Saturday, 25 November 2017

Healthcare as an algebraic system

Throughout the history of homo sapiens, wars, famine and diseases are the main killing machines.  For the first time, we have recently defeated famine and lost appetite for wars. We now turn our attention to the most basic need of all: health. Who doesn't want to live a healthy life and die in peace?

But how do understand a healthcare system, from a modeler point of view? Healthcare is a complex business. A battle field that can determine outcome of election, which may change the course of history.

I've always speculated that healthcare is an algebraic system. Medical objects such as disease, treatment, medication, theater, department and even doctor can be represented as algebraic objects. Processes, protocols, rules and the like can be defined as algebraic operators.

One simplest object representation is vector. And this is very powerful, given the fact that most data manipulation machineries are developed for vectors. Matricestensors, graphs and other more sophisticated representations are much less developed.

The algebraic view of things in the world has been there for long. Recently it comes in "embedding" of the objects, from word to sentence to document to graph to anything2vec.

In our recent work "Finding Algebraic Structure of Care in Time: A Deep Learning Approach", we take this view to its full. Diseases and treatments are embedded into vectors. A hospital visit is also a vector, which is computed as a difference of illness vector and treatment vector. This gives rise to simple modelling of disease-treatment motifs, and visit-visit transitions. The entire temporal progression can be modelled as recurrence of simple linear matrix-vector multiplications, or a more sophisticated LSTM.

Once the health state at each visit can be determined, decision making can be acted upon, based on the entire trajectory, with attention to the recent events, or in absence of any time-specific knowledge, using content-based addressing.

After all, healthcare is like a computer execution of a health program, which is jointly determined by the three processes: the illness, the care and the recording. It is time for a Turing machine.

Stay tuned. The future is so bright that you need to wear sun glasses.

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