My naive (ha!) Gaussian Naive Bayes classifier is too slow
$begingroup$
I am trying to build a film review classifier where I determine if a given review is positive or negative (w/ Python). I'm trying to avoid any other ML libraries so that I can better understand the processes. Here is my approach and the problems that I am facing:
- I mine thousands of film reviews as training sets and classify them as positive or negative.
- I parse through my training set and for each class, I build an array of unique words.
- For each document, I build a vector of TF-IDF values where the vector size is my number of unique words.
- I use a Gaussian classifier to determine: $$P(C_i|w)=P(C_i)P(w|C)=P(C_i)*dfrac{1}{sqrt{2pi}sigma_i}e^{-(1/2)(w-mu_i)^Tsigma_i^{-1}(w-mu_i)}$$ where $w$ is the my document in a vector, $C_i$ is a particular class, $mu_i$ is the mean vector and $sigma_i$ is my covariance matrix.
This approach seems to makes sense. My problem is that my algorithm is much too slow. As an example, I have sampled over 1,500 documents and I have determined over 40,000 unique words. This mean that each of my document vectors has 40,000 entries and if I were to build a covariance matrix, it would have dimensions 40,000 by 40,000. Even I were able to generate the entirety of $sigma_i$, but then I would have to compute the matrix product in the exponent, which will take an extraordinarily long time just to classify one document.
I have experimented with a multinomial approach, which is working well. I very curious on how to make this work more efficiently. I realise the matrix multiplication runtime can't be improved, and I was hoping for insight on how others are able to do this.
Some things I have tried:
- Filtered any stop words (but this still leaves me with tens of thousands of words)
- Estimated $sigma_i$ by summing over a couple of documents.
machine-learning python naive-bayes-classifier tfidf
asked 5 mins ago
Ayumu KasuganoAyumu Kasugano
101
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Ayumu Kasugano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$begingroup$
I am trying to build a film review classifier where I determine if a given review is positive or negative (w/ Python). I'm trying to avoid any other ML libraries so that I can better understand the processes. Here is my approach and the problems that I am facing:
- I mine thousands of film reviews as training sets and classify them as positive or negative.
- I parse through my training set and for each class, I build an array of unique words.
- For each document, I build a vector of TF-IDF values where the vector size is my number of unique words.
- I use a Gaussian classifier to determine: $$P(C_i|w)=P(C_i)P(w|C)=P(C_i)*dfrac{1}{sqrt{2pi}sigma_i}e^{-(1/2)(w-mu_i)^Tsigma_i^{-1}(w-mu_i)}$$ where $w$ is the my document in a vector, $C_i$ is a particular class, $mu_i$ is the mean vector and $sigma_i$ is my covariance matrix.
This approach seems to makes sense. My problem is that my algorithm is much too slow. As an example, I have sampled over 1,500 documents and I have determined over 40,000 unique words. This mean that each of my document vectors has 40,000 entries and if I were to build a covariance matrix, it would have dimensions 40,000 by 40,000. Even I were able to generate the entirety of $sigma_i$, but then I would have to compute the matrix product in the exponent, which will take an extraordinarily long time just to classify one document.
I have experimented with a multinomial approach, which is working well. I very curious on how to make this work more efficiently. I realise the matrix multiplication runtime can't be improved, and I was hoping for insight on how others are able to do this.
Some things I have tried:
- Filtered any stop words (but this still leaves me with tens of thousands of words)
- Estimated $sigma_i$ by summing over a couple of documents.
machine-learning python naive-bayes-classifier tfidf
asked 5 mins ago
Ayumu KasuganoAyumu Kasugano
101
New contributor
Ayumu Kasugano 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 |
$begingroup$
I am trying to build a film review classifier where I determine if a given review is positive or negative (w/ Python). I'm trying to avoid any other ML libraries so that I can better understand the processes. Here is my approach and the problems that I am facing:
- I mine thousands of film reviews as training sets and classify them as positive or negative.
- I parse through my training set and for each class, I build an array of unique words.
- For each document, I build a vector of TF-IDF values where the vector size is my number of unique words.
- I use a Gaussian classifier to determine: $$P(C_i|w)=P(C_i)P(w|C)=P(C_i)*dfrac{1}{sqrt{2pi}sigma_i}e^{-(1/2)(w-mu_i)^Tsigma_i^{-1}(w-mu_i)}$$ where $w$ is the my document in a vector, $C_i$ is a particular class, $mu_i$ is the mean vector and $sigma_i$ is my covariance matrix.
This approach seems to makes sense. My problem is that my algorithm is much too slow. As an example, I have sampled over 1,500 documents and I have determined over 40,000 unique words. This mean that each of my document vectors has 40,000 entries and if I were to build a covariance matrix, it would have dimensions 40,000 by 40,000. Even I were able to generate the entirety of $sigma_i$, but then I would have to compute the matrix product in the exponent, which will take an extraordinarily long time just to classify one document.
I have experimented with a multinomial approach, which is working well. I very curious on how to make this work more efficiently. I realise the matrix multiplication runtime can't be improved, and I was hoping for insight on how others are able to do this.
Some things I have tried:
- Filtered any stop words (but this still leaves me with tens of thousands of words)
- Estimated $sigma_i$ by summing over a couple of documents.
machine-learning python naive-bayes-classifier tfidf
asked 5 mins ago
Ayumu KasuganoAyumu Kasugano
101
New contributor
Ayumu Kasugano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I am trying to build a film review classifier where I determine if a given review is positive or negative (w/ Python). I'm trying to avoid any other ML libraries so that I can better understand the processes. Here is my approach and the problems that I am facing:
- I mine thousands of film reviews as training sets and classify them as positive or negative.
- I parse through my training set and for each class, I build an array of unique words.
- For each document, I build a vector of TF-IDF values where the vector size is my number of unique words.
- I use a Gaussian classifier to determine: $$P(C_i|w)=P(C_i)P(w|C)=P(C_i)*dfrac{1}{sqrt{2pi}sigma_i}e^{-(1/2)(w-mu_i)^Tsigma_i^{-1}(w-mu_i)}$$ where $w$ is the my document in a vector, $C_i$ is a particular class, $mu_i$ is the mean vector and $sigma_i$ is my covariance matrix.
This approach seems to makes sense. My problem is that my algorithm is much too slow. As an example, I have sampled over 1,500 documents and I have determined over 40,000 unique words. This mean that each of my document vectors has 40,000 entries and if I were to build a covariance matrix, it would have dimensions 40,000 by 40,000. Even I were able to generate the entirety of $sigma_i$, but then I would have to compute the matrix product in the exponent, which will take an extraordinarily long time just to classify one document.
I have experimented with a multinomial approach, which is working well. I very curious on how to make this work more efficiently. I realise the matrix multiplication runtime can't be improved, and I was hoping for insight on how others are able to do this.
Some things I have tried:
- Filtered any stop words (but this still leaves me with tens of thousands of words)
- Estimated $sigma_i$ by summing over a couple of documents.
machine-learning python naive-bayes-classifier tfidf
machine-learning python naive-bayes-classifier tfidf
asked 5 mins ago
Ayumu KasuganoAyumu Kasugano
101
New contributor
Ayumu Kasugano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 mins ago
Ayumu KasuganoAyumu Kasugano
101
New contributor
Ayumu Kasugano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 mins ago
Ayumu KasuganoAyumu Kasugano
101
New contributor
Ayumu Kasugano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 mins ago
Ayumu KasuganoAyumu Kasugano
101
asked 5 mins ago
Ayumu KasuganoAyumu Kasugano
101
101
New contributor
Ayumu Kasugano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Ayumu Kasugano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Ayumu Kasugano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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