It really depends on the data you use for analysis. We can't clearly specify that a particular ML algorithm is superior than the rest without knowing the details of dataset. That said, generally we can find that neural network approaches has various advantages when it comes to non-linear applications.
First, I think that you need to explain better your question because is a bit general question.
But I recommend you two types of models, K-NN ( k-nearest neighbors) because in this type of methods spatial information is taken into account and RF (Random forest) because in most cases RF have the best results.
All algorithms belonging to the branch of Machine Learning can be used for making predictions in the form of maps. You can start with the simplest algorithms, such as KNN, Naïve Bayes Classifier, or Logistic Regression (if you need to detect a class as output target), or Classification and Regression Tree (CART). If you want something probably more efficient and reliable, you should implement bagged (like Random Forest) or Boosted (like Boosted Regression Trees) models. The Support Vector Machine also deserves to be implemented in order to avoid the piece-wise function approximation of tree-based algorithms. Finally, if you are interested in maintaining the spatial relationships that exist between inputs, then you should choose a neural network, such as Convolutional Neural Networks.
First of all, you need to be more precise concerning the question you are trying to answer and the data that you have.
That is said, if you want to build a spatial model that predict poverty rate base on some variables, i can suggest geographical weighted regression if spatial dimension matter , or random forest in case all your data are continuous
On the other hand, if you want to predict poverty category like High, Medium or Low, Random Forest can be used as well as ANN
GWR and RF can be easely implemented in software like ArcGIS or R
It really depends on the data you use for analysis. We can't clearly specify that a particular ML algorithm is superior than the rest without knowing the details of dataset. That said, generally we can find that neural network approaches has various advantages when it comes to non-linear applications.