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 59 mins ago
Bryan Krause
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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 59 mins ago
Bryan Krause
697212
$endgroup$
add a comment |
$begingroup$
Not sure where to begin with this question, can anyone help out?
machine-learning self-study mathematical-statistics
edited 59 mins 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 59 mins ago
Bryan Krause
697212
edited 59 mins ago
Bryan Krause
697212
edited 59 mins ago
Bryan Krause
697212
edited 59 mins ago
Bryan Krause
697212
edited 59 mins ago
Bryan Krause
697212
697212
asked 1 hour ago
user239276
add a comment |
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 1 hour ago
gunesgunes
5,2901113
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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
1 hour ago
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yes, sorry for ambiguity.
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– gunes
1 hour ago
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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.
$endgroup$
– Bryan Krause
1 hour ago
1
$begingroup$
(+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
46 mins ago
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
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active
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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 1 hour ago
gunesgunes
5,2901113
$endgroup$
$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
$endgroup$
– user239276
1 hour ago
$begingroup$
yes, sorry for ambiguity.
$endgroup$
– gunes
1 hour 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
1 hour ago
1
$begingroup$
(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
$endgroup$
– Cliff AB
46 mins 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 1 hour ago
gunesgunes
5,2901113
$endgroup$
$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
$endgroup$
– user239276
1 hour ago
$begingroup$
yes, sorry for ambiguity.
$endgroup$
– gunes
1 hour 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
1 hour ago
1
$begingroup$
(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
$endgroup$
– Cliff AB
46 mins 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 1 hour ago
gunesgunes
5,2901113
$endgroup$
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 1 hour ago
gunesgunes
5,2901113
edited 1 hour ago
answered 1 hour ago
gunesgunes
5,2901113
answered 1 hour ago
gunesgunes
5,2901113
answered 1 hour ago
gunesgunes
5,2901113
5,2901113
$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
$endgroup$
– user239276
1 hour ago
$begingroup$
yes, sorry for ambiguity.
$endgroup$
– gunes
1 hour 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
1 hour ago
1
$begingroup$
(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
$endgroup$
– Cliff AB
46 mins ago
add a comment |
$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
$endgroup$
– user239276
1 hour ago
$begingroup$
yes, sorry for ambiguity.
$endgroup$
– gunes
1 hour 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
1 hour ago
1
$begingroup$
(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
$endgroup$
– Cliff AB
46 mins ago
$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
$endgroup$
– user239276
1 hour ago
$begingroup$
By log-reg, do you mean a logistic regression model? Thanks for your help by the way!
$endgroup$
– user239276
1 hour ago
$begingroup$
yes, sorry for ambiguity.
$endgroup$
– gunes
1 hour ago
$begingroup$
yes, sorry for ambiguity.
$endgroup$
– gunes
1 hour 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
1 hour 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
1 hour ago
1
1
$begingroup$
(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
$endgroup$
– Cliff AB
46 mins ago
$begingroup$
(+1) It's worth noting that this is essentially using a very simple Radial Basis Network with logistic loss
$endgroup$
– Cliff AB
46 mins ago
add a comment |
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