Predicting with both continuous and categorical features Some predictive modeling techniques are more designed for handling continuous predictors, while others are better for handling categorical or discrete variables.  Of course there exist techniques to transform one type to another (discretization, dummy variables, etc.).  However, are there any predictive modeling techniques that designed to handle both types of input at the same time without simply transforming the type of the features?  If so, do these modeling techniques tend to work better on data for which they are a more natural fit?
The closest thing that I know of would be that usually decision trees handle discrete data well and they handle continuous data without requiring an up front discretization.  However, this isn't quite what I was looking for since effectively the splits on continuous features are just a form of dynamic discretization.
For reference, here are some related, non-duplicate questions:


*

*How should decision tree splits be implemented when predicting continuous variables?

*Can I use multiple regression when I have mixed categorical and continuous predictors?

*Does it ever make sense to treat categorical data as continuous?

*Continuous and Categorical variable data analysis
 A: As far as I know, and I've researched this issue deeply in the past, there are no predictive modeling techniques (beside trees, XgBoost, etc.) that are designed to handle both types of input at the same time without simply transforming the type of the features.
Note that algorithms like Random Forest and XGBoost accept an input of mixed features, but they apply some logic to handle them during split of a node. 
Make sure you understand the logic "under the hood" and that you're OK with whatever is happening in the black-box.
Yet, distance/kernel based models (e.g., K-NN, NN regression, support vector machines) can be used to handle mixed type feature space by defining a “special” distance function. Such that, for every feature, applies an appropriate distance metric (e.g., for a numeric feature we’ll calculate the Euclidean distance of 2 numbers while for a categorical feature we’ll simple calculate the overlap distance of 2 string values). 
So, the distance/similarity between user $u_1$ and $u_2$ in feature $f_i$, as follows:
$d(u_1,u_2 )_{f_i}=(dis-categorical(u_1,u_2 )_{f_i} $ if feature $f_i$  is categorical,
$d(u_1,u_2 )_{f_i}=dis-numeric(u_1,u_2 )_{f_i} $ if feature $f_i$  is numerical. and 1 if feature $f_i$ is not defined in $u_1$ or $u_2$.
Some known distance function for categorical features:


*

*Levenshtien distance (or any form of "edit distance")

*Longest common subsequence metric

*Gower distance

*And more metrics here


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*Boriah, S., Chandola and V., Kumar, V. (2008). Similarity measures for categorical data: A comparative evaluation. In: Proceedings of the 8th SIAM International Conference on Data Mining, SIAM, p. 243-254.


A: I know it's been a while since this question was posted, but if you're still looking at this problem (or similar ones) you may want to consider using generalized additive models (GAM's). I'm no expert, but these models allow you to combine different models to create a single prediction. The process used to find coefficients for the models you put in solves for all of them at once, so you can send a generalized additive model your favorite model for categorical predictors and your favorite model for continuous predictors and get a single model that minimizes RSS or whatever other error criterion you want to use. 
Off the top of my head, the only software package which I know has an implementation of GAM's is the language R, but I'm sure there are others. 
A: While discretization transforms continous data to discrete data it can hardly be said that dummy variables transform categorical data to continous data. Indeed, since algorithms can be run on computers there can hardly be a classificator algorithm which does NOT transform categorical data into dummy variables.
In the same sense a classificator ultimately transforms it predictors into a discrete variable indicating class belonging (even if it outputs a class probability, you ultimately choose a cutoff). De facto many classificators like logistic regression, random forest, decision trees and SVM all work fine with both types of data. 
I suspect it would be hard to find an algorithm which works with continous data but cannot handle categorical data at all. Usually I tend to find it makes more difference on what type of data you have on the left side of your model.
A: This is a deep philosophical question which is commonly addressed from the statistical as well as machine learning end. Some say, categorizing is better for discrete to categorical indicator, so that the packages can easily digest the model inputs. Others say, that binning can cause information loss, but however categorical variables can/must be converted to {1,0} indicator variables leaving out the last class for the model residuals.  
The book - Applied linear regression (Kutner et al. )  mentions about the logic of introducing indicator variables in the model in the first few chapters. There may be other similar text too.
My take on this maybe a bit too far-fetched: If we imagine the categorical variables like blocks in an experimental design, the indicator variable is a natural extension to non-experiment based data analysis. With respect to data mining algorithms (decision tree families), categorization is inevitable (either manually or automated-binning) which has to be fed to the model.  
Hence, there may not be a model that is specialized for numerical as well as categorical variables in the same way (without binning-numerical or using indicators-categorical). 
