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I am trying to model a health outcome as a function of climate variables. I have many observations of health outcomes at different times and locations (but NOT a sequence at one location). For each health observation, I have the temperature and rainfall for every month before the health observation up to 24 months. Lets say I have 25,000 observations.

So my outcome is the shape (25000, ) and each is a rate from 0 to 1.

My predictors are the shape (25000, 24, 2), i.e., 24000 observations, over 24 months, for two features.

In trying to get a sense of what neural network architecture I should use, I keep coming across LSTMs. However, most applications seem to use a times series of some training variable (say, stocks prices, rainfall levels, or a sequence of text) to learn trends and the make predictions of that same variable. But I want use weather data to predict a different variable, and my outcome is a single value (not a sequence).

Is LSTM appropriate for this application? If not, what type of architecture should I look into here?

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LSTM (and GRUs, and Recurrent Neural Networks more generally) predict the next item $x_n$ in a sequence X of items $[x_1, ..., x_{n-1}]$, as you mentionned.

However, you can combine them with a feed forward network (as simple as a perceptron), either as a separate layer or a new network, to take the prediction at each set (the $x_i$) and from this $x_i$ predict your two variables/features ($y_{i1}$ and ${y_i2}$).

You would train both layers/networks jointly, one on predicting $x_i$ from $[x_1, ..., x_{i-1}]$ and the other on predicting $y_{i1}$ and $y_{i2}$ from $x_i$.

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