Smoothing With Split Linear Fits

Improving non-linear fits

In this notes we describe an algorithm for non-linear fitting which incorporates some of the features of linear least squares into a general minimum χ fit and provide a pure Python implementation of the algorithm. It consists of the variable projection method (varpro), combined with a Newton optimizer and stabilized using the steepest descent with an adaptative step. The algorithm includes a te...

Multi-item sales forecasting with total and split exponential smoothing

Efficient supply chain management relies on accurate demand forecasting. Typically, forecasts are required at frequent intervals for many items. Forecasting methods suitable for this application are those that can be relied upon to produce robust and accurate predictions when implemented within an automated procedure. Exponential smoothing methods are a common choice. In this empirical case stu...

REACT Fits to Linear Models and Scatterplots

REACT estimators for the mean of a linear model involve three steps: transforming the model to a canonical form that provides an economical representation of the unknown mean vector, estimating the risks of a class of candidate linear shrinkage estimators, and adaptively selecting the candidate estimator that minimizes estimated risk. When the mean vector is smooth, the desired canonical form o...

Smoothing of Piecewise Linear Paths

The pointwise traversal of a given path is a popular task in the area of robotics, e.g. in mobile, industrial or surgical robotics. The easiest method to describe paths is by a sequence of linear segments, and for many tasks the precision of a path approximated by linear segments is sufficient. The movements to be accomplished by a mobile robot or the robot’s end-effector are described by a seq...

On Optimal Linear Smoothing Theory