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I am using a convolutional neural network to predict the number of occurrences of a certain pattern in time series data. Since there might be potentially any count of such patterns in a time series, I am dealing with regression, rather than with classification. Normally, for regression, mean squared error (MSE) is used as loss and MSE and mean absolute error (MAE) are used as evaluation metrics. However, if I use them in my network, they give me float numbers for both predictions and evaluation metric values. This is useful, but I would ideally like to have integer numbers for both predictions and evaluation metric values, since the occurrence of patterns is count data.

From my statistics classes I remember that the poisson function is often used for modelling count data. However, my teacher always called the poisson distribution "the distribution of rare events", meaning that it assumes that a low number of occurrences of the event is more likely than a large number of occurrences. This, however, is not necessarily true for my problem: The patterns I am looking for might occur never, but also 5, 10, 20 or 30 times within a time series.

For this problem, which loss and evaluation metric is suitable in order to get integer numbers for predictions on test data?

As an example, this is the part of my Keras model where the issue is rooted:

model.compile(optimizer=Adam(learning_rate = 0.001), loss = 'poisson', metrics = ['mae', 'mse']) 

Note: Using the poisson loss in combination with mae and mse as metrics yielded very bad results. I could not find any metric that worked well in combination with the poisson loss. But maybe you know one, or you can recommend me a better loss-metric-combination for the problem.

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  • $\begingroup$ Welcome to Cross Validated! Why do you want the evaluation metrics to give integer values? $\endgroup$
    – Dave
    Commented May 16, 2022 at 17:07
  • $\begingroup$ @Dave You are right, it does not make sense. I edited my post. $\endgroup$
    – lonyen11
    Commented Jun 7, 2022 at 9:59

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The Poisson distribution is one integer-valued distribution among many alternatives. You can experiment with alternative losses.

The model's predictions for the Poisson model is the conditional expectation, so there's no reason for it to be restricted to integers in general. To simplify, consider that the average of $(1,2,3,4)$ is not an integer, even though each of the elements is an integer. Naturally, you can do stuff like rounding to obtain integers -- whether or not it's the best choice depends on your goals and how you define "best."

The metric isn't the reason that you have poor fit, it's just a thing that measures how good the fit is. A better model will improve the fit (tautologically).

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  • $\begingroup$ Thank you. Very helpful. But is it true that the Poisson distribution should predominantly be used for events which occur rarely? If yes, what does rarely mean then? In some cases 1 occurrence can be considered as rare, in others maybe 10 or 100. $\endgroup$
    – lonyen11
    Commented Jun 7, 2022 at 10:04
  • $\begingroup$ It sounds like you have a new question. The best way to get started answering it is to do a search (here's one to get you started stats.stackexchange.com/…) and if can't find the answer you're looking for, then ask a new question using the ASK QUESTION button. $\endgroup$
    – Sycorax
    Commented Jun 7, 2022 at 14:12

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