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Let's say I am trying to predict whether a cat will be adopted, and I have found the ratio purred_when_petted / total_times_petted aka p / n to have predictive power. However, for some cats I have much more data than others. For example:

Cat A:
    p: 1
    n: 1

Cat B:
    p: 9
    n: 10

I would like my neural network to consider that there is more data for Cat B and possible consider that it is more likely to be adopted. How should I tell it about both the ratio and the sample size?

Here are some ideas I have so far:

  1. Use ratio as input feature and don't worry about sample size
  2. Use ratio and sample size as separate input features
  3. Use $p$ and $n$ as separate input features, and let the NN do what it wants with them.
  4. Use an average of the cat statistic and the average population statistic over all $M$ cats weighted by number of samples: $$ x_i = \beta * (\frac{p_i}{n_i}) + (1-\beta) * (\frac{1}{M}\sum_{j=1}^{M}\frac{p_j}{n_j}) $$ where $\beta \in [0,1]$ is an increasing function of sample size $n_i$.
  5. Use a Binomial proportion confidence interval

Is there a standard way to do this? I am most interested in neural networks but also open to advice relevant to any other type of model.

Note that I also have other categorical and numeric features such as color and age that also need to be fed in to my model.

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