choice / True-False / matching, etc. Delivered on Canvas." + "text": "F Final exam\nMonday, December 18 at 12-2pm, location TBA\n\n\nIn person attendance is required (per Faculty of Science guidelines)\nYou must bring your computer as the exam will be given through Canvas\nPlease arrange to borrow one from the library if you do not have your own. Let me know ASAP if this may pose a problem.\nYou may bring 2 sheets of front/back 8.5x11 paper with any notes you want to use. 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McDonald\nLast modified – 09 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 – 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\\]" }, { "objectID": "schedule/slides/17-nonlinear-classifiers.html#last-time", "href": "schedule/slides/17-nonlinear-classifiers.html#last-time", "title": "UBC Stat406 2023W", "section": "Last time", - "text": "Last time\nWe reviewed logistic regression\n\\[\\begin{aligned}\n\\P(Y = 1 \\given X=x) & = \\frac{\\exp\\{\\beta_0 + \\beta^{\\top}x\\}}{1 + \\exp\\{\\beta_0 + \\beta^{\\top}x\\}} \\\\\n\\P(Y = 0 \\given X=x) & = \\frac{1}{1 + \\exp\\{\\beta_0 + \\beta^{\\top}x\\}}=1-\\frac{\\exp\\{\\beta_0 + \\beta^{\\top}x\\}}{1 + \\exp\\{\\beta_0 + \\beta^{\\top}x\\}}\\end{aligned}\\]" + "text": "Last time\nWe reviewed logistic regression\n\\[\\begin{aligned}\nPr(Y = 1 \\given X=x) & = \\frac{\\exp\\{\\beta_0 + \\beta^{\\top}x\\}}{1 + \\exp\\{\\beta_0 + \\beta^{\\top}x\\}} \\\\\nPr(Y = 0 \\given X=x) & = \\frac{1}{1 + \\exp\\{\\beta_0 + \\beta^{\\top}x\\}}=1-\\frac{\\exp\\{\\beta_0 + \\beta^{\\top}x\\}}{1 + \\exp\\{\\beta_0 + \\beta^{\\top}x\\}}\\end{aligned}\\]" }, { "objectID": "schedule/slides/17-nonlinear-classifiers.html#make-it-nonlinear", diff --git a/sitemap.xml b/sitemap.xml index 87f45b1..45346a0 100644 --- a/sitemap.xml +++ b/sitemap.xml @@ -2,166 +2,166 @@ https://github.com/UBC-STAT/stat-406/schedule/handouts/lab00-git.html - 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