class static
analytics.TimeWindowGk

Source: analyticsdoc.js:2778

Greenwald - Khanna algorithm for quantile estimation on sliding windows. Given a cumulative probability p, the algorithm returns the approximate value of the p-th quantile of all the values in a sliding window.

The algorithm works by keeping a summary of buckets. Each bucket summarizes a range of values. Through the run of the algorithm, new buckets are created and old ones merged. To allow for the computation on a sliding window, each bucket uses an Exponential Histogram structure to remember how many values it summarizes.

It is summarized in: "Online Algorithm for Approximate Quantile Queries on Sliding Windows" http://dl.acm.org/citation.cfm?id=2954329

The error is not bounded by the absolute value of the output, but by the error in rank of the output element. For instance, if we have 100 elements and query the median, we could get the 48-th (p=0.48), 50-th (p=0.5), 51-th (p=0.51), etc. element.

The algorithms error is bounded by two factors. The first is the quantile estimation factor quantileEps occurs because of the summary structure and defines the maximum size of the buckets. The second type of error countEps occurs because of the Exponential Histograms inside the buckets.

The worst-case error is bounded by (quantileEps + 2*countEps + O(countEps^2)), although in practice the error is lower.

This version of the algorithm uses a time-based fixed duration sliding window.

Methods

partialFit(timestamp[, value])
save(fout)
getParams()
predict(p)

new TimeWindowGk([arg])

Example 

// import modules
var qm = require('qminer');
var fs = qm.fs;
var analytics = qm.analytics;

// create the default object
var gk = new analytics.TimeWindowGk({
    window: 5,
    quantileEps: 0.001,
    countEps: 0.0005
});

// create the data used for calculating quantiles
var inputs = [10, 1, 2, 8, 9, 5, 6, 4, 7, 3];
var times = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];

// fit the model
for (var i = 0; i < inputs.length; i++) {
    gk.partialFit(times[i], inputs[i]);
}

// make the prediction for the 0.1 quantile
var prediction = gk.predict(0.1);
// save the model
gk.save(fs.openWrite('gk.bin')).close();
// open the gk model under a new variable
var gk2 = new analytics.TimeWindowGk(fs.openRead('gk.bin'));

Parameter

Name Type Optional Description

arg

(module:analytics~TimeWindowGkParam or module:fs.FIn)

Yes

Construction arguments. There are two ways of constructing:
1. Using the module:analytics~TimeWindowGkParam object,
2. using the file input stream module:fs.FIn.

Methods

static
partialFit(timestamp[, value]) → module:analytics.TimeWindowGk

Adds a new observation to the window. The window is updated with the provided timestamp, all records which fall outside the new window are forgotten.

Example 

var qm = require('qminer');

var gk = new qm.analytics.TimeWindowGk({
    window: 1000*60*60*24*2    // window is 2 days
});
gk.partialFit(new Date('2017-06-06'), 1.0);
gk.partialFit(new Date('2017-06-07').getTime(), 1.0);
gk.partialFit(new Date('2017-06-08'));  // only move the time window, the first value is forgotten

Parameters

Name Type Optional Description

timestamp

(number or Date)

 

time of the observation

value

number

Yes

the observation
Returns

module:analytics.TimeWindowGk reference to self

static
save(fout) → module:fs.FOut

Saves the objects state into a binary file.

Example 

var qm = require('qminer');
var fs = qm.fs;
var gk = new qm.analytics.TimeWindowGk({
    window: 100    // window is 2 days
});
gk.partialFit(0, 1.0);
gk.partialFit(1, 1.0);
gk.partialFit(2, 1.0);
gk.partialFit(3, 1.0);
gk.partialFit(4, 1.0);
// save the model
gk.save(fs.openWrite('gk.bin')).close();
// open the model under a new variable
var gk = new analytics.TimeWindowGk(fs.openRead('gk.bin'));

Parameter

Name Type Optional Description

fout

module:fs.FOut

 

the output stream
Returns

module:fs.FOut the output stream fout

getParams() → module:analytics~TimeWindowGkParam

Returns the models' parameters as a JavaScript object (JSON). These parameters are the same as are set through the constructor.

Returns

module:analytics~TimeWindowGkParam The construction parameters.

var qm = require('qminer'); var fs = qm.fs; var analytics = qm.analytics;

// create the default object var gk = new analytics.TimeWindowGk({ window: 5, quantileEps: 0.001, countEps: 0.0005 });

// create the data used for calculating quantiles var inputs = [10, 1, 2, 8, 9, 5, 6, 4, 7, 3]; var times = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];

// fit the model for (var i = 0; i < inputs.length; i++) { gk.partialFit(times[i], inputs[i]); } var params = gk.getParams();

console.log(params.window); console.log(params.quantileEps); console.log(params.countEps);

predict(p) → number

Given an input cumulative probability, returns a quantile associated with that probability (e.g. for input 0.5 it will return the median).

Example 

var qm = require('qminer');

var gk = new qm.analytics.TimeWindowGk({
    window: 100    // window is 2 days
});
gk.partialFit(0, 1.0);
gk.partialFit(1, 1.0);
gk.partialFit(2, 1.0);
gk.partialFit(3, 1.0);
gk.partialFit(4, 1.0);

console.log(gk.predict(0.01));   // prints the first percentile
console.log(gk.predict(0.25));   // prints the first quartile
console.log(gk.predict(0.5));    // prints the median

Parameter

Name Type Optional Description

p

number

 

cumulative probability between 0 and 1 (both inclusive)
Returns

number quantile associated with p