for those who follow.. is this still the case?
i feel like i hear less and less about markov chains
are they still in research and use?
is page rank still the most prominent search algo? does page rank still use markov models?
i always felt these probabilistic models were a conflation of correlation and causation
i feel like i hear less and less about markov chains are they still in research and use?
Markov chains will always be important, because they are a fairly fundamental concept (going back to the early 20th century).
They idea is certainly still widely used: two major classes of applications are Hidden Markov Models (where you attempt to infer the hidden state of a system from observations that depend on the state) [1], and Markov-Chain Monte Carlo (MCMC) [2] (where you sample from a probability distribution function by constructing a markov chain whose equilibrium distibution is that distribution).
is page rank still the most prominent search algo?
PageRank is really a ranking algorithm, rather than a search algorithm. It's been applied to many things other than web searching, and has many variants (e.g. see the review article "PageRank Beyond the Web" [3). That said, Google rankings depend on many things other than PageRank.
i always felt these probabilistic models were a conflation of correlation and causation
What do you mean?
[1]: https://en.wikipedia.org/wiki/Hidden_Markov_model#Applicatio...
> What do you mean?
the example from the post of weather events is a simplified version of what i mean
the collected data expresses that there is a probability of 50/50 rain versus shine
the first string of possible outputs is scattered and more random than the real data, so weights are introduced to nuance to the output and the second string is more closely representative of the data
but this introduces a relative psuedo causation, what the author refers to as stickyness
it's reminiscent of the monty hall problem(o)
altering the state of the model causes its probability to change relative to a specific potential, but only within the limited scope of the probable space
choosing one door causes the probabilities associated with the state to change but the system itself is unchanged by the choice
and what you see with the weather is a simulation of the collected data stead the underlying system, which i feel conflates correlation with causation
Markov chains have never (in the work I have seen at least) tried to imply causation - purely correlation/probability. There is other recent research on causality (see the work of Pearl), but just because one thing very likely follows another doesn't mean the preceding event "caused" the next one, as both events could be side effects from the same (unobserved) root cause.
whereas markov chains start from a place of probability and require it
the construction stage of the markov model agrees with your statement:
> just because one thing very likely follows another doesn't mean the preceding event "caused" the next one
but when in use the current state is the cause of the following state informed by your model
nn can simulate a system whereas an mc can only simulate data from a system
Look at reinforcement learning - loads of stuff making the Markov assumption and doing quite well on complex tasks, though once again this is quite different than a Markov chain.
In theory (at least my opinion on theory) if we had an infinite size "state" it would be possible to just encode all past information in every state, and use Markov rules. It is just not practical, and much easier to extend lookup to multiple timesteps in the past especially with better understanding of optimizing things like RNNs.
Choosing the maximum p(X_t+1 | X_t) does not infer causality in any way in my mind - only saying that given the data when X_t happens, some event at X_t+1 is likely to happen. Classic correlation. I don't see where you are seeing causality in that part. I also don't see a distinction in simulating a system and data from a system - to me it is just that NNs can model much more complex systems than typical Markov chains.
In general I agree with you, but I find these two concepts are much, much more similar than they are different.
i wanted to think about this, and i thought maybe you could have a purely markov model if it were a self constructing self similar model
a markov fractal
at each event the chain reconstructs itself from its new perspective in the fractal
but even done elegantly i think it would be more undue overhead to constantly reconstruct the model than just feeding a self similar model constantly reconstructed inputs, which i see a more clear affinity to neural networks or something wholly different than either
It doesn't necessarily matter whether they're still in use. All of these tools are worth learning, so that if a problem ever comes up that can be solved by markov chaining, you'll know it right away.
Same for all the other tools, though. And there are a lot of them.
What? That paper even says: Stochastic processes of the type described above are known mathematically as discrete Markoff processes and have been extensively studied in the literature; the corresponding footnote says "For a detailed treatment see M. Frechet ... 1938".