# Time series forecasting for multiple objects with common features

I know the title of this question may raise an eyebrow, but I can't find the technical terms to define or investigate the actual problem.

To demonstrate my problem with a simple hypothetical scenario: Let's say you have dataset pretraining to fruits!

• The dataset contains $$N$$ fruits

• Each fruit has properties $${\{p}\}$$, for example, $$p_1$$ is type, $$p_2$$ is color, $$p_3$$ flavour. It is important to note that (i) these properties are communal across all fruits (all fruits have the properties above) and (ii) these properties are constant for each individual fruit (for a fruit,$${\{p}\}_n$$ stays constant over time).

• Each fruit has a time series $$\{W_t\}_n$$ which relate to, for example, measured weight over time. It is important to note that the fruits aren't measured at regular, or the same intervals. Therefore, each fruit in the dataset will have a different weight time series.

• Therefore the aggregated dataset will have $$\sum_{n=1}^{N} dim(\{W_t\}_n)$$ observations

• Let's assume there is some hidden correlation between the weight for a fruit $$\{W_t\}_n$$ over time and the fruit properties $${\{p}\}$$.

So the problem is: What model(s) can we use that it is able to predict the next weight values $$\{W_{(t+1)}\}$$? More formally stated $$f(\{p\}_n,\{W_t\}_n) = \{W_{(t+1)}\}_n$$ ?

The challenges here is:

• We want to maintain the 'uniqueness' of each fruit, that is, we can't simply say if two fruits have the same properties $${\{p}\}$$ then they will have the same weight changes over time. To conceptualize this, imagine things happen to certain fruits during their life time, the model is supposed to remember this has happened to those specific fruits and incorporate that into the prediction.
• Our measurement device was bought at IKEA and sometimes it provides inaccurate readings, so we can't expect a linear or smooth weight time series per fruit.
• We don't have a lot of weight measurements, let's say 10 on average, but we have a lot of fruits, let's say 100 000.

I have some experience with vanilla and stacked LSTM's. However, I struggle to consolidate my understanding of LSTM's in the abovementioned scenario.

Thank you for reading. I hope this will get the creative juices flowing, or give you a fun mental challenge at least.

• Hello. You can use latex/mathjax on this site, so I would suggest that you edit your post to format your math symbols with it.
– nbro
Jul 24 at 11:45
• Oh thank you, I was unaware of that. Jul 24 at 13:57