tanh_saturation#

pymc_marketing.mmm.transformers.tanh_saturation(x, b=0.5, c=0.5)[source]#

Tanh saturation transformation.

\[f(x) = b \tanh \left( \frac{x}{bc} \right)\]

The tanh saturation function has a nice property that is useful when setting priors. The slope of the function when x is zero is \(\frac{1}{c}\). This means that you can set a prior by considering how many units of media are required to acquire the first customer. Unlike most other saturation functions, the slope at 0 is independent of the saturation point.

(Source code, png, hires.png, pdf)

../../_images/pymc_marketing-mmm-transformers-tanh_saturation-1.png

Parameters:

xtensor: Input tensor.
bfloat, by default 0.5: The saturation point. It represents the maximium number of customers that could be acquired through this channel at any point time. Must be non-negative.
cfloat, by default 0.5: Initial cost per user. Larger values represent less efficient channels. Must be non-zero.

Returns:

tensor: Transformed tensor.

References

See https://www.pymc-labs.com/blog-posts/reducing-customer-acquisition-costs-how-we-helped-optimizing-hellofreshs-marketing-budget/ # noqa: E501