An interesting, rather open-ended question. The fact that we don't really have a proper understanding of the mechanism that results in the taste, combined with the fact that taste is also different from individual to individual makes it borderline impossible to set up a good physical model for this question.
However, this has never stopped cheminformaticians before. There's a vast majority of properties, more and less abstract ones, that can be correlated to known properties of the molecules (so-called descriptors). For example you will find a lot of equation that let's you characterize the efficiency of a drug molecule if you know for example its size, water/octanol solubility ratio, acidity constants and similar descriptors. This problem of finding drug efficiency from these rather simple quantities shows that predicting taste should indeed be possible.
So how could someone do this? First of all, since you don't have a physical/chemical theory, you need a somewhat reliable dataset - this is actually available. If you have your data ready, you should select a set of good descriptors, either by using serious statistical tests, or using your own intuition. Then you need to establish a relationship between the descriptors and the predicted properties. This step is usually done using a variety of machine learning tools.
In fact, a quick Googling shows me that this approach had recently been taken up in the literature, and taste prediction of a chemical compound does exist: look here, or here for example.
I hope I explained the idea in layman's terms well enough that you can understand the point of these publications as well as search for similar ones yourself.