Is MCMC (or any sampling for that matter) explainable?
Recently, at an interview, I was asked if you use MCMC to build Maximum a posteriori (MAP), and use it for an inference, will the system you create have an explainability?
Now, explainability is somewhat vague in the way people are using it in every possible context, in my opinion. My definition of explainability is: Given a model $Z = P(X, Y)$ and an unseen data point $x_i in X$, if we are able to generate a graph of underlying causal structure that is - why we reached conclusion $y_i in Y$, given $(Z, x_i)$, and with what probability we are certain that $y_i$ is the right answer, then and only then, system can be said to have explainability property.
I explained this to interviewer. He did not agree, his point was MCMC is a bayesian system, and all the bayesian systems are explainable by their very nature.
I fail to understand, how sampling, in general, can be explainable? If we are drawing bunch of samples AT RANDOM from a distribution, and are computing an expected value of MAP, if something has an inherent randomness, that cannot be explained. Isn't this one of the characteristics of randomness in the first place?
We discussed exact same thing about (Loopy) Belief Propagation, and I think that is explainable. Interviewer was making a point that if LBP is explainable, why MCMC is not? I had no clue why he said so, in my best understanding LBP is based on factor graphs (not necessary to have a causal structure in the first place)
What would you argue?
probability intuition bayesian sampling
asked Nov 27 '18 at 2:11
Adorn
1086
add a comment |
Recently, at an interview, I was asked if you use MCMC to build Maximum a posteriori (MAP), and use it for an inference, will the system you create have an explainability?
Now, explainability is somewhat vague in the way people are using it in every possible context, in my opinion. My definition of explainability is: Given a model $Z = P(X, Y)$ and an unseen data point $x_i in X$, if we are able to generate a graph of underlying causal structure that is - why we reached conclusion $y_i in Y$, given $(Z, x_i)$, and with what probability we are certain that $y_i$ is the right answer, then and only then, system can be said to have explainability property.
I explained this to interviewer. He did not agree, his point was MCMC is a bayesian system, and all the bayesian systems are explainable by their very nature.
I fail to understand, how sampling, in general, can be explainable? If we are drawing bunch of samples AT RANDOM from a distribution, and are computing an expected value of MAP, if something has an inherent randomness, that cannot be explained. Isn't this one of the characteristics of randomness in the first place?
We discussed exact same thing about (Loopy) Belief Propagation, and I think that is explainable. Interviewer was making a point that if LBP is explainable, why MCMC is not? I had no clue why he said so, in my best understanding LBP is based on factor graphs (not necessary to have a causal structure in the first place)
What would you argue?
probability intuition bayesian sampling
asked Nov 27 '18 at 2:11
Adorn
1086
add a comment |
Recently, at an interview, I was asked if you use MCMC to build Maximum a posteriori (MAP), and use it for an inference, will the system you create have an explainability?
Now, explainability is somewhat vague in the way people are using it in every possible context, in my opinion. My definition of explainability is: Given a model $Z = P(X, Y)$ and an unseen data point $x_i in X$, if we are able to generate a graph of underlying causal structure that is - why we reached conclusion $y_i in Y$, given $(Z, x_i)$, and with what probability we are certain that $y_i$ is the right answer, then and only then, system can be said to have explainability property.
I explained this to interviewer. He did not agree, his point was MCMC is a bayesian system, and all the bayesian systems are explainable by their very nature.
I fail to understand, how sampling, in general, can be explainable? If we are drawing bunch of samples AT RANDOM from a distribution, and are computing an expected value of MAP, if something has an inherent randomness, that cannot be explained. Isn't this one of the characteristics of randomness in the first place?
We discussed exact same thing about (Loopy) Belief Propagation, and I think that is explainable. Interviewer was making a point that if LBP is explainable, why MCMC is not? I had no clue why he said so, in my best understanding LBP is based on factor graphs (not necessary to have a causal structure in the first place)
What would you argue?
probability intuition bayesian sampling
asked Nov 27 '18 at 2:11
Adorn
1086
Recently, at an interview, I was asked if you use MCMC to build Maximum a posteriori (MAP), and use it for an inference, will the system you create have an explainability?
Now, explainability is somewhat vague in the way people are using it in every possible context, in my opinion. My definition of explainability is: Given a model $Z = P(X, Y)$ and an unseen data point $x_i in X$, if we are able to generate a graph of underlying causal structure that is - why we reached conclusion $y_i in Y$, given $(Z, x_i)$, and with what probability we are certain that $y_i$ is the right answer, then and only then, system can be said to have explainability property.
I explained this to interviewer. He did not agree, his point was MCMC is a bayesian system, and all the bayesian systems are explainable by their very nature.
I fail to understand, how sampling, in general, can be explainable? If we are drawing bunch of samples AT RANDOM from a distribution, and are computing an expected value of MAP, if something has an inherent randomness, that cannot be explained. Isn't this one of the characteristics of randomness in the first place?
We discussed exact same thing about (Loopy) Belief Propagation, and I think that is explainable. Interviewer was making a point that if LBP is explainable, why MCMC is not? I had no clue why he said so, in my best understanding LBP is based on factor graphs (not necessary to have a causal structure in the first place)
What would you argue?
probability intuition bayesian sampling
probability intuition bayesian sampling
asked Nov 27 '18 at 2:11
Adorn
1086
asked Nov 27 '18 at 2:11
Adorn
1086
asked Nov 27 '18 at 2:11
Adorn
1086
asked Nov 27 '18 at 2:11
Adorn
1086
asked Nov 27 '18 at 2:11
Adorn
1086
1086
add a comment |
add a comment |
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