# Language impediments to inference of real-time streaming models

I’m debating whether to attempt a Julia solution to a particular “streaming” inference problem in which a global data model is constantly being updated with new data. I’m new to the language, but there seems to be language-related complications; Julia seems to favor statically-defined, rather than dynamically-generated, functions. I am aware Julia’s metaprogramming facilities, but would rather not delve into that if I can avoid it.

Here’s the problem. I want to perform inference on a global model (a parametric likelihood function) of real-time streaming data which is being modified in real time as follows. Incoming data is clustered; each cluster defines a parametric likelihood function of its constituent data; the global likelihood function is updated by multiplication by the likelihoods of the new data clusters. For example: Initial global model f_0(x|\theta); new-data likelihood g(y|\theta); updated likelihood is f(x,y|\theta)=f_0(x|\theta)\cdot g(y|\theta).

Questions:

1. How to do inference on the current model? This seems problematic since the global likelihood function cannot be recompiled in the same Julia session. (True?) How then do I take code that performed inference against f_0 and point it at f(x,y)? What is the Julian approach? Use Revise? Rename the global model whenever I update with new data? My concern there is having potentially thousands of global models sitting around in memory indefinitely.
2. Should I be worried about the latency of compiling the updated model? In the example above, f_0(x|\theta) may be very complex; g is relatively simple by comparison. When Julia compiles the new global model, f(x,y), does it efficiently reuse the previously compiled f_0, or is the latter recompiled along with g?
3. Does anyone know of an existing Julia project doing something like this already?

Thanks!

I would use an approach with higher order functions, chaining together the likelihood incrementally.

You can define X as [x, y1, y2, y3] and define f(X) = f0(X[1]) * prod(g, X[2:end]). If you have more data, just push! it to X and call f again on X.

Edit: although if you are multiplying many such terms, I would work in terms of the log and add instead to avoid underflow.

Edit 2: to avoid re-computing terms, you can make f a callable struct with a cache field and save the results of f0(X[1]) and every computed value in the cache field in f. Alternatively, there is Memoization.jl to memoize the functions automatically.

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I did several projects related to BNP and dynamic compositional likelihoods. In my cases those compositions usually get quite complicated as they are also nested and, therefore, I always used an approach similar to what @mohamed82008 suggested for you in (2). But there are many approaches in Julia to do this and I in my experience Julia is one of the more suited language for this.

Thank you! Have you, by chance, used this approach with automatic-differentiation packages, in particular ReverseDiff? Do they play nicely together?

Thanks very much. Can you describe or point me to examples of the other approaches you alluded to?

ReverseDiff should be fine yes. If it is not, please open an issue with a minimal working example.