Is it correct to say the Neural Networks are an alternative way of performing Maximum Likelihood Estimation? if not, why? The 2019 Stack Overflow Developer Survey Results Are InCan we use MLE to estimate Neural Network weights?Are loss functions what define the identity of each supervised machine learning algorithm?What can we say about the likelihood function, besides using it in maximum likelihood estimation?Why is maximum likelihood estimation considered to be a frequentist techniqueMaximum Likelihood Estimation — why it is used despite being biased in many casesWhat is the objective of maximum likelihood estimation?Maximum Likelihood estimation and the Kalman filterWhy does Maximum Likelihood estimation maximizes probability density instead of probabilityWhy are the Least-Squares and Maximum-Likelihood methods of regression not equivalent when the errors are not normally distributed?the relationship between maximizing the likelihood and minimizing the cross-entropythe meaning of likelihood in maximum likelihood estimationHow to construct a cross-entropy loss for general regression targets?
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Is it correct to say the Neural Networks are an alternative way of performing Maximum Likelihood Estimation? if not, why?
The 2019 Stack Overflow Developer Survey Results Are InCan we use MLE to estimate Neural Network weights?Are loss functions what define the identity of each supervised machine learning algorithm?What can we say about the likelihood function, besides using it in maximum likelihood estimation?Why is maximum likelihood estimation considered to be a frequentist techniqueMaximum Likelihood Estimation — why it is used despite being biased in many casesWhat is the objective of maximum likelihood estimation?Maximum Likelihood estimation and the Kalman filterWhy does Maximum Likelihood estimation maximizes probability density instead of probabilityWhy are the Least-Squares and Maximum-Likelihood methods of regression not equivalent when the errors are not normally distributed?the relationship between maximizing the likelihood and minimizing the cross-entropythe meaning of likelihood in maximum likelihood estimationHow to construct a cross-entropy loss for general regression targets?
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
We often say that minimizing the (negative) cross-entropy error is the same as maximizing the likelihood. So can we say that NN are just an alternative way of performing Maximum Likelihood Estimation? if not, why?
neural-networks maximum-likelihood
asked 8 hours ago
aca06aca06
161
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aca06 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$
add a comment |
$begingroup$
We often say that minimizing the (negative) cross-entropy error is the same as maximizing the likelihood. So can we say that NN are just an alternative way of performing Maximum Likelihood Estimation? if not, why?
neural-networks maximum-likelihood
asked 8 hours ago
aca06aca06
161
New contributor
aca06 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Possible duplicate of Can we use MLE to estimate Neural Network weights?
$endgroup$
– Sycorax
6 hours ago
add a comment |
$begingroup$
We often say that minimizing the (negative) cross-entropy error is the same as maximizing the likelihood. So can we say that NN are just an alternative way of performing Maximum Likelihood Estimation? if not, why?
neural-networks maximum-likelihood
asked 8 hours ago
aca06aca06
161
New contributor
aca06 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
We often say that minimizing the (negative) cross-entropy error is the same as maximizing the likelihood. So can we say that NN are just an alternative way of performing Maximum Likelihood Estimation? if not, why?
neural-networks maximum-likelihood
neural-networks maximum-likelihood
asked 8 hours ago
aca06aca06
161
New contributor
aca06 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
aca06aca06
161
New contributor
aca06 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
aca06aca06
161
New contributor
aca06 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
aca06aca06
161
asked 8 hours ago
aca06aca06
161
161
New contributor
aca06 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
aca06 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
aca06 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Possible duplicate of Can we use MLE to estimate Neural Network weights?
$endgroup$
– Sycorax
6 hours ago
add a comment |
1
$begingroup$
Possible duplicate of Can we use MLE to estimate Neural Network weights?
$endgroup$
– Sycorax
6 hours ago
1
1
$begingroup$
Possible duplicate of Can we use MLE to estimate Neural Network weights?
$endgroup$
– Sycorax
6 hours ago
$begingroup$
Possible duplicate of Can we use MLE to estimate Neural Network weights?
$endgroup$
– Sycorax
6 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
In abstract terms, neural networks are models, or if you prefer, functions with unknown parameters, where we try to learn the parameter by minimizing loss function (not just cross entropy, there are many other possibilities). In general, minimizing loss is in most cases equivalent to maximizing some likelihood function, but as discussed in this thread, it's not that simple.
You cannot say that they are equivalent, because minimizing loss, or maximizing likelihood is a method of finding the parameters, while neural network is the function defined in terms of those parameters.
answered 6 hours ago
Tim♦Tim
60k9133229
$endgroup$
1
$begingroup$
I'm trying to parse the distinction that you draw in the second paragraph. If I understand correctly, you would approve of a statement such as "My neural network model maximizes a certain log-likelihood" but not the statement "Neural networks and maximum likelihood estimators are the same concept." Is this a fair assessment?
$endgroup$
– Sycorax
5 hours ago
1
$begingroup$
@Sycorax yes, that is correct. If it is unclear and you have idea for better re-phrasing, feel free to suggest edit.
$endgroup$
– Tim♦
5 hours ago
1
$begingroup$
What if instead, we compare gradient descent and MLE ? It seems to me that they are just two methods for finding the best parameters.
$endgroup$
– aca06
5 hours ago
2
$begingroup$
@aca06 gradient descent is an optimization algorithm, MLE is a method of estimating parameters. You can use gradient descent to find minimum of negative likelihood function (or gradient ascent for maximizing likelihood).
$endgroup$
– Tim♦
5 hours ago
add a comment |
$begingroup$
These are fairly orthogonal topics.
Neural networks are a type of model which has a very large number of parameters. Maximum Likelihood Estimation is a very common method for estimating parameters from a given model and data. Typically, a model will allow you to compute a likelihood function from a model, data and parameter values. Since we don't know what the actual parameter values are, one way of estimating them is to use the value that maximizes the given likelihood. Neural networks are our model, maximum likelihood estimation is one method for estimating the parameters of our model.
One slightly technical note is that often, Maximum Likelihood Estimation is not exactly used in Neural Networks. That is, there are a lot of regularization methods used that imply we're not actually maximizing a likelihood function. These include:
(1) Penalized maximum likelihood. This one is a bit of a cop-out, as it doesn't actually take too much effort to think of Penalized likelihoods as actually just a different likelihood (i.e., one with priors) that one is maximizing.
(2) Random drop out. In especially a lot of the newer architectures, parameter values will randomly be set to 0 during training. This procedure is more definitely outside the realm of maximum likelihood estimation.
(3) Early stopping. It's not the most popular method at all, but one way to prevent overfitting is just to stop the optimization algorithm before it converges. Again, this is technically not maximum likelihood estimation, it's really just an ad-hoc solution to overfitting.
(4) Bayesian methods, probably the most common alternative to Maximum Likelihood Estimation in the statistics world, are also used for estimating the parameter values of a neural network. However, this is often too computationally intensive for large networks.
answered 3 hours ago
Cliff ABCliff AB
13.8k12567
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
In abstract terms, neural networks are models, or if you prefer, functions with unknown parameters, where we try to learn the parameter by minimizing loss function (not just cross entropy, there are many other possibilities). In general, minimizing loss is in most cases equivalent to maximizing some likelihood function, but as discussed in this thread, it's not that simple.
You cannot say that they are equivalent, because minimizing loss, or maximizing likelihood is a method of finding the parameters, while neural network is the function defined in terms of those parameters.
answered 6 hours ago
Tim♦Tim
60k9133229
$endgroup$
1
$begingroup$
I'm trying to parse the distinction that you draw in the second paragraph. If I understand correctly, you would approve of a statement such as "My neural network model maximizes a certain log-likelihood" but not the statement "Neural networks and maximum likelihood estimators are the same concept." Is this a fair assessment?
$endgroup$
– Sycorax
5 hours ago
1
$begingroup$
@Sycorax yes, that is correct. If it is unclear and you have idea for better re-phrasing, feel free to suggest edit.
$endgroup$
– Tim♦
5 hours ago
1
$begingroup$
What if instead, we compare gradient descent and MLE ? It seems to me that they are just two methods for finding the best parameters.
$endgroup$
– aca06
5 hours ago
2
$begingroup$
@aca06 gradient descent is an optimization algorithm, MLE is a method of estimating parameters. You can use gradient descent to find minimum of negative likelihood function (or gradient ascent for maximizing likelihood).
$endgroup$
– Tim♦
5 hours ago
add a comment |
$begingroup$
In abstract terms, neural networks are models, or if you prefer, functions with unknown parameters, where we try to learn the parameter by minimizing loss function (not just cross entropy, there are many other possibilities). In general, minimizing loss is in most cases equivalent to maximizing some likelihood function, but as discussed in this thread, it's not that simple.
You cannot say that they are equivalent, because minimizing loss, or maximizing likelihood is a method of finding the parameters, while neural network is the function defined in terms of those parameters.
answered 6 hours ago
Tim♦Tim
60k9133229
$endgroup$
1
$begingroup$
I'm trying to parse the distinction that you draw in the second paragraph. If I understand correctly, you would approve of a statement such as "My neural network model maximizes a certain log-likelihood" but not the statement "Neural networks and maximum likelihood estimators are the same concept." Is this a fair assessment?
$endgroup$
– Sycorax
5 hours ago
1
$begingroup$
@Sycorax yes, that is correct. If it is unclear and you have idea for better re-phrasing, feel free to suggest edit.
$endgroup$
– Tim♦
5 hours ago
1
$begingroup$
What if instead, we compare gradient descent and MLE ? It seems to me that they are just two methods for finding the best parameters.
$endgroup$
– aca06
5 hours ago
2
$begingroup$
@aca06 gradient descent is an optimization algorithm, MLE is a method of estimating parameters. You can use gradient descent to find minimum of negative likelihood function (or gradient ascent for maximizing likelihood).
$endgroup$
– Tim♦
5 hours ago
add a comment |
$begingroup$
In abstract terms, neural networks are models, or if you prefer, functions with unknown parameters, where we try to learn the parameter by minimizing loss function (not just cross entropy, there are many other possibilities). In general, minimizing loss is in most cases equivalent to maximizing some likelihood function, but as discussed in this thread, it's not that simple.
You cannot say that they are equivalent, because minimizing loss, or maximizing likelihood is a method of finding the parameters, while neural network is the function defined in terms of those parameters.
answered 6 hours ago
Tim♦Tim
60k9133229
$endgroup$
In abstract terms, neural networks are models, or if you prefer, functions with unknown parameters, where we try to learn the parameter by minimizing loss function (not just cross entropy, there are many other possibilities). In general, minimizing loss is in most cases equivalent to maximizing some likelihood function, but as discussed in this thread, it's not that simple.
You cannot say that they are equivalent, because minimizing loss, or maximizing likelihood is a method of finding the parameters, while neural network is the function defined in terms of those parameters.
answered 6 hours ago
Tim♦Tim
60k9133229
answered 6 hours ago
Tim♦Tim
60k9133229
answered 6 hours ago
Tim♦Tim
60k9133229
answered 6 hours ago
Tim♦Tim
60k9133229
60k9133229
1
$begingroup$
I'm trying to parse the distinction that you draw in the second paragraph. If I understand correctly, you would approve of a statement such as "My neural network model maximizes a certain log-likelihood" but not the statement "Neural networks and maximum likelihood estimators are the same concept." Is this a fair assessment?
$endgroup$
– Sycorax
5 hours ago
1
$begingroup$
@Sycorax yes, that is correct. If it is unclear and you have idea for better re-phrasing, feel free to suggest edit.
$endgroup$
– Tim♦
5 hours ago
1
$begingroup$
What if instead, we compare gradient descent and MLE ? It seems to me that they are just two methods for finding the best parameters.
$endgroup$
– aca06
5 hours ago
2
$begingroup$
@aca06 gradient descent is an optimization algorithm, MLE is a method of estimating parameters. You can use gradient descent to find minimum of negative likelihood function (or gradient ascent for maximizing likelihood).
$endgroup$
– Tim♦
5 hours ago
add a comment |
1
$begingroup$
I'm trying to parse the distinction that you draw in the second paragraph. If I understand correctly, you would approve of a statement such as "My neural network model maximizes a certain log-likelihood" but not the statement "Neural networks and maximum likelihood estimators are the same concept." Is this a fair assessment?
$endgroup$
– Sycorax
5 hours ago
1
$begingroup$
@Sycorax yes, that is correct. If it is unclear and you have idea for better re-phrasing, feel free to suggest edit.
$endgroup$
– Tim♦
5 hours ago
1
$begingroup$
What if instead, we compare gradient descent and MLE ? It seems to me that they are just two methods for finding the best parameters.
$endgroup$
– aca06
5 hours ago
2
$begingroup$
@aca06 gradient descent is an optimization algorithm, MLE is a method of estimating parameters. You can use gradient descent to find minimum of negative likelihood function (or gradient ascent for maximizing likelihood).
$endgroup$
– Tim♦
5 hours ago
1
1
$begingroup$
I'm trying to parse the distinction that you draw in the second paragraph. If I understand correctly, you would approve of a statement such as "My neural network model maximizes a certain log-likelihood" but not the statement "Neural networks and maximum likelihood estimators are the same concept." Is this a fair assessment?
$endgroup$
– Sycorax
5 hours ago
$begingroup$
I'm trying to parse the distinction that you draw in the second paragraph. If I understand correctly, you would approve of a statement such as "My neural network model maximizes a certain log-likelihood" but not the statement "Neural networks and maximum likelihood estimators are the same concept." Is this a fair assessment?
$endgroup$
– Sycorax
5 hours ago
1
1
$begingroup$
@Sycorax yes, that is correct. If it is unclear and you have idea for better re-phrasing, feel free to suggest edit.
$endgroup$
– Tim♦
5 hours ago
$begingroup$
@Sycorax yes, that is correct. If it is unclear and you have idea for better re-phrasing, feel free to suggest edit.
$endgroup$
– Tim♦
5 hours ago
1
1
$begingroup$
What if instead, we compare gradient descent and MLE ? It seems to me that they are just two methods for finding the best parameters.
$endgroup$
– aca06
5 hours ago
$begingroup$
What if instead, we compare gradient descent and MLE ? It seems to me that they are just two methods for finding the best parameters.
$endgroup$
– aca06
5 hours ago
2
2
$begingroup$
@aca06 gradient descent is an optimization algorithm, MLE is a method of estimating parameters. You can use gradient descent to find minimum of negative likelihood function (or gradient ascent for maximizing likelihood).
$endgroup$
– Tim♦
5 hours ago
$begingroup$
@aca06 gradient descent is an optimization algorithm, MLE is a method of estimating parameters. You can use gradient descent to find minimum of negative likelihood function (or gradient ascent for maximizing likelihood).
$endgroup$
– Tim♦
5 hours ago
add a comment |
$begingroup$
These are fairly orthogonal topics.
Neural networks are a type of model which has a very large number of parameters. Maximum Likelihood Estimation is a very common method for estimating parameters from a given model and data. Typically, a model will allow you to compute a likelihood function from a model, data and parameter values. Since we don't know what the actual parameter values are, one way of estimating them is to use the value that maximizes the given likelihood. Neural networks are our model, maximum likelihood estimation is one method for estimating the parameters of our model.
One slightly technical note is that often, Maximum Likelihood Estimation is not exactly used in Neural Networks. That is, there are a lot of regularization methods used that imply we're not actually maximizing a likelihood function. These include:
(1) Penalized maximum likelihood. This one is a bit of a cop-out, as it doesn't actually take too much effort to think of Penalized likelihoods as actually just a different likelihood (i.e., one with priors) that one is maximizing.
(2) Random drop out. In especially a lot of the newer architectures, parameter values will randomly be set to 0 during training. This procedure is more definitely outside the realm of maximum likelihood estimation.
(3) Early stopping. It's not the most popular method at all, but one way to prevent overfitting is just to stop the optimization algorithm before it converges. Again, this is technically not maximum likelihood estimation, it's really just an ad-hoc solution to overfitting.
(4) Bayesian methods, probably the most common alternative to Maximum Likelihood Estimation in the statistics world, are also used for estimating the parameter values of a neural network. However, this is often too computationally intensive for large networks.
answered 3 hours ago
Cliff ABCliff AB
13.8k12567
$endgroup$
add a comment |
$begingroup$
These are fairly orthogonal topics.
Neural networks are a type of model which has a very large number of parameters. Maximum Likelihood Estimation is a very common method for estimating parameters from a given model and data. Typically, a model will allow you to compute a likelihood function from a model, data and parameter values. Since we don't know what the actual parameter values are, one way of estimating them is to use the value that maximizes the given likelihood. Neural networks are our model, maximum likelihood estimation is one method for estimating the parameters of our model.
One slightly technical note is that often, Maximum Likelihood Estimation is not exactly used in Neural Networks. That is, there are a lot of regularization methods used that imply we're not actually maximizing a likelihood function. These include:
(1) Penalized maximum likelihood. This one is a bit of a cop-out, as it doesn't actually take too much effort to think of Penalized likelihoods as actually just a different likelihood (i.e., one with priors) that one is maximizing.
(2) Random drop out. In especially a lot of the newer architectures, parameter values will randomly be set to 0 during training. This procedure is more definitely outside the realm of maximum likelihood estimation.
(3) Early stopping. It's not the most popular method at all, but one way to prevent overfitting is just to stop the optimization algorithm before it converges. Again, this is technically not maximum likelihood estimation, it's really just an ad-hoc solution to overfitting.
(4) Bayesian methods, probably the most common alternative to Maximum Likelihood Estimation in the statistics world, are also used for estimating the parameter values of a neural network. However, this is often too computationally intensive for large networks.
answered 3 hours ago
Cliff ABCliff AB
13.8k12567
$endgroup$
add a comment |
$begingroup$
These are fairly orthogonal topics.
Neural networks are a type of model which has a very large number of parameters. Maximum Likelihood Estimation is a very common method for estimating parameters from a given model and data. Typically, a model will allow you to compute a likelihood function from a model, data and parameter values. Since we don't know what the actual parameter values are, one way of estimating them is to use the value that maximizes the given likelihood. Neural networks are our model, maximum likelihood estimation is one method for estimating the parameters of our model.
One slightly technical note is that often, Maximum Likelihood Estimation is not exactly used in Neural Networks. That is, there are a lot of regularization methods used that imply we're not actually maximizing a likelihood function. These include:
(1) Penalized maximum likelihood. This one is a bit of a cop-out, as it doesn't actually take too much effort to think of Penalized likelihoods as actually just a different likelihood (i.e., one with priors) that one is maximizing.
(2) Random drop out. In especially a lot of the newer architectures, parameter values will randomly be set to 0 during training. This procedure is more definitely outside the realm of maximum likelihood estimation.
(3) Early stopping. It's not the most popular method at all, but one way to prevent overfitting is just to stop the optimization algorithm before it converges. Again, this is technically not maximum likelihood estimation, it's really just an ad-hoc solution to overfitting.
(4) Bayesian methods, probably the most common alternative to Maximum Likelihood Estimation in the statistics world, are also used for estimating the parameter values of a neural network. However, this is often too computationally intensive for large networks.
answered 3 hours ago
Cliff ABCliff AB
13.8k12567
$endgroup$
These are fairly orthogonal topics.
Neural networks are a type of model which has a very large number of parameters. Maximum Likelihood Estimation is a very common method for estimating parameters from a given model and data. Typically, a model will allow you to compute a likelihood function from a model, data and parameter values. Since we don't know what the actual parameter values are, one way of estimating them is to use the value that maximizes the given likelihood. Neural networks are our model, maximum likelihood estimation is one method for estimating the parameters of our model.
One slightly technical note is that often, Maximum Likelihood Estimation is not exactly used in Neural Networks. That is, there are a lot of regularization methods used that imply we're not actually maximizing a likelihood function. These include:
(1) Penalized maximum likelihood. This one is a bit of a cop-out, as it doesn't actually take too much effort to think of Penalized likelihoods as actually just a different likelihood (i.e., one with priors) that one is maximizing.
(2) Random drop out. In especially a lot of the newer architectures, parameter values will randomly be set to 0 during training. This procedure is more definitely outside the realm of maximum likelihood estimation.
(3) Early stopping. It's not the most popular method at all, but one way to prevent overfitting is just to stop the optimization algorithm before it converges. Again, this is technically not maximum likelihood estimation, it's really just an ad-hoc solution to overfitting.
(4) Bayesian methods, probably the most common alternative to Maximum Likelihood Estimation in the statistics world, are also used for estimating the parameter values of a neural network. However, this is often too computationally intensive for large networks.
answered 3 hours ago
Cliff ABCliff AB
13.8k12567
edited 3 hours ago
answered 3 hours ago
Cliff ABCliff AB
13.8k12567
answered 3 hours ago
Cliff ABCliff AB
13.8k12567
answered 3 hours ago
Cliff ABCliff AB
13.8k12567
13.8k12567
add a comment |
add a comment |
aca06 is a new contributor. Be nice, and check out our Code of Conduct.
aca06 is a new contributor. Be nice, and check out our Code of Conduct.
aca06 is a new contributor. Be nice, and check out our Code of Conduct.
aca06 is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
Possible duplicate of Can we use MLE to estimate Neural Network weights?
$endgroup$
– Sycorax
6 hours ago