Helper library to perform operations on Observable Markov Models (OMMs). Markov chains are really useful.
Can be used from node or the browser.
Editorial: I actually use this library for some projects, so there are touches that make it more practical than most. For example, charts have names for the columns because the order really doesn't matter. Names are also useful to link up to other math models or to real events. It much more practical to link the click event to a column actually named 'click' rather than row and column 7. I could have used a look up table, but then I'm wrapping my math in more math.
Warning: I haven't got the speed requirements up to where they should be yet. Using these for AI is only useful for time steps up to 10. If you're doing more than that, you should probably be trying to calculate the limit/isotope of a particular outcome instead. I talk more about that in the examples below.
#markov.Chain
Create an instance of a Chain with a transition chart to calculate the probabilities of states.
##Example 1
var chart = {
'a': {'a': 0.2, 'b': 0.65, 'c': 0.15},
'b': {'a': 0.1, 'b': 0.8, 'c': 0.1},
'c': {'a': 0.7, 'b': 0.25, 'c': 0.05}
};
chain = new Chain(chart);
chain.getProbabilityOf('a', 'b'); //0.65 65%
chain.getProbabilityOf('a', 'b', 'a'); //0.065 6.5%
chain.getProbabilityOf('a', 'b', 'c', 'a'); //0.0455 4.55%##Example 2
In this example, we're walking through each possibility between start to end, which moves toward an isotope. The isotope forms because we're adding all the possible paths between start and end. Since we can move between all of them, the start and end points matter less as we add more steps.
chain.getProbabilityFromTo('c', 'a', 1); //0.7
chain.getProbabilityFromTo('c', 'a', 2); //0.19999999999999998 20%
chain.getProbabilityFromTo('c', 'a', 3); //0.19949999999999998 19%
chain.getProbabilityFromTo('c', 'a', 4); //0.18197499999999997 18%
chain.getProbabilityFromTo('c', 'a', 5); //0.18197499999999997 18%
chain.getProbabilityFromTo('c', 'a', 6); //0.18197499999999997 18%
chain.getProbabilityFromTo('a', 'b', 1); //0.65
chain.getProbabilityFromTo('a', 'b', 2); //0.6875
chain.getProbabilityFromTo('a', 'b', 3); //0.712125
chain.getProbabilityFromTo('a', 'b', 4); //0.7146687500000002 71.5%
chain.getProbabilityFromTo('a', 'b', 5); //0.7146687500000002 71.5%
chain.getProbabilityFromTo('a', 'b', 6); //0.7146687500000002 71.5%
chain.getProbabilityFromTo('a', 'b', 7); //0.7146687500000002 71.5%##Following the example from Wikipedia
// with a transition matrix like this:
var transition = {
'bull market': {
'bull market': 0.9,
'bear market': 0.075,
'stagnant market': 0.025
},
'bear market': {
'bull market': 0.15,
'bear market': 0.8,
'stagnant market': 0.05
},
'stagnant market': {
'bull market': 0.25,
'bear market': 0.25,
'stagnant market': 0.5
}
};
// three time periods later, we should get this:
var threeTimePeriodsLater = {
'bull market': {
'bull market': 0.7745,
'bear market': 0.17875,
'stagnant market': 0.04675
},
'bear market': {
'bull market': 0.3575,
'bear market': 0.56825,
'stagnant market': 0.07425
},
'stagnant market': {
'bull market': 0.4675,
'bear market': 0.37125,
'stagnant market': 0.16125
}
};
var chain = new Chain(transition),
ticks = 3;
// calculate!
var result = {
'bull market': {
'bull market':
chain.getProbabilityFromTo('bull market', 'bull market', ticks),
'bear market':
chain.getProbabilityFromTo('bull market', 'bear market', ticks),
'stagnant market':
chain.getProbabilityFromTo('bull market', 'stagnant market', ticks)
},
'bear market': {
'bull market':
chain.getProbabilityFromTo('bear market', 'bull market', ticks),
'bear market':
chain.getProbabilityFromTo('bear market', 'bear market', ticks),
'stagnant market':
chain.getProbabilityFromTo('bear market', 'stagnant market', ticks)
},
'stagnant market': {
'bull market':
chain.getProbabilityFromTo('stagnant market', 'bull market', ticks),
'bear market':
chain.getProbabilityFromTo('stagnant market', 'bear market', ticks),
'stagnant market':
chain.getProbabilityFromTo('stagnant market', 'stagnant market', ticks)
}
};
// the expected result and our result are equal
// expected result is rounded to 5 decimal places, so we have to round as well
expect(Chain.chartEqualWithin(result, threeTimePeriodsLater, 5)).to.be.true;
#markov.Tokenizer
Creating transition charts by hand is annoying, so here is a useful tool to do it for you. Give the tokenizer your separator as regex and a string (or a stream), and it will count each state transition between tokens and put the totals into a chart. This is useful for importing files, database results, or network requests, and it is optimized for loading large data-sets, as long as you can hold the resulting chart in memory.
It does not normalize the transition chart. Data often comes from multiple sources, so we need to wait until we're done gathering information. When all state transitions have been counted, then you can normalize the data.
##Example of importing data into a chart
var tokenizer = new Tokenizer({separator: /\W/});
var chart = tokenizer.readString('beep beep boop'); //give string
console.log(chart); // outputs {"beep": { "beep": 1, "boop": 1 }}##Another example of importing data into a chart
var mock = new MockReadable(['beep beep boop']);
var tokenizer = new Tokenizer({separator: /\W/}); //divide by whitespace
tokenizer.readStream(mock, function (err, chart) {
console.log(chart); // outputs {"beep": { "beep": 1, "boop": 1 }}
});##Normalization
var markov = require('general-markov');
var stream = new MockReadable(['beep beep boop']);
var tokenizer = new markov.Tokenizer(Tokenizer.Defaults.Words);
tokenizer.readStream(stream, function (err, result) {
var chain = new markov.Chain(result).normalize();
console.log(chain.transitions); // {"beep": { "beep": 0.5, "boop": 0.5 }}
});##To DO
- Add support for Hidden Markov Models
- Add support for ANOVAs to look for better data to use as columns
- Add support for more matrix math