I'm very new to machine learning, and have a problem I'm trying to solve but don't know where to get started.

I've got a set of feature vectors that are "matched pairs," so

D={(x1,y1), (x2,y2), ..., (xn,yn)}

where each xi and yi are vectors of some length. xi and yi have the same length, but different pairs of xi and yi may have different lengths.

I want to have some algorithm learn the difference of x's and y's, such that, if I have another vector, I want to predict whether it's more like x's or more like y's.

Can someone point me in the right direction that I might try? I'm not sure what types of algorithms or methods I should be looking into, so even just the names of appropriate algorithms or methods would be great.

  • $\begingroup$ This seems a little unusual. Can you provide a simple example? $\endgroup$ – gung - Reinstate Monica Jan 16 '16 at 1:28
  • $\begingroup$ An example would be a study of genetic mutations. So x's and y's are genetic sequences, where y is a mutation of x. For example: x1=ACCTGG, and y1=GGCTGG, so the "AC" in x1 mutates to become "GG" in y1. In this example, I would be trying to find if there is some pattern in the mutation so that I can determine if a new sequence is likely to be x (unmutated) or y (mutated). $\endgroup$ – leontp587 Jan 16 '16 at 17:54

What you are asking is not ML. In your case, if you have a lot of $x$'s and $y$'s, then simply determine the correlation matrix for all pairwise combinations of all of your $x$'s and $y$'s. Then look at the values and statistical significance of each correlation coefficient. Your question really is asking if a given $y$ is associated more strongly with a given $x$.

  • $\begingroup$ Correlation testing is one valid approach, but it's certainly not the only one. This is a pretty open-ended problem. $\endgroup$ – shadowtalker Jan 16 '16 at 7:42
  • $\begingroup$ @LEP: I'm not sure if I understand, I'm asking if I have a new vector that I don't know whether belongs to X or Y, then I'm trying to determine whether it's more likely to belong to X or belong to Y? I'm not trying to ask if a given y is associated more strongly with a given x. $\endgroup$ – leontp587 Jan 16 '16 at 18:01
  • $\begingroup$ Ok, then how about replacing each base with 1,2,3,4 and then determine the Euclidean distance, d(x,y), between the two vectors? The same vectors will give you a distance of zero. You can also weight the distance and reward with a 1 if the vectors are the same and near zero if very different by using: exp(-d(x,y)). This called a radial basis function, RBF. Why are you not using a pairwise alignment for two DNA sequences? $\endgroup$ – user32398 Jan 17 '16 at 13:28

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