My understanding of the problem of induction is this. You want to hypothesise that the future is like the past (let us call this hypothesis H), and so justify the scientific practice of making inferences about the future from present data. However Hume points out that just because in the past the future was like the past doesn't mean this will continue to be true, and to assume otherwise is to assume the very thing you're trying to prove. Thus any apparent evidence that the future will be like the past is really circular and so doesn't count as evidence.
But it seems to me this is not really problematic, and what it really shows is that a certain kind of reductionism is false. What Hume's argument shows is that "the data don't speak for themselves," i.e. you always need to assume some hypotheses to have any idea what counts as evidence for or against something. If you assume H, one finds that the evidence, interpreted according to H, fits H, and so overall you have a "coherent picture." In other words, it implies a certain form of coherentism and/or Quinean holism. This doesn't mean that we can assume any hypothesis we like, because there is no guarantee that any hypothesis or set of hypotheses will form such a coherent picture. The reason Hume wasn't able to produce any evidence that the future will be like the past is he imagined that you could evaluate evidence for a single hypothesis without making any assumptions at all, which seems to me to be the kind of reductionism Quine attacked in Two Dogmas.
Do philosophers agree with this interpretation?