Recipe/Rephrasing

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What a recipe exactly is, seems sufficiently defined. But how can we determine this recipe.

Black box

The problem is that a product is a black box. We are looking at the output of a factory, but we do not know what goes on inside. Image a factory that makes Apple syrups. If we can look at the factory through binoculars we can see farmers with pallets full of apples go inside and trucks with port of apple syrup going out. By smartly counting what goes in and comes out we make a recipe estimation for the apple syrups in that factor. If we could observe more of such factories we could estimate the average recipe of apple syrup.

Unfortunately we cannot observe these factories. We only have the results of various products from different factories. And we have some characteristics of the products in the form of ingredients and nutritional values. The ingredients of a product are pretty vague and lack details. The amount of apples used in the various product might vary wildly.

In order to get a feel for the amount of apples we could assume a specific kind of apple and use its nutritional values. But what apple to use? And what kind of data do we have for apples? Only for the apple pulp? Or does it include the skin and will we get a number for the amount of raw apples as they come from the tree?

Factoring

We only know that an ingredient is a factor in a product. But not which ingredient exactly, nor how large the factor is. If we use a single ingredient to find the amount, we might be wildly off. We can only look at this from a statistical point of view, by correlating multiple ingredients with multiple products of the same category. This will give an average amount and thus an average recipe.

If we look at a single product we might say how well it fits to an average recipe for a product category.

Rephrased problem

We can rephrase the recipe problem as:

What is amount of ingredients necessary to explain the nutritional values of a product category based on the dominant ingredients and the nutritional values of the corresponding ingredients category?

The emphasis in this definition lies on:

  • categories for products and ingredients;
  • dominant ingredients;
  • independence between product category and ingredient categories;
  • statistical problem;