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- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
diff --git a/doc/pub/week38/html/._week38-bs026.html b/doc/pub/week38/html/._week38-bs026.html
index c64a771a0..6cacb4fbf 100644
--- a/doc/pub/week38/html/._week38-bs026.html
+++ b/doc/pub/week38/html/._week38-bs026.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
diff --git a/doc/pub/week38/html/._week38-bs027.html b/doc/pub/week38/html/._week38-bs027.html
index 6470a452e..c75ec01a0 100644
--- a/doc/pub/week38/html/._week38-bs027.html
+++ b/doc/pub/week38/html/._week38-bs027.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
diff --git a/doc/pub/week38/html/._week38-bs028.html b/doc/pub/week38/html/._week38-bs028.html
index e70a6f3de..2917864d8 100644
--- a/doc/pub/week38/html/._week38-bs028.html
+++ b/doc/pub/week38/html/._week38-bs028.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
@@ -227,7 +224,16 @@ f(y_i\vert x_i)=\beta_0+\beta_1 x_i.
$$
-This expression implies however that \( f(y_i\vert x_i) \) could take any value from minus infinity to plus infinity. If we however let \( f(y\vert y) \) be represented by the mean value, the above example shows us that we can constain to be between zero and one, that is we have \( 0 \le f(y_i\vert x_i) \le 1 \). Looking at our last curve we see also that it has an S-shaped form. This leads us to a very popular model for the function \( f \), namely the so-called Sigmoid function or logistic model. We will consider this function as representing the probability for finding a value of \( y_i \) with a given \( x_i \).
+This expression implies however that \( f(y_i\vert x_i) \) could take any
+value from minus infinity to plus infinity. If we however let
+\( f(y\vert y) \) be represented by the mean value, the above example
+shows us that we can constrain the function to take values between
+zero and one, that is we have \( 0 \le f(y_i\vert x_i) \le 1 \). Looking
+at our last curve we see also that it has an S-shaped form. This leads
+us to a very popular model for the function \( f \), namely the so-called
+Sigmoid function or logistic model. We will consider this function as
+representing the probability for finding a value of \( y_i \) with a given
+\( x_i \).
diff --git a/doc/pub/week38/html/._week38-bs029.html b/doc/pub/week38/html/._week38-bs029.html
index 0f7ff1fe9..20c2fa424 100644
--- a/doc/pub/week38/html/._week38-bs029.html
+++ b/doc/pub/week38/html/._week38-bs029.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
@@ -205,10 +202,11 @@ MathJax.Hub.Config({
The logistic function
-The perceptron is an example of a ``hard classification" model. We
+Another widely studied model, is the so-called
+perceptron model, which is an example of a ``hard classification" model. We
will encounter this model when we discuss neural networks as
well. Each datapoint is deterministically assigned to a category (i.e
-\( y_i=0 \) or \( y_i=1 \)). In many cases, it is favorable to have a "soft"
+\( y_i=0 \) or \( y_i=1 \)). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a "soft"
classifier that outputs the probability of a given category rather
than a single value. For example, given \( x_i \), the classifier
outputs the probability of being in a category \( k \). Logistic regression
diff --git a/doc/pub/week38/html/._week38-bs030.html b/doc/pub/week38/html/._week38-bs030.html
index cc1cebd3b..f458a7741 100644
--- a/doc/pub/week38/html/._week38-bs030.html
+++ b/doc/pub/week38/html/._week38-bs030.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
diff --git a/doc/pub/week38/html/._week38-bs031.html b/doc/pub/week38/html/._week38-bs031.html
index e2aba6c74..b9699d485 100644
--- a/doc/pub/week38/html/._week38-bs031.html
+++ b/doc/pub/week38/html/._week38-bs031.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
diff --git a/doc/pub/week38/html/._week38-bs032.html b/doc/pub/week38/html/._week38-bs032.html
index 6f09cc533..02ef24a08 100644
--- a/doc/pub/week38/html/._week38-bs032.html
+++ b/doc/pub/week38/html/._week38-bs032.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
diff --git a/doc/pub/week38/html/._week38-bs033.html b/doc/pub/week38/html/._week38-bs033.html
index 57be81cd2..2589430ac 100644
--- a/doc/pub/week38/html/._week38-bs033.html
+++ b/doc/pub/week38/html/._week38-bs033.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
diff --git a/doc/pub/week38/html/._week38-bs034.html b/doc/pub/week38/html/._week38-bs034.html
index f1b9c1478..e50cc6557 100644
--- a/doc/pub/week38/html/._week38-bs034.html
+++ b/doc/pub/week38/html/._week38-bs034.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
diff --git a/doc/pub/week38/html/._week38-bs035.html b/doc/pub/week38/html/._week38-bs035.html
index fee8ab1a2..b4337a8bd 100644
--- a/doc/pub/week38/html/._week38-bs035.html
+++ b/doc/pub/week38/html/._week38-bs035.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
diff --git a/doc/pub/week38/html/._week38-bs036.html b/doc/pub/week38/html/._week38-bs036.html
index 81892a42b..ee6ff28b4 100644
--- a/doc/pub/week38/html/._week38-bs036.html
+++ b/doc/pub/week38/html/._week38-bs036.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
diff --git a/doc/pub/week38/html/._week38-bs037.html b/doc/pub/week38/html/._week38-bs037.html
index 9a110eefc..c13820d37 100644
--- a/doc/pub/week38/html/._week38-bs037.html
+++ b/doc/pub/week38/html/._week38-bs037.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
@@ -207,13 +204,13 @@ MathJax.Hub.Config({
Till now we have mainly focused on two classes, the so-called binary
system. Suppose we wish to extend to \( K \) classes. Let us for the sake
-of simplicity assume we have only two predictors. We have then
-following model
+of simplicity assume we have only two predictors. We have then following model
$$
\log{\frac{p(C=1\vert x)}{p(K\vert x)}} = \beta_{10}+\beta_{11}x_1,
$$
+and
$$
\log{\frac{p(C=2\vert x)}{p(K\vert x)}} = \beta_{20}+\beta_{21}x_1,
$$
diff --git a/doc/pub/week38/html/._week38-bs038.html b/doc/pub/week38/html/._week38-bs038.html
index d6a0f53a4..9d406fca8 100644
--- a/doc/pub/week38/html/._week38-bs038.html
+++ b/doc/pub/week38/html/._week38-bs038.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
@@ -240,7 +237,7 @@ discussed in the material on Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
@@ -202,7 +199,7 @@ MathJax.Hub.Config({
-Cancer Data again now with Decision Trees and other Methods
+Wisconsin Cancer Data
diff --git a/doc/pub/week38/html/._week38-bs040.html b/doc/pub/week38/html/._week38-bs040.html
index de5e38927..08c3e5ee0 100644
--- a/doc/pub/week38/html/._week38-bs040.html
+++ b/doc/pub/week38/html/._week38-bs040.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
diff --git a/doc/pub/week38/html/week38-bs.html b/doc/pub/week38/html/week38-bs.html
index f2793887f..a32b32744 100644
--- a/doc/pub/week38/html/week38-bs.html
+++ b/doc/pub/week38/html/week38-bs.html
@@ -102,10 +102,7 @@ Automatically generated HTML file from DocOnce source
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -185,7 +182,7 @@ MathJax.Hub.Config({
Extending to more predictors
Including more classes
More classes
- Cancer Data again now with Decision Trees and other Methods
+ Wisconsin Cancer Data
Other measures in classification studies: Cancer Data again
diff --git a/doc/pub/week38/html/week38-reveal.html b/doc/pub/week38/html/week38-reveal.html
index 14f91e77d..893051f4c 100644
--- a/doc/pub/week38/html/week38-reveal.html
+++ b/doc/pub/week38/html/week38-reveal.html
@@ -1435,7 +1435,16 @@ $$
-This expression implies however that \( f(y_i\vert x_i) \) could take any value from minus infinity to plus infinity. If we however let \( f(y\vert y) \) be represented by the mean value, the above example shows us that we can constain to be between zero and one, that is we have \( 0 \le f(y_i\vert x_i) \le 1 \). Looking at our last curve we see also that it has an S-shaped form. This leads us to a very popular model for the function \( f \), namely the so-called Sigmoid function or logistic model. We will consider this function as representing the probability for finding a value of \( y_i \) with a given \( x_i \).
+This expression implies however that \( f(y_i\vert x_i) \) could take any
+value from minus infinity to plus infinity. If we however let
+\( f(y\vert y) \) be represented by the mean value, the above example
+shows us that we can constrain the function to take values between
+zero and one, that is we have \( 0 \le f(y_i\vert x_i) \le 1 \). Looking
+at our last curve we see also that it has an S-shaped form. This leads
+us to a very popular model for the function \( f \), namely the so-called
+Sigmoid function or logistic model. We will consider this function as
+representing the probability for finding a value of \( y_i \) with a given
+\( x_i \).
@@ -1443,10 +1452,11 @@ This expression implies however that \( f(y_i\vert x_i) \) could take any value
The logistic function
-The perceptron is an example of a ``hard classification" model. We
+Another widely studied model, is the so-called
+perceptron model, which is an example of a ``hard classification" model. We
will encounter this model when we discuss neural networks as
well. Each datapoint is deterministically assigned to a category (i.e
-\( y_i=0 \) or \( y_i=1 \)). In many cases, it is favorable to have a "soft"
+\( y_i=0 \) or \( y_i=1 \)). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a "soft"
classifier that outputs the probability of a given category rather
than a single value. For example, given \( x_i \), the classifier
outputs the probability of being in a category \( k \). Logistic regression
@@ -1687,8 +1697,7 @@ $$
Till now we have mainly focused on two classes, the so-called binary
system. Suppose we wish to extend to \( K \) classes. Let us for the sake
-of simplicity assume we have only two predictors. We have then
-following model
+of simplicity assume we have only two predictors. We have then following model
$$
@@ -1696,6 +1705,7 @@ $$
$$
+and
$$
\log{\frac{p(C=2\vert x)}{p(K\vert x)}} = \beta_{20}+\beta_{21}x_1,
@@ -1758,12 +1768,12 @@ discussed in the material on Cancer Data again now with Decision Trees and other Methods
+Wisconsin Cancer Data
diff --git a/doc/pub/week38/html/week38-solarized.html b/doc/pub/week38/html/week38-solarized.html
index 75f0d99f2..a4811059f 100644
--- a/doc/pub/week38/html/week38-solarized.html
+++ b/doc/pub/week38/html/week38-solarized.html
@@ -96,10 +96,7 @@ div { text-align: justify; text-justify: inter-word; }
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -1365,7 +1362,16 @@ f(y_i\vert x_i)=\beta_0+\beta_1 x_i.
$$
-This expression implies however that \( f(y_i\vert x_i) \) could take any value from minus infinity to plus infinity. If we however let \( f(y\vert y) \) be represented by the mean value, the above example shows us that we can constain to be between zero and one, that is we have \( 0 \le f(y_i\vert x_i) \le 1 \). Looking at our last curve we see also that it has an S-shaped form. This leads us to a very popular model for the function \( f \), namely the so-called Sigmoid function or logistic model. We will consider this function as representing the probability for finding a value of \( y_i \) with a given \( x_i \).
+This expression implies however that \( f(y_i\vert x_i) \) could take any
+value from minus infinity to plus infinity. If we however let
+\( f(y\vert y) \) be represented by the mean value, the above example
+shows us that we can constrain the function to take values between
+zero and one, that is we have \( 0 \le f(y_i\vert x_i) \le 1 \). Looking
+at our last curve we see also that it has an S-shaped form. This leads
+us to a very popular model for the function \( f \), namely the so-called
+Sigmoid function or logistic model. We will consider this function as
+representing the probability for finding a value of \( y_i \) with a given
+\( x_i \).
@@ -1373,10 +1379,11 @@ This expression implies however that \( f(y_i\vert x_i) \) could take any value
The logistic function
-The perceptron is an example of a ``hard classification" model. We
+Another widely studied model, is the so-called
+perceptron model, which is an example of a ``hard classification" model. We
will encounter this model when we discuss neural networks as
well. Each datapoint is deterministically assigned to a category (i.e
-\( y_i=0 \) or \( y_i=1 \)). In many cases, it is favorable to have a "soft"
+\( y_i=0 \) or \( y_i=1 \)). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a "soft"
classifier that outputs the probability of a given category rather
than a single value. For example, given \( x_i \), the classifier
outputs the probability of being in a category \( k \). Logistic regression
@@ -1590,13 +1597,13 @@ $$
Till now we have mainly focused on two classes, the so-called binary
system. Suppose we wish to extend to \( K \) classes. Let us for the sake
-of simplicity assume we have only two predictors. We have then
-following model
+of simplicity assume we have only two predictors. We have then following model
$$
\log{\frac{p(C=1\vert x)}{p(K\vert x)}} = \beta_{10}+\beta_{11}x_1,
$$
+and
$$
\log{\frac{p(C=2\vert x)}{p(K\vert x)}} = \beta_{20}+\beta_{21}x_1,
$$
@@ -1651,12 +1658,12 @@ discussed in the material on Cancer Data again now with Decision Trees and other Methods
+Wisconsin Cancer Data
diff --git a/doc/pub/week38/html/week38.html b/doc/pub/week38/html/week38.html
index b5f0b3409..bbd78590e 100644
--- a/doc/pub/week38/html/week38.html
+++ b/doc/pub/week38/html/week38.html
@@ -101,10 +101,7 @@ div { text-align: justify; text-justify: inter-word; }
('Extending to more predictors', 2, None, '___sec35'),
('Including more classes', 2, None, '___sec36'),
('More classes', 2, None, '___sec37'),
- ('Cancer Data again now with Decision Trees and other Methods',
- 2,
- None,
- '___sec38'),
+ ('Wisconsin Cancer Data', 2, None, '___sec38'),
('Other measures in classification studies: Cancer Data again',
2,
None,
@@ -1370,7 +1367,16 @@ f(y_i\vert x_i)=\beta_0+\beta_1 x_i.
$$
-This expression implies however that \( f(y_i\vert x_i) \) could take any value from minus infinity to plus infinity. If we however let \( f(y\vert y) \) be represented by the mean value, the above example shows us that we can constain to be between zero and one, that is we have \( 0 \le f(y_i\vert x_i) \le 1 \). Looking at our last curve we see also that it has an S-shaped form. This leads us to a very popular model for the function \( f \), namely the so-called Sigmoid function or logistic model. We will consider this function as representing the probability for finding a value of \( y_i \) with a given \( x_i \).
+This expression implies however that \( f(y_i\vert x_i) \) could take any
+value from minus infinity to plus infinity. If we however let
+\( f(y\vert y) \) be represented by the mean value, the above example
+shows us that we can constrain the function to take values between
+zero and one, that is we have \( 0 \le f(y_i\vert x_i) \le 1 \). Looking
+at our last curve we see also that it has an S-shaped form. This leads
+us to a very popular model for the function \( f \), namely the so-called
+Sigmoid function or logistic model. We will consider this function as
+representing the probability for finding a value of \( y_i \) with a given
+\( x_i \).
@@ -1378,10 +1384,11 @@ This expression implies however that \( f(y_i\vert x_i) \) could take any value
The logistic function
-The perceptron is an example of a ``hard classification" model. We
+Another widely studied model, is the so-called
+perceptron model, which is an example of a ``hard classification" model. We
will encounter this model when we discuss neural networks as
well. Each datapoint is deterministically assigned to a category (i.e
-\( y_i=0 \) or \( y_i=1 \)). In many cases, it is favorable to have a "soft"
+\( y_i=0 \) or \( y_i=1 \)). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a "soft"
classifier that outputs the probability of a given category rather
than a single value. For example, given \( x_i \), the classifier
outputs the probability of being in a category \( k \). Logistic regression
@@ -1595,13 +1602,13 @@ $$
Till now we have mainly focused on two classes, the so-called binary
system. Suppose we wish to extend to \( K \) classes. Let us for the sake
-of simplicity assume we have only two predictors. We have then
-following model
+of simplicity assume we have only two predictors. We have then following model
$$
\log{\frac{p(C=1\vert x)}{p(K\vert x)}} = \beta_{10}+\beta_{11}x_1,
$$
+and
$$
\log{\frac{p(C=2\vert x)}{p(K\vert x)}} = \beta_{20}+\beta_{21}x_1,
$$
@@ -1656,12 +1663,12 @@ discussed in the material on Cancer Data again now with Decision Trees and other Methods
+Wisconsin Cancer Data
diff --git a/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz b/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz
index cce4836c8..b951a6bcf 100644
Binary files a/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz and b/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz differ
diff --git a/doc/pub/week38/ipynb/week38.ipynb b/doc/pub/week38/ipynb/week38.ipynb
index 41f29f5a3..525559fe8 100644
--- a/doc/pub/week38/ipynb/week38.ipynb
+++ b/doc/pub/week38/ipynb/week38.ipynb
@@ -1691,14 +1691,24 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "This expression implies however that $f(y_i\\vert x_i)$ could take any value from minus infinity to plus infinity. If we however let $f(y\\vert y)$ be represented by the mean value, the above example shows us that we can constain to be between zero and one, that is we have $0 \\le f(y_i\\vert x_i) \\le 1$. Looking at our last curve we see also that it has an S-shaped form. This leads us to a very popular model for the function $f$, namely the so-called Sigmoid function or logistic model. We will consider this function as representing the probability for finding a value of $y_i$ with a given $x_i$. \n",
+ "This expression implies however that $f(y_i\\vert x_i)$ could take any\n",
+ "value from minus infinity to plus infinity. If we however let\n",
+ "$f(y\\vert y)$ be represented by the mean value, the above example\n",
+ "shows us that we can constrain the function to take values between\n",
+ "zero and one, that is we have $0 \\le f(y_i\\vert x_i) \\le 1$. Looking\n",
+ "at our last curve we see also that it has an S-shaped form. This leads\n",
+ "us to a very popular model for the function $f$, namely the so-called\n",
+ "Sigmoid function or logistic model. We will consider this function as\n",
+ "representing the probability for finding a value of $y_i$ with a given\n",
+ "$x_i$.\n",
"\n",
"## The logistic function\n",
"\n",
- "The perceptron is an example of a ``hard classification\" model. We\n",
+ "Another widely studied model, is the so-called \n",
+ "perceptron model, which is an example of a ``hard classification\" model. We\n",
"will encounter this model when we discuss neural networks as\n",
"well. Each datapoint is deterministically assigned to a category (i.e\n",
- "$y_i=0$ or $y_i=1$). In many cases, it is favorable to have a \"soft\"\n",
+ "$y_i=0$ or $y_i=1$). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a \"soft\"\n",
"classifier that outputs the probability of a given category rather\n",
"than a single value. For example, given $x_i$, the classifier\n",
"outputs the probability of being in a category $k$. Logistic regression\n",
@@ -2030,32 +2040,23 @@
"\n",
"Till now we have mainly focused on two classes, the so-called binary\n",
"system. Suppose we wish to extend to $K$ classes. Let us for the sake\n",
- "of simplicity assume we have only two predictors. We have then\n",
- "following model"
+ "of simplicity assume we have only two predictors. We have then following model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "4\n",
- "0\n",
- " \n",
- "<\n",
- "<\n",
- "<\n",
- "!\n",
- "!\n",
- "M\n",
- "A\n",
- "T\n",
- "H\n",
- "_\n",
- "B\n",
- "L\n",
- "O\n",
- "C\n",
- "K"
+ "$$\n",
+ "\\log{\\frac{p(C=1\\vert x)}{p(K\\vert x)}} = \\beta_{10}+\\beta_{11}x_1,\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "and"
]
},
{
@@ -2145,13 +2146,13 @@
"discussed in the material on [optimization\n",
"methods](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html).\n",
"\n",
- "This will be discussed next week.\n",
+ "This will be discussed next week. Before we develop our own codes for logistic regression, we end this lecture by studying the functionality that **Scikit-learn** offers. \n",
"\n",
"\n",
"\n",
"\n",
"\n",
- "## Cancer Data again now with Decision Trees and other Methods"
+ "## Wisconsin Cancer Data"
]
},
{