For non-parametric regression which one has better interpretation and properties, GAM or quantile regression? As in the topic. I want to interpret data for which I have no clues about the distribution. It's neither count, percentage, continuous. I don't want any transformations. Instead I would like to analyze it with either GAM or quantile regression. Regarding the quantile regression, the interpretation is quite simple. With GAM it's not so simple. Do you have any recommendations on choosing between the two?
What I search is an interpretable non-parametric model. By interpretable I mean something like this: "For unit change in the predictor X, ceteris paribus, the conditional expected value / median will increase/decrease..."
I know how to interpret the quantile regression, but I am not sure how to interpret the GAM, namely the predictors treated with smoothing function. Is there a similar kind of interpretation of the GAMs?
If so, which method would you recommend?
 A: In a GAM, you model the condition mean (and derive or possibly estimate any other parameters required, depending on how strict your definition of a GAM is) given the stated/assumed distribution of the response. Your comment

With GAM - I'm not sure how to interpret the "smoothed" predictors. Both [GAM and QR] seem to not assume any underlying conditional distribution of the response.

is incorrect in so far as it pertains to GAMs — we categorically require the user to specify the conditional distribution of the response (via the family argument typically in R).
What the GAM does is relax the linearity assumption of linear regression (or linearity on the link scale in GLMs) in a flexible way so that one can learn the shape of the relationship between the response and covariate(s) without having to specify the actual functional form of the relationship oneself.
To interpret the fitted smooth function(s) in a GAM, you would need to evaluate the model at the covariate values of interest, say $x_1 = 10$ and $x_2 = 11$ (holding other covariates, if present, at some representative values) to get the estimated change in $y$ for a unit increase in $x$. You can get a feel for this by looking at the plot(s) of the smooth function(s) in the model, but if you want a specific value for the change in $y$ you need to state the pair of covariate values over which you want to know the change in $y$.
Whilst we typically model only the conditional mean in a GAM, we do derive the full conditional distribution of the response. If you are interested in an extreme quantile of this distribution, you might be better off directly estimating the specific conditional quantile that is of interest. Likewise, if you want to assume nothing about the conditional distribution of the response but simply model the conditional "middle", then estimating the conditional median of the data might be more appropriate.
You can certainly combine both features of GAMs and QR, but estimating the conditional quantile(s) using smooth functions of covariates: the quantreg package and the qgam package are two examples that implement quantile GAMs (the gamlss and VGAM packages also can do quantile regression and the latter does expectiles too).
It seems, to me at least, that you are conflating features of GAMs and QR and it is that which is causing confusion. Basically;


*

*GAMs estimate the full conditional distribution of the response using a combination of smooth and parametric effects, where as

*QR estimates one or more conditional quantiles of the response using a combination of smooth and parametric effects.

