incrmrmse

Compute a moving root mean squared error (RMSE) incrementally.

For a window of size W, the root mean squared error (also known as the root mean square error (RMSE) and root mean square deviation (RMSD)) is defined as

upper R upper M upper S upper E equals StartRoot StartFraction 1 Over upper W EndFraction sigma-summation Underscript i equals 0 Overscript upper W minus 1 Endscripts left-parenthesis y Subscript i Baseline minus x Subscript i Baseline right-parenthesis squared EndRoot

Usage

var incrmrmse = require( '@stdlib/stats/incr/mrmse' );

incrmrmse( window )

Returns an accumulator function which incrementally computes a moving root mean squared error. The window parameter defines the number of values over which to compute the moving root mean squared error.

var accumulator = incrmrmse( 3 );

accumulator( [x, y] )

If provided input values x and y, the accumulator function returns an updated root mean squared error. If not provided input values x and y, the accumulator function returns the current root mean squared error.

var accumulator = incrmrmse( 3 );

var r = accumulator();
// returns null

// Fill the window...
r = accumulator( 2.0, 3.0 ); // [(2.0,3.0)]
// returns 1.0

r = accumulator( -1.0, 4.0 ); // [(2.0,3.0), (-1.0,4.0)]
// returns ~3.61

r = accumulator( 3.0, 9.0 ); // [(2.0,3.0), (-1.0,4.0), (3.0,9.0)]
// returns ~4.55

// Window begins sliding...
r = accumulator( -7.0, 3.0 ); // [(-1.0,4.0), (3.0,9.0), (-7.0,3.0)]
// returns ~7.33

r = accumulator( -5.0, -3.0 ); // [(3.0,9.0), (-7.0,3.0), (-5.0,-3.0)]
// returns ~6.83

r = accumulator();
// returns ~6.83

Notes

  • Input values are not type checked. If provided NaN or a value which, when used in computations, results in NaN, the accumulated value is NaN for at least W-1 future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.
  • As W (x,y) pairs are needed to fill the window buffer, the first W-1 returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.

Examples

var randu = require( '@stdlib/random/base/randu' );
var incrmrmse = require( '@stdlib/stats/incr/mrmse' );

var accumulator;
var v1;
var v2;
var i;

// Initialize an accumulator:
accumulator = incrmrmse( 5 );

// For each simulated datum, update the moving root mean squared error...
for ( i = 0; i < 100; i++ ) {
    v1 = ( randu()*100.0 ) - 50.0;
    v2 = ( randu()*100.0 ) - 50.0;
    accumulator( v1, v2 );
}
console.log( accumulator() );