Corss Validation regarding Bayesian Bayes Decision Theory
$begingroup$
Given a training data with 2 categories and validation data.
From the training data, a gaussian distribution is estimated for each category, i.e. the mean and covariance matrix.
The validation is used only for computing the threshold which will distinguish between the two distributions. My question is regarding the prior probabilities since for computing the posterior probability one need to use Bayes Rule which will involve the prior probabilities.
Are the prior probabilities (of the categories) derived from the training data (which makes more sense, since the distributions were computed upon this data), or from the validation?
Please advise.
probability-theory machine-learning bayesian bayes-theorem
asked Dec 18 '18 at 8:06
user3492773user3492773
18914
$endgroup$
add a comment |
$begingroup$
Given a training data with 2 categories and validation data.
From the training data, a gaussian distribution is estimated for each category, i.e. the mean and covariance matrix.
The validation is used only for computing the threshold which will distinguish between the two distributions. My question is regarding the prior probabilities since for computing the posterior probability one need to use Bayes Rule which will involve the prior probabilities.
Are the prior probabilities (of the categories) derived from the training data (which makes more sense, since the distributions were computed upon this data), or from the validation?
Please advise.
probability-theory machine-learning bayesian bayes-theorem
asked Dec 18 '18 at 8:06
user3492773user3492773
18914
$endgroup$
1
$begingroup$
Shouldn't the prior be chosen before you observe any data? If you are using an empirical Bayes method (en.wikipedia.org/wiki/Empirical_Bayes_method), where you use the data to inform the prior, then you should derive it from the training data, as you shouldn't use information in the validation data to tweak your posterior model before you estimate performance on the validation data. The validation data is a proxy for unseen data - you can't estimate some parameters on unseen data and then use these parameters to predict the unseen data.
$endgroup$
– Alex
Dec 21 '18 at 22:31
add a comment |
$begingroup$
Given a training data with 2 categories and validation data.
From the training data, a gaussian distribution is estimated for each category, i.e. the mean and covariance matrix.
The validation is used only for computing the threshold which will distinguish between the two distributions. My question is regarding the prior probabilities since for computing the posterior probability one need to use Bayes Rule which will involve the prior probabilities.
Are the prior probabilities (of the categories) derived from the training data (which makes more sense, since the distributions were computed upon this data), or from the validation?
Please advise.
probability-theory machine-learning bayesian bayes-theorem
asked Dec 18 '18 at 8:06
user3492773user3492773
18914
$endgroup$
Given a training data with 2 categories and validation data.
From the training data, a gaussian distribution is estimated for each category, i.e. the mean and covariance matrix.
The validation is used only for computing the threshold which will distinguish between the two distributions. My question is regarding the prior probabilities since for computing the posterior probability one need to use Bayes Rule which will involve the prior probabilities.
Are the prior probabilities (of the categories) derived from the training data (which makes more sense, since the distributions were computed upon this data), or from the validation?
Please advise.
probability-theory machine-learning bayesian bayes-theorem
probability-theory machine-learning bayesian bayes-theorem
asked Dec 18 '18 at 8:06
user3492773user3492773
18914
asked Dec 18 '18 at 8:06
user3492773user3492773
18914
asked Dec 18 '18 at 8:06
user3492773user3492773
18914
asked Dec 18 '18 at 8:06
user3492773user3492773
18914
asked Dec 18 '18 at 8:06
user3492773user3492773
18914
18914
1
$begingroup$
Shouldn't the prior be chosen before you observe any data? If you are using an empirical Bayes method (en.wikipedia.org/wiki/Empirical_Bayes_method), where you use the data to inform the prior, then you should derive it from the training data, as you shouldn't use information in the validation data to tweak your posterior model before you estimate performance on the validation data. The validation data is a proxy for unseen data - you can't estimate some parameters on unseen data and then use these parameters to predict the unseen data.
$endgroup$
– Alex
Dec 21 '18 at 22:31
add a comment |
1
$begingroup$
Shouldn't the prior be chosen before you observe any data? If you are using an empirical Bayes method (en.wikipedia.org/wiki/Empirical_Bayes_method), where you use the data to inform the prior, then you should derive it from the training data, as you shouldn't use information in the validation data to tweak your posterior model before you estimate performance on the validation data. The validation data is a proxy for unseen data - you can't estimate some parameters on unseen data and then use these parameters to predict the unseen data.
$endgroup$
– Alex
Dec 21 '18 at 22:31
1
1
$begingroup$
Shouldn't the prior be chosen before you observe any data? If you are using an empirical Bayes method (en.wikipedia.org/wiki/Empirical_Bayes_method), where you use the data to inform the prior, then you should derive it from the training data, as you shouldn't use information in the validation data to tweak your posterior model before you estimate performance on the validation data. The validation data is a proxy for unseen data - you can't estimate some parameters on unseen data and then use these parameters to predict the unseen data.
$endgroup$
– Alex
Dec 21 '18 at 22:31
$begingroup$
Shouldn't the prior be chosen before you observe any data? If you are using an empirical Bayes method (en.wikipedia.org/wiki/Empirical_Bayes_method), where you use the data to inform the prior, then you should derive it from the training data, as you shouldn't use information in the validation data to tweak your posterior model before you estimate performance on the validation data. The validation data is a proxy for unseen data - you can't estimate some parameters on unseen data and then use these parameters to predict the unseen data.
$endgroup$
– Alex
Dec 21 '18 at 22:31
add a comment |
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$begingroup$
Shouldn't the prior be chosen before you observe any data? If you are using an empirical Bayes method (en.wikipedia.org/wiki/Empirical_Bayes_method), where you use the data to inform the prior, then you should derive it from the training data, as you shouldn't use information in the validation data to tweak your posterior model before you estimate performance on the validation data. The validation data is a proxy for unseen data - you can't estimate some parameters on unseen data and then use these parameters to predict the unseen data.
$endgroup$
– Alex
Dec 21 '18 at 22:31