How to model a conditional probability without estimating joint PDF?

Question

I've around 3e3 two-dimensional data points,

   x,   d
1  1, 0.1
2  3, 0.1
3  2, 0.2
4  1, 0.5

range(x) = [-600, 600], range(d) = [0, 1]

We are trying to model d with a probability model. I believe the distribution of d should be dependent on x. So I'm up to model $Pr(d|x)$ rather than $Pr(d)$.

To do this, I am now using kernel density distribution to estimate the joint distribution of $Pr(d, x)$ and divide it by $Pr(x)$.

However, the number of data is enough to model $Pr(d)$ with kernel density estimation while insufficient to model $Pr(d,x)$.

So I'm wondering about this:

Is there any model you suggest that can model d in a conditional way without modeling the joint distrubution?

I have the following thoughts:

I can use SVM to deal with the short of data. However is there a way to train a "conditional SVM"?

Answer 1

You are searching for regression. A wide definition of a regression model is conditional modeling, see Definition and delimitation of regression model. So to model the conditional expectation of $D \mid X$ you can use some kind of regression model, maybe a nonparametric one. You have not given sufficient details or context to say much more ... but for an example of copula regression, see Conditional expectation of two identical marginal normal random variables.

You could simply start with a scatterplot smoother, such as lowess, or at least show us a plot of your data!