WTOnlineLinearRegression

What

WTOnlineLinearRegression allows you to perform linear regression on one-dimensional data, with or without uncertainties in the dependent quantity, and it does so by updating its internal state in constant time on the number of data points, for each new data point, resulting in an overall linear time complexity.

In other words, it performs online regression, updating its internal state without recomputing everything from scratch on every addition, which would use the entire data set every time a new data point is added, hence incurring on an overall quadratic runtime.

You can also remove data points that have been previously added to the data set. Removing, however, runs in linear time on the size of the data set, per removal, since it must scan the data set to guarantee that the data point being removed was once added.

Additionally, WTOnlineLinearRegression optionally keeps a history of every data point addition or removal, as full snapshots of the regression at the time each data point was added or removed.

Usage

An Observation instance represents a pair of values (x,y) where the dependent value, y, may also have some uncertainty associated with it, in the form of its variance (or, equivalently, its standard deviation).

Given a series of N such observations, {(xi, yi, dyi), 1 ≤ i ≤ N}, one might be interested in finding the straight line y = a * x + b that best fits those observations. That’s the task of the LinearRegression object and since it’s possible that the y values in the actual observations could be uncertain, the estimated slope a and the estimated intercept b will, themselves, have some uncertainty.

In other words, the best line that fits the series of observations will have an equation of the form y = (a ± da) * x + (b ± db), where I’m using d• to refer to the standard deviation of the quantity in front of it.

LinearRegression performs the regression and computes the slope a ± da, the Y-intercept b ± db, three measures of error (mean total squared error, mean squared residual error, and mean squared regression error), and the coefficient of fitness known as r-squared. You may also inspect various sums that are used to compute those quantities.

You may also optionally request LinearRegression to record the history of changes, as data points are added or removed from the data set. Each entry in the history is a full snapshot of the regression at the time the entry was processed.

Documentation

Full documentation is provided in the source files. Additionally, the main mathematical results used to implement WTOnlineLinearRegression are available in a pdf document here.

Demo app

Check out the demo app.

Tests

WTOnlineLinearRegression is verified by 134 tests, with 100% coverage.

Changelog

Changes to WTOnlineLinearRegression are listed here.

Installation

WTOnlineLinearRegression is available through CocoaPods. To install it, simply add the following line to your Podfile:

ruby pod "WTOnlineLinearRegression"

Author

Wagner Truppel, [email protected]

License

WTOnlineLinearRegression is available under the MIT license. See the LICENSE file for more info.