# Basis of Binary Classification Probability

I am fairly new to Machine Learning and recently I have built a binary classification model and the model architecture is an MLP with two hidden layers. I am predicting, from a protein sequence, the probability of a residue being mutated ("1") or not ("0"). I had a query regarding the output that we receive after the model predicts the binary classified output.

I can receive the output in two forms from a binary classifier. One is the binary class i.e. "0" or "1" and another is the probability of a residue being a "0" or "1". I wanted to know on what basis the probability is being calculated. For eg, suppose there are 100 students and 4 students pass the exam. Then the probability of passing the exam becomes 4/100 or 0.04. We say that "out of 100 students" 4 passes the exam. Now I have a sequence of amino acids where the total length of the sequence is 700 and my model gives me the probability of each residue being mutated ("1") or not ("0"). Now I get a probability of 0.356 for a particular residue, say at position 10. Now I know that the residue at position 10 has a probability of 0.356 suggesting that it has a 35.6% chance of being mutated. But can I say that "out of 700 residues", the residue at position 10 has a probability of being mutated? Because then the probability will become 1/700 which is less than 0.356.

I get the understanding that the binary classification will have a Bernoulli distribution and every position will have a specific value. My concern is on what basis the probability is being calculated? How does the model calculate the probability of a particular value, say there are total of 100 values?

• Welcome to Cross Validated! Do you understand logistic regression?
– Dave
Nov 10, 2021 at 10:51
• Yes I understand logistic regression but not the very intricate details about it. Nov 10, 2021 at 11:22
• Do you understand maximum likelihood estimation?
– Dave
Nov 10, 2021 at 11:36
• I have read some basics but I don't have a thorough understanding of the method as I am a beginner in the field of ML. Nov 10, 2021 at 12:20
• What about a simpler maximum likelihood estimation, such as the mean of a Gaussian or the probability of a Bernoulli?
– Dave
Nov 10, 2021 at 13:03