# how many parameters do we need to estimate for a general probabilistic model

Its a question from a test in machine learning. I have 3 binary variables x1,x2 and x3 (which means that each one of them can be either 1 or 0), each one of them has a binary output y (can be 0 or 1). for a general probabilistic classifier (it could be any probabilistic model except that its not a model that relies on Naive Bayes), how many parameters do we need in order to estimate it? you cant assume Naive Bayes independency

I saw that the answer is 16 but I dont know why I want to clarify that when I mean parameters I mean which Probability I will need such as P[Y=1] or P[X1=1|Y=1] ect'

• What do you mean by an "output" of a "variable"? Please edit your question to clarify. What do you mean by parameters needed to estimate it? What is your approach to the question? – D.W. Mar 2 at 16:27
• its a probabilistic model so probably I will need to know maybe what is P[Y=1] or P[Y=0] or maybe P[X1=1|Y=0] and ect' – user116449 Mar 2 at 17:27
• What is the probability model? What are the random variables, and what are you assuming about their relationship (are some independent from others, conditionally independent, etc.)? What is the definition of a "general probabilistic classifier"? It would be helpful if you could formalize the situation in a systematic and precise way. – D.W. Mar 2 at 22:24
• a model that relies on probability, from looking how many times x1=1 and how many times x2=0, the random variables are x1, x2, x3 and y and I said specifically that you cant assume that there is independence between the variables, that's the only assumption about the relationship between them – user116449 Mar 3 at 9:29