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I am confused as to what I should be using to derive an appropriate metric. The objective here is to find out if knowing if a person has X, Y, Z can help indicate if they are in the binary bucket A or B.

The total number of people in the experiment is let's say: 10000, of those 8000 are in A the others (2,000) are in B. [This is mutually exclusive] and there might or might not be a class imbalance

I have ten thousand features that are not mutually exclusive, A and B can or cannot have some feature like HNS or FEX. For example,

variable: Number in A that have variable: Number in B that have it:
1. HNS: 1,000: 500:
2. FEX: 100: 200:

and like that....

So I want to see, Given a new person that has the variable what are the probability that I can categorize them in A or B?

I can run a logistic regression using but this not a traditional problem. I guess I can do a multinomial logistic regression but exclude the changes that not in A or not in B. Alternatively, I was thinking of getting probabilities and I am confused which method is preferable.

For example, looking at HNS, 1000/1500 people have it, therefore there is a 2/3 chance from A and 1/3 chance from B. Alternatively, one can say that out of the 8,000 people from A only 1,000 have it ==> 12.5% and out of the 2,000 people in B, 500/2000 have it ==> 25%, therefore for a new person that has HNS, you should classify them as 12.5%/37.5% = 1/3 for A and 25%/37.5% = 2/3 for B.

A little confused on how to approach this problem and if this is more so a simple percentage or bayesian problem

I can run a logistic regression using but this not a traditional problem. I guess I can do a multinomial logistic regression but exclude the changes that not in A or not in B. Alternatively, I was thinking of getting probabilities and I am confused which method is preferable.

For example, looking at HNS, 1000/1500 people have it, therefore there is a 2/3 chance from A and 1/3 chance from B. Alternatively, one can say that out of the 8,000 people from A only 1,000 have it ==> 12.5% and out of the 2,000 people in B, 500/2000 have it ==> 25%, therefore for a new person that has HNS, you should classify them as 12.5%/37.5% = 1/3 for A and 25%/37.5% = 2/3 for B.

output would be a probability score for A or B given variable numbers like HNS.

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  • 3
    $\begingroup$ What speaks against logistic regression? Seems like it would fit your task $\endgroup$ – emilaz Apr 8 at 20:24
  • $\begingroup$ Do you have the individual values of the 10,000 features for each of the people? Or do you only have overall ratios of features for each of groups A and B, as the answer from @jhill515 assumes? $\endgroup$ – EdM Apr 8 at 21:36
  • $\begingroup$ Jhill does a great job of describing this. Based on your description, it doesn't seem like your dataset is a set of feature vectors; rather it's simply a description of the ratios appearing in the population describing the original dataset. Standard statistical learning methods aren't going to help because you're already dealing with statistic descriptors instead of raw data. Particularly, this dataset cannot describe the occurrence of covariance. $\endgroup$ – Hider1466 Apr 10 at 6:16
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Based on your description, it doesn't seem like your dataset is a set of feature vectors; rather it's simply a description of the ratios appearing in the population describing the original dataset. Standard statistical learning methods aren't going to help because you're already dealing with statistic descriptors instead of raw data. Particularly, this dataset cannot describe the occurrence of covariance.

I'd first seek to achieve some form of dimensionality reduction. Starting with only the ratios, this is going to be weak: features whose ratios are close to 1.0 or 0.0 clearly contain the most descriptor "information", and you could build a decision tree based upon that. A hand-built one should focus on the features with the strongest descriptors first, and weakest descriptors last.

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