Finding a logistic regression model which can achieve zero error on a training set training data for a binary...
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Not sure where to begin with this question, can anyone help out?
machine-learning self-study mathematical-statistics
edited 12 hours ago
Bryan Krause
697212
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add a comment |
$begingroup$
Not sure where to begin with this question, can anyone help out?
machine-learning self-study mathematical-statistics
edited 12 hours ago
Bryan Krause
697212
$endgroup$
1
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Is this from a book? If so can you share the title?
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– grayQuant
10 hours ago
add a comment |
$begingroup$
Not sure where to begin with this question, can anyone help out?
machine-learning self-study mathematical-statistics
edited 12 hours ago
Bryan Krause
697212
$endgroup$
Not sure where to begin with this question, can anyone help out?
machine-learning self-study mathematical-statistics
machine-learning self-study mathematical-statistics
edited 12 hours ago
Bryan Krause
697212
edited 12 hours ago
Bryan Krause
697212
edited 12 hours ago
Bryan Krause
697212
edited 12 hours ago
Bryan Krause
697212
edited 12 hours ago
Bryan Krause
697212
697212
asked 12 hours ago
user239276
1
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Is this from a book? If so can you share the title?
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– grayQuant
10 hours ago
add a comment |
1
$begingroup$
Is this from a book? If so can you share the title?
$endgroup$
– grayQuant
10 hours ago
1
1
$begingroup$
Is this from a book? If so can you share the title?
$endgroup$
– grayQuant
10 hours ago
$begingroup$
Is this from a book? If so can you share the title?
$endgroup$
– grayQuant
10 hours ago
add a comment |
1 Answer
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Logistic regression is a linear classifier, i.e. it draws a line (2D datasets) and classifies accordingly (one side is class 0, other side is class 1). So, if classes can be distinguished by a line (or hyperplane in higher dimensions), it is said that the dataset is linearly separable, though this dataset is not. One way to tackle this issue is creating new features, or applying transformations. For example, this dataset seems to be separable if you think radially, i.e. $R>alpha$, where $R$ is the radius, or distance to origin, which can be found by $R=sqrt{X_1^2+X_2^2}$. Constructing a logistic regression using this feature only, results in perfect classification.
answered 12 hours ago
gunesgunes
5,4001115
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$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
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– user239276
12 hours ago
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yes, sorry for ambiguity.
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– gunes
12 hours ago
1
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@gunes This might be a bit too much of an answer for a self-study question, although I don't typically police those here and am not certain where exactly the community falls on these sorts of questions besides what is included in the tag info.
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– Bryan Krause
12 hours ago
2
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(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
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– Cliff AB
11 hours ago
1
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It may be worth noting that this will cause the logistic regression to not converge! The parameter estimate for R will tend to infinity!
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– Matthew Drury
8 hours ago
add a comment |
protected by gung♦ 2 hours ago
Thank you for your interest in this question.
Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).
Would you like to answer one of these unanswered questions instead?
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Logistic regression is a linear classifier, i.e. it draws a line (2D datasets) and classifies accordingly (one side is class 0, other side is class 1). So, if classes can be distinguished by a line (or hyperplane in higher dimensions), it is said that the dataset is linearly separable, though this dataset is not. One way to tackle this issue is creating new features, or applying transformations. For example, this dataset seems to be separable if you think radially, i.e. $R>alpha$, where $R$ is the radius, or distance to origin, which can be found by $R=sqrt{X_1^2+X_2^2}$. Constructing a logistic regression using this feature only, results in perfect classification.
answered 12 hours ago
gunesgunes
5,4001115
$endgroup$
$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
$endgroup$
– user239276
12 hours ago
$begingroup$
yes, sorry for ambiguity.
$endgroup$
– gunes
12 hours ago
1
$begingroup$
@gunes This might be a bit too much of an answer for a self-study question, although I don't typically police those here and am not certain where exactly the community falls on these sorts of questions besides what is included in the tag info.
$endgroup$
– Bryan Krause
12 hours ago
2
$begingroup$
(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
$endgroup$
– Cliff AB
11 hours ago
1
$begingroup$
It may be worth noting that this will cause the logistic regression to not converge! The parameter estimate for R will tend to infinity!
$endgroup$
– Matthew Drury
8 hours ago
add a comment |
$begingroup$
Logistic regression is a linear classifier, i.e. it draws a line (2D datasets) and classifies accordingly (one side is class 0, other side is class 1). So, if classes can be distinguished by a line (or hyperplane in higher dimensions), it is said that the dataset is linearly separable, though this dataset is not. One way to tackle this issue is creating new features, or applying transformations. For example, this dataset seems to be separable if you think radially, i.e. $R>alpha$, where $R$ is the radius, or distance to origin, which can be found by $R=sqrt{X_1^2+X_2^2}$. Constructing a logistic regression using this feature only, results in perfect classification.
answered 12 hours ago
gunesgunes
5,4001115
$endgroup$
$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
$endgroup$
– user239276
12 hours ago
$begingroup$
yes, sorry for ambiguity.
$endgroup$
– gunes
12 hours ago
1
$begingroup$
@gunes This might be a bit too much of an answer for a self-study question, although I don't typically police those here and am not certain where exactly the community falls on these sorts of questions besides what is included in the tag info.
$endgroup$
– Bryan Krause
12 hours ago
2
$begingroup$
(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
$endgroup$
– Cliff AB
11 hours ago
1
$begingroup$
It may be worth noting that this will cause the logistic regression to not converge! The parameter estimate for R will tend to infinity!
$endgroup$
– Matthew Drury
8 hours ago
add a comment |
$begingroup$
Logistic regression is a linear classifier, i.e. it draws a line (2D datasets) and classifies accordingly (one side is class 0, other side is class 1). So, if classes can be distinguished by a line (or hyperplane in higher dimensions), it is said that the dataset is linearly separable, though this dataset is not. One way to tackle this issue is creating new features, or applying transformations. For example, this dataset seems to be separable if you think radially, i.e. $R>alpha$, where $R$ is the radius, or distance to origin, which can be found by $R=sqrt{X_1^2+X_2^2}$. Constructing a logistic regression using this feature only, results in perfect classification.
answered 12 hours ago
gunesgunes
5,4001115
$endgroup$
Logistic regression is a linear classifier, i.e. it draws a line (2D datasets) and classifies accordingly (one side is class 0, other side is class 1). So, if classes can be distinguished by a line (or hyperplane in higher dimensions), it is said that the dataset is linearly separable, though this dataset is not. One way to tackle this issue is creating new features, or applying transformations. For example, this dataset seems to be separable if you think radially, i.e. $R>alpha$, where $R$ is the radius, or distance to origin, which can be found by $R=sqrt{X_1^2+X_2^2}$. Constructing a logistic regression using this feature only, results in perfect classification.
answered 12 hours ago
gunesgunes
5,4001115
edited 12 hours ago
answered 12 hours ago
gunesgunes
5,4001115
answered 12 hours ago
gunesgunes
5,4001115
answered 12 hours ago
gunesgunes
5,4001115
5,4001115
$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
$endgroup$
– user239276
12 hours ago
$begingroup$
yes, sorry for ambiguity.
$endgroup$
– gunes
12 hours ago
1
$begingroup$
@gunes This might be a bit too much of an answer for a self-study question, although I don't typically police those here and am not certain where exactly the community falls on these sorts of questions besides what is included in the tag info.
$endgroup$
– Bryan Krause
12 hours ago
2
$begingroup$
(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
$endgroup$
– Cliff AB
11 hours ago
1
$begingroup$
It may be worth noting that this will cause the logistic regression to not converge! The parameter estimate for R will tend to infinity!
$endgroup$
– Matthew Drury
8 hours ago
add a comment |
$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
$endgroup$
– user239276
12 hours ago
$begingroup$
yes, sorry for ambiguity.
$endgroup$
– gunes
12 hours ago
1
$begingroup$
@gunes This might be a bit too much of an answer for a self-study question, although I don't typically police those here and am not certain where exactly the community falls on these sorts of questions besides what is included in the tag info.
$endgroup$
– Bryan Krause
12 hours ago
2
$begingroup$
(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
$endgroup$
– Cliff AB
11 hours ago
1
$begingroup$
It may be worth noting that this will cause the logistic regression to not converge! The parameter estimate for R will tend to infinity!
$endgroup$
– Matthew Drury
8 hours ago
$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
$endgroup$
– user239276
12 hours ago
$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
$endgroup$
– user239276
12 hours ago
$begingroup$
yes, sorry for ambiguity.
$endgroup$
– gunes
12 hours ago
$begingroup$
yes, sorry for ambiguity.
$endgroup$
– gunes
12 hours ago
1
1
$begingroup$
@gunes This might be a bit too much of an answer for a self-study question, although I don't typically police those here and am not certain where exactly the community falls on these sorts of questions besides what is included in the tag info.
$endgroup$
– Bryan Krause
12 hours ago
$begingroup$
@gunes This might be a bit too much of an answer for a self-study question, although I don't typically police those here and am not certain where exactly the community falls on these sorts of questions besides what is included in the tag info.
$endgroup$
– Bryan Krause
12 hours ago
2
2
$begingroup$
(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
$endgroup$
– Cliff AB
11 hours ago
$begingroup$
(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
$endgroup$
– Cliff AB
11 hours ago
1
1
$begingroup$
It may be worth noting that this will cause the logistic regression to not converge! The parameter estimate for R will tend to infinity!
$endgroup$
– Matthew Drury
8 hours ago
$begingroup$
It may be worth noting that this will cause the logistic regression to not converge! The parameter estimate for R will tend to infinity!
$endgroup$
– Matthew Drury
8 hours ago
add a comment |
protected by gung♦ 2 hours ago
Thank you for your interest in this question.
Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).
Would you like to answer one of these unanswered questions instead?
1
$begingroup$
Is this from a book? If so can you share the title?
$endgroup$
– grayQuant
10 hours ago