# Introduction#

Cyclic Boosting is a simple yet powerful machine learning method for structured data. It is robust and fast, features individual explainability of predictions (in the style of Generalized Additive Models) and good predictability of rare observations, takes into account multiplicative effects in a natural way, supports categorical features of high cardinality, and enables highly complex models by means of interaction terms.

Furthermore, model building with Cyclic Boosting is very convenient:

few hyperparameters to be tuned

not much data pre-processing needed

easily configurable for different data types

supporting missing values in input data

assisting model development with individual analysis plots for features

Instead of estimating parameters in the sense of coefficients in linear regression or weights in neural networks, Cyclic Boosting estimates factors (or summands in additive regression mode) for each bin of the different features. This allows a natural interpretation of each individual prediction in terms of the different feature values, i.e., individual explainability.

The Cyclic Boosting base algorithm is quite generic and can be adapted for both regression (in several modes) and classification tasks.

## Regression#

The two main regression modes are multiplicative regression and additive regression mode. Topology-wise, the first resembles Poisson regression, i.e., a Generalized Linear model with a log link function, covering the target range \([0, \infty]\) and supporting multiplicative dependencies, while the latter is similar to linear regression, covering the target range \([-\infty, \infty]\) and supporting additive dependencies. It should be noted though that, in contrast to Generalized Linear Models, Cyclic Boosting in either mode enables highly non-linear models, similar to Generalized Additive Models. Instead of minimizing the mean squared error as objective function in each feature bin (as it is the case for the modes mentioned above), it is also possible to use another loss function (also possible for classification tasks). An important example for this is optimizing for an arbitrary quantile (e.g., the median), aka quantile regression. By means of several estimated quantiles, one can also approximate full individual probability distributions via quantile matching (especially Quantile-Parameterized Distributions).

## Classification#

The classification mode resembles logistic regression (Generalized Linear Model with logit link) and predicts probabilities, i.e., covering the target range \([0, 1]\). It supports multiplicative dependencies between features and target odds.

## The Story behind Cyclic Boosting#

The idea of many of the building blocks of Cyclic Boosting, e.g., binning and smoothing, originated from an algorithm called NeuroBayes, a feed-forward neural network with lots of pre-processing steps, developed by Professor Michael Feindt and some students from his experimental particle physics group at University of Karlsruhe back in the 90s. (The Bayes part comes from the interpretation of network outputs as a posteriori probabilities in classificiation tasks, the usage of Bayesian statistics for regularization, and taking into account a priori knowledge in the form of inclusive distributions.)

In a spin-off company called PhiI-T, which was later rebranded to Blue Yonder, NeuroBayes was then used for various business problems, one of which was demand forecasting for retailers. Although the NeuroBayes model was pretty successful for this use case, it exhibited several shortcomings like lack of individual explainability of predictions, difficulties to predict rare observations, or dedicated treatment of mulitplicative effects. Therefore, Cyclic Boosting (to be exact, its multiplicative regression mode) was developed as successor algorithm to overcome these issues. Although initially, Cyclic Boosting was developed specifically for retail demand forecasting, it is a general-purpose algorithm that can also be employed for many other use cases, including classification tasks.

Because demand forecasts are often used as input for order optimization (replenishment), the prediction of full probability distributions, rather than mere point estimates (typically the conditional mean for most machine learning methods), is desirable to properly minimize realistic cost functions. For that reason, a width mode was added to Cyclic Boosting to estimate individual negative binomial distributions.

The price of products is one of the main influencing factors of demand, and estimating individual price-demand elasticities can improve demand models significantly. And the price-demand elasticities are also directly helpful for another important use case in retail, namely dynamic pricing. For these reasons, an exponential elasticity mode was added to Cyclic Boosting.

Later, yet another background subtraction mode, was added for the use case of customer targeting, where a specific action like coupon sending only affects a small portion of customers and the bulk of unaffected customers needs to be statistically removed to identify causal effects.

There is a bunch of people who contributed to the development of the Cyclic Boosting library over the years. Without guarantee of completeness, here is a list in alphabetic order: Bruno Daniel, Michael Feindt, Martin Hahn, Uwe Korn, Holger Peters, Thomas Pfaff, Jörg Rittinger, Daniel Stemmer, Felix Wick, Moritz Wolf