# Does optimizing the parameters in an exponential smoothing model constitute “learning”?

I'm having an argument at work with a colleague who's saying that we need to use machine learning models instead of the current exponential smoothing models (Holt, Holt-Winters) for demand forecasting, because according to him, our current software doesn't do any "learning" from data the way an ML method does.

The software we use has optimization routines that find the optimal $$\alpha$$, $$\beta$$ and $$\gamma$$ for a Holt-Winters model that we use for demand forecasting, by minimizing the BIC. As far as I know this constitutes "learning" in the Machine Learning sense, albeit a simplified version of learning compared to what a deep learning model or xgboost model would learn. But it is nonetheless learning.

He is insisting that it doesn't constitute learning, because it is not incrementally improvable the way learning in a more complex model is (for example a NNet can learn more after 2000 epochs than it can after 100 epochs, etc...).

So does optimizing the parameters of an exponential smoothing model (or ARIMA model) using the BIC (or the AIC) constitute proper "learning" in the ML sense of the word?

• This is the problem with ML there's a lot of advertising talk...'learning' sounds a lot cooler than model estimation. So I would agree with you. You could use gradient descent to estimate the parameters,and then this would constitute learning for your colleague. But the results would most likely be worse. You could presumably replace the bic optimisation with crossvalidation and that could perform better. – seanv507 Oct 14 '18 at 9:02

## 1 Answer

Honestly, this is quite a funny question!

My two cents:

Usually, one might use exponential smoothing to obtain a "mean" series or a trend and it has a well defined structure. A lot of times, the smoothing parameter is chosen by eye-balling a graph, to satisfy some kind of a need the modeller has in his mind (e.g. perhaps s/he needs the smoothing to account for just the time series trend, other times, they might also be interested in capturing the seasonality, etc.). Here, perhaps there's no explicit "learning" (does human enforced learning count? Hmmmm...)

On the other hand, one might express a clear objective function (e.g. minimising the sum of squared forecast errors $$\sum (y_i - \hat y_{i|i-1})^2$$), and here, parameters are optimised to minimize the objective. I'd argue this is would be "learning" in the traditional sense.

Minimising any objective, by definition, will improve the "loss" or whatever the objective is, so the argument that there's no incremental "gain" doesn't hold up.

Regarding the AIC/BIC, aren't all of these some kind of penalised likelihood approximations? You're maximising some kind of a penalised likelihood, in other words, minimising the negative of a penalised likelihood, which is the objective here.