How will Occam's Razor principle work in Machine learningHow exactly does a validation data-set work work in...
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How will Occam's Razor principle work in Machine learning
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The following question displayed in the image was asked during one of the exams recently. I am not sure if I have correctly understood the Occam's Razor principle or not. According to the distributions and decision boundaries given in the question and following the Occam's Razor the decision boundary B in both the cases should be the answer. Because as per Occam's Razor, choose the simpler classifier which does a decent job rather than the complex one.
Can someone please testify if my understanding is correct and the answer chosen is appropriate or not?
Please help as I am just a beginner in machine learning
machine-learning classification
asked yesterday
user1479198user1479198
334
New contributor
user1479198 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
The following question displayed in the image was asked during one of the exams recently. I am not sure if I have correctly understood the Occam's Razor principle or not. According to the distributions and decision boundaries given in the question and following the Occam's Razor the decision boundary B in both the cases should be the answer. Because as per Occam's Razor, choose the simpler classifier which does a decent job rather than the complex one.
Can someone please testify if my understanding is correct and the answer chosen is appropriate or not?
Please help as I am just a beginner in machine learning
machine-learning classification
asked yesterday
user1479198user1479198
334
New contributor
user1479198 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
3.328 "If a sign is not necessary then it is meaningless. That is the meaning of Occam's Razor." From the Tractatus Logico-Philosophicus by Wittgenstein
$endgroup$
– Jorge Barrios
18 hours ago
add a comment |
$begingroup$
The following question displayed in the image was asked during one of the exams recently. I am not sure if I have correctly understood the Occam's Razor principle or not. According to the distributions and decision boundaries given in the question and following the Occam's Razor the decision boundary B in both the cases should be the answer. Because as per Occam's Razor, choose the simpler classifier which does a decent job rather than the complex one.
Can someone please testify if my understanding is correct and the answer chosen is appropriate or not?
Please help as I am just a beginner in machine learning
machine-learning classification
asked yesterday
user1479198user1479198
334
New contributor
user1479198 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
The following question displayed in the image was asked during one of the exams recently. I am not sure if I have correctly understood the Occam's Razor principle or not. According to the distributions and decision boundaries given in the question and following the Occam's Razor the decision boundary B in both the cases should be the answer. Because as per Occam's Razor, choose the simpler classifier which does a decent job rather than the complex one.
Can someone please testify if my understanding is correct and the answer chosen is appropriate or not?
Please help as I am just a beginner in machine learning
machine-learning classification
machine-learning classification
asked yesterday
user1479198user1479198
334
New contributor
user1479198 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
user1479198user1479198
334
New contributor
user1479198 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
user1479198user1479198
334
New contributor
user1479198 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
user1479198user1479198
334
asked yesterday
user1479198user1479198
334
334
New contributor
user1479198 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user1479198 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user1479198 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
3.328 "If a sign is not necessary then it is meaningless. That is the meaning of Occam's Razor." From the Tractatus Logico-Philosophicus by Wittgenstein
$endgroup$
– Jorge Barrios
18 hours ago
add a comment |
1
$begingroup$
3.328 "If a sign is not necessary then it is meaningless. That is the meaning of Occam's Razor." From the Tractatus Logico-Philosophicus by Wittgenstein
$endgroup$
– Jorge Barrios
18 hours ago
1
1
$begingroup$
3.328 "If a sign is not necessary then it is meaningless. That is the meaning of Occam's Razor." From the Tractatus Logico-Philosophicus by Wittgenstein
$endgroup$
– Jorge Barrios
18 hours ago
$begingroup$
3.328 "If a sign is not necessary then it is meaningless. That is the meaning of Occam's Razor." From the Tractatus Logico-Philosophicus by Wittgenstein
$endgroup$
– Jorge Barrios
18 hours ago
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Occam’s razor principle:
Having two hypotheses (here, decision boundaries) that has the same empirical risk (here, training error), a short explanation (here, a boundary with fewer parameters) tends to be more valid than a long explanation.
In your example, both A and B have zero training error, thus B (shorter explanation) is preferred.
What if training error is not the same?
If boundary A had a smaller training error than B, selecting becomes tricky. We need to quantify "explanation size" the same as "empirical risk" and combine the two in one scoring function, then proceed to compare A and B. An example would be Akaike Information Criterion (AIC) that combines empirical risk (measured with negative log-likelihood) and explanation size (measured with the number of parameters) in one score.
As a side note, AIC cannot be used for all models, there are many alternatives to AIC too.
Relation to cross-validation
In many practical cases, when model progresses toward more complexity (larger explanation) to reach lower training error, AIC and the like can be replaced with a validation set (a set on which the model is not trained). We stop the progress when validation error (error of model on validation set) starts to increase. This way, we strike a balance between low training error and short explanation.
answered 21 hours ago
EsmailianEsmailian
3865
$endgroup$
add a comment |
$begingroup$
Occam Razor is just a synonym to Parsimony principal. (KISS, Keep it simple and stupid.)
Most algos work in this principal.
In above question one has to think in designing the simple separable boundaries,
like in first picture D1 answer is B.
As it define the best line separating 2 samples, as a is polynomial and may end up in over-fitting. (if I would have used SVM that line would have come)
similarly in figure 2 D2 answer is B.
answered 21 hours ago
Gaurav DograGaurav Dogra
312
New contributor
Gaurav Dogra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Occam’s razor in data-fitting tasks :
- First try linear equation
- If (1) don't helps much - choose a non-linear one with less terms and/or smaller degrees of variables.
D2
B clearly wins, because it's linear boundary which nicely separates data. (What is "nicely" I can't currently define. You have to develop this feeling with experience). A boundary is highly non-linear which seems like a jittered sine wave.
D1
However I am not sure about this one. A boundary is like a circle and B is strictly linear. IMHO, for me - boundary line is neither circle segment nor a line segment,- it's parabola-like curve :
So I opt for a C :-)
answered 15 hours ago
Agnius VasiliauskasAgnius Vasiliauskas
1213
New contributor
Agnius Vasiliauskas is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
I'm still unsure of why you want an in-between line for D1. Occam's Razor says to use the simple solution that works. Absent more data, B is a perfectly valid division that fits the data. If we received more data that suggests more of a curve to B's data set then I could see your argument, but requesting C goes against your point (1), since it's a linear boundary that works.
$endgroup$
– Delioth
9 hours ago
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Occam’s razor principle:
Having two hypotheses (here, decision boundaries) that has the same empirical risk (here, training error), a short explanation (here, a boundary with fewer parameters) tends to be more valid than a long explanation.
In your example, both A and B have zero training error, thus B (shorter explanation) is preferred.
What if training error is not the same?
If boundary A had a smaller training error than B, selecting becomes tricky. We need to quantify "explanation size" the same as "empirical risk" and combine the two in one scoring function, then proceed to compare A and B. An example would be Akaike Information Criterion (AIC) that combines empirical risk (measured with negative log-likelihood) and explanation size (measured with the number of parameters) in one score.
As a side note, AIC cannot be used for all models, there are many alternatives to AIC too.
Relation to cross-validation
In many practical cases, when model progresses toward more complexity (larger explanation) to reach lower training error, AIC and the like can be replaced with a validation set (a set on which the model is not trained). We stop the progress when validation error (error of model on validation set) starts to increase. This way, we strike a balance between low training error and short explanation.
answered 21 hours ago
EsmailianEsmailian
3865
$endgroup$
add a comment |
$begingroup$
Occam’s razor principle:
Having two hypotheses (here, decision boundaries) that has the same empirical risk (here, training error), a short explanation (here, a boundary with fewer parameters) tends to be more valid than a long explanation.
In your example, both A and B have zero training error, thus B (shorter explanation) is preferred.
What if training error is not the same?
If boundary A had a smaller training error than B, selecting becomes tricky. We need to quantify "explanation size" the same as "empirical risk" and combine the two in one scoring function, then proceed to compare A and B. An example would be Akaike Information Criterion (AIC) that combines empirical risk (measured with negative log-likelihood) and explanation size (measured with the number of parameters) in one score.
As a side note, AIC cannot be used for all models, there are many alternatives to AIC too.
Relation to cross-validation
In many practical cases, when model progresses toward more complexity (larger explanation) to reach lower training error, AIC and the like can be replaced with a validation set (a set on which the model is not trained). We stop the progress when validation error (error of model on validation set) starts to increase. This way, we strike a balance between low training error and short explanation.
answered 21 hours ago
EsmailianEsmailian
3865
$endgroup$
add a comment |
$begingroup$
Occam’s razor principle:
Having two hypotheses (here, decision boundaries) that has the same empirical risk (here, training error), a short explanation (here, a boundary with fewer parameters) tends to be more valid than a long explanation.
In your example, both A and B have zero training error, thus B (shorter explanation) is preferred.
What if training error is not the same?
If boundary A had a smaller training error than B, selecting becomes tricky. We need to quantify "explanation size" the same as "empirical risk" and combine the two in one scoring function, then proceed to compare A and B. An example would be Akaike Information Criterion (AIC) that combines empirical risk (measured with negative log-likelihood) and explanation size (measured with the number of parameters) in one score.
As a side note, AIC cannot be used for all models, there are many alternatives to AIC too.
Relation to cross-validation
In many practical cases, when model progresses toward more complexity (larger explanation) to reach lower training error, AIC and the like can be replaced with a validation set (a set on which the model is not trained). We stop the progress when validation error (error of model on validation set) starts to increase. This way, we strike a balance between low training error and short explanation.
answered 21 hours ago
EsmailianEsmailian
3865
$endgroup$
Occam’s razor principle:
Having two hypotheses (here, decision boundaries) that has the same empirical risk (here, training error), a short explanation (here, a boundary with fewer parameters) tends to be more valid than a long explanation.
In your example, both A and B have zero training error, thus B (shorter explanation) is preferred.
What if training error is not the same?
If boundary A had a smaller training error than B, selecting becomes tricky. We need to quantify "explanation size" the same as "empirical risk" and combine the two in one scoring function, then proceed to compare A and B. An example would be Akaike Information Criterion (AIC) that combines empirical risk (measured with negative log-likelihood) and explanation size (measured with the number of parameters) in one score.
As a side note, AIC cannot be used for all models, there are many alternatives to AIC too.
Relation to cross-validation
In many practical cases, when model progresses toward more complexity (larger explanation) to reach lower training error, AIC and the like can be replaced with a validation set (a set on which the model is not trained). We stop the progress when validation error (error of model on validation set) starts to increase. This way, we strike a balance between low training error and short explanation.
answered 21 hours ago
EsmailianEsmailian
3865
edited 20 hours ago
answered 21 hours ago
EsmailianEsmailian
3865
answered 21 hours ago
EsmailianEsmailian
3865
answered 21 hours ago
EsmailianEsmailian
3865
3865
add a comment |
add a comment |
$begingroup$
Occam Razor is just a synonym to Parsimony principal. (KISS, Keep it simple and stupid.)
Most algos work in this principal.
In above question one has to think in designing the simple separable boundaries,
like in first picture D1 answer is B.
As it define the best line separating 2 samples, as a is polynomial and may end up in over-fitting. (if I would have used SVM that line would have come)
similarly in figure 2 D2 answer is B.
answered 21 hours ago
Gaurav DograGaurav Dogra
312
New contributor
Gaurav Dogra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Occam Razor is just a synonym to Parsimony principal. (KISS, Keep it simple and stupid.)
Most algos work in this principal.
In above question one has to think in designing the simple separable boundaries,
like in first picture D1 answer is B.
As it define the best line separating 2 samples, as a is polynomial and may end up in over-fitting. (if I would have used SVM that line would have come)
similarly in figure 2 D2 answer is B.
answered 21 hours ago
Gaurav DograGaurav Dogra
312
New contributor
Gaurav Dogra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Occam Razor is just a synonym to Parsimony principal. (KISS, Keep it simple and stupid.)
Most algos work in this principal.
In above question one has to think in designing the simple separable boundaries,
like in first picture D1 answer is B.
As it define the best line separating 2 samples, as a is polynomial and may end up in over-fitting. (if I would have used SVM that line would have come)
similarly in figure 2 D2 answer is B.
answered 21 hours ago
Gaurav DograGaurav Dogra
312
New contributor
Gaurav Dogra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Occam Razor is just a synonym to Parsimony principal. (KISS, Keep it simple and stupid.)
Most algos work in this principal.
In above question one has to think in designing the simple separable boundaries,
like in first picture D1 answer is B.
As it define the best line separating 2 samples, as a is polynomial and may end up in over-fitting. (if I would have used SVM that line would have come)
similarly in figure 2 D2 answer is B.
answered 21 hours ago
Gaurav DograGaurav Dogra
312
New contributor
Gaurav Dogra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 21 hours ago
Gaurav DograGaurav Dogra
312
New contributor
Gaurav Dogra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 21 hours ago
Gaurav DograGaurav Dogra
312
answered 21 hours ago
Gaurav DograGaurav Dogra
312
312
New contributor
Gaurav Dogra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Gaurav Dogra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Gaurav Dogra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
$begingroup$
Occam’s razor in data-fitting tasks :
- First try linear equation
- If (1) don't helps much - choose a non-linear one with less terms and/or smaller degrees of variables.
D2
B clearly wins, because it's linear boundary which nicely separates data. (What is "nicely" I can't currently define. You have to develop this feeling with experience). A boundary is highly non-linear which seems like a jittered sine wave.
D1
However I am not sure about this one. A boundary is like a circle and B is strictly linear. IMHO, for me - boundary line is neither circle segment nor a line segment,- it's parabola-like curve :
So I opt for a C :-)
answered 15 hours ago
Agnius VasiliauskasAgnius Vasiliauskas
1213
New contributor
Agnius Vasiliauskas is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
I'm still unsure of why you want an in-between line for D1. Occam's Razor says to use the simple solution that works. Absent more data, B is a perfectly valid division that fits the data. If we received more data that suggests more of a curve to B's data set then I could see your argument, but requesting C goes against your point (1), since it's a linear boundary that works.
$endgroup$
– Delioth
9 hours ago
add a comment |
$begingroup$
Occam’s razor in data-fitting tasks :
- First try linear equation
- If (1) don't helps much - choose a non-linear one with less terms and/or smaller degrees of variables.
D2
B clearly wins, because it's linear boundary which nicely separates data. (What is "nicely" I can't currently define. You have to develop this feeling with experience). A boundary is highly non-linear which seems like a jittered sine wave.
D1
However I am not sure about this one. A boundary is like a circle and B is strictly linear. IMHO, for me - boundary line is neither circle segment nor a line segment,- it's parabola-like curve :
So I opt for a C :-)
answered 15 hours ago
Agnius VasiliauskasAgnius Vasiliauskas
1213
New contributor
Agnius Vasiliauskas is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
I'm still unsure of why you want an in-between line for D1. Occam's Razor says to use the simple solution that works. Absent more data, B is a perfectly valid division that fits the data. If we received more data that suggests more of a curve to B's data set then I could see your argument, but requesting C goes against your point (1), since it's a linear boundary that works.
$endgroup$
– Delioth
9 hours ago
add a comment |
$begingroup$
Occam’s razor in data-fitting tasks :
- First try linear equation
- If (1) don't helps much - choose a non-linear one with less terms and/or smaller degrees of variables.
D2
B clearly wins, because it's linear boundary which nicely separates data. (What is "nicely" I can't currently define. You have to develop this feeling with experience). A boundary is highly non-linear which seems like a jittered sine wave.
D1
However I am not sure about this one. A boundary is like a circle and B is strictly linear. IMHO, for me - boundary line is neither circle segment nor a line segment,- it's parabola-like curve :
So I opt for a C :-)
answered 15 hours ago
Agnius VasiliauskasAgnius Vasiliauskas
1213
New contributor
Agnius Vasiliauskas is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Occam’s razor in data-fitting tasks :
- First try linear equation
- If (1) don't helps much - choose a non-linear one with less terms and/or smaller degrees of variables.
D2
B clearly wins, because it's linear boundary which nicely separates data. (What is "nicely" I can't currently define. You have to develop this feeling with experience). A boundary is highly non-linear which seems like a jittered sine wave.
D1
However I am not sure about this one. A boundary is like a circle and B is strictly linear. IMHO, for me - boundary line is neither circle segment nor a line segment,- it's parabola-like curve :
So I opt for a C :-)
answered 15 hours ago
Agnius VasiliauskasAgnius Vasiliauskas
1213
New contributor
Agnius Vasiliauskas is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 15 hours ago
Agnius VasiliauskasAgnius Vasiliauskas
1213
New contributor
Agnius Vasiliauskas is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 15 hours ago
Agnius VasiliauskasAgnius Vasiliauskas
1213
answered 15 hours ago
Agnius VasiliauskasAgnius Vasiliauskas
1213
1213
New contributor
Agnius Vasiliauskas is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Agnius Vasiliauskas is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Agnius Vasiliauskas is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
I'm still unsure of why you want an in-between line for D1. Occam's Razor says to use the simple solution that works. Absent more data, B is a perfectly valid division that fits the data. If we received more data that suggests more of a curve to B's data set then I could see your argument, but requesting C goes against your point (1), since it's a linear boundary that works.
$endgroup$
– Delioth
9 hours ago
add a comment |
$begingroup$
I'm still unsure of why you want an in-between line for D1. Occam's Razor says to use the simple solution that works. Absent more data, B is a perfectly valid division that fits the data. If we received more data that suggests more of a curve to B's data set then I could see your argument, but requesting C goes against your point (1), since it's a linear boundary that works.
$endgroup$
– Delioth
9 hours ago
$begingroup$
I'm still unsure of why you want an in-between line for D1. Occam's Razor says to use the simple solution that works. Absent more data, B is a perfectly valid division that fits the data. If we received more data that suggests more of a curve to B's data set then I could see your argument, but requesting C goes against your point (1), since it's a linear boundary that works.
$endgroup$
– Delioth
9 hours ago
$begingroup$
I'm still unsure of why you want an in-between line for D1. Occam's Razor says to use the simple solution that works. Absent more data, B is a perfectly valid division that fits the data. If we received more data that suggests more of a curve to B's data set then I could see your argument, but requesting C goes against your point (1), since it's a linear boundary that works.
$endgroup$
– Delioth
9 hours ago
add a comment |
user1479198 is a new contributor. Be nice, and check out our Code of Conduct.
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1
$begingroup$
3.328 "If a sign is not necessary then it is meaningless. That is the meaning of Occam's Razor." From the Tractatus Logico-Philosophicus by Wittgenstein
$endgroup$
– Jorge Barrios
18 hours ago