Should Laplace smoothing use alpha=1?
Laplace smoothing is a technique used to smooth the probabilities of events in a data set, particularly when dealing with sparse data. The alpha parameter in Laplace smoothing is a smoothing factor that determines the strength of the smoothing applied to the probabilities.

When using Laplace smoothing, the choice of alpha depends on the nature of the data and the specific application. In general, an alpha value of 1 is a common default choice and often provides reasonable results. However, the optimal alpha value may vary depending on the data set and the specific problem being addressed.

In some cases, a smaller alpha value may be preferred if the data is already relatively dense, while a larger alpha value may be preferred if the data is very sparse. Ultimately, the choice of alpha will depend on the specific requirements of the problem and may require some experimentation to determine the best value.
If I had a slightly dense dataset, what would you recommend?
If your dataset is slightly dense, meaning that most of the events have already been observed and have non-zero counts, you may not need much smoothing at all. In this case, using a very small alpha value, such as 0.1 or 0.01, may be sufficient to improve the estimates without significantly altering the probabilities.

It's also important to note that Laplace smoothing is just one of many smoothing techniques available, and there may be other techniques that are better suited to your specific dataset and application. Some alternative techniques include Lidstone smoothing and Jelinek-Mercer smoothing, among others.

In general, it's a good idea to experiment with different smoothing techniques and values to determine the optimal approach for your specific problem. Cross-validation and other model evaluation techniques can also be used to assess the performance of different smoothing techniques and values.