The primary task in supervised learning is to construct a model from training data that generalize well to new inputs. State-of-the-art methods based on ReLU neural networks have a continuous and piecewise-linear (CPWL) input-output relation. The aim of this project is to develop an alternative approach for constructing a CPWL model for 3-dimensional data. For this purpose, we define a learning problem on a controlled search space spanned by piecewise-linear basis functions (box splines). Moreover, we add a sparsity-promoting regularizer that favors solutions with few facets. The student will implement the method and compare it with neural networks and kernel methods on 3d data. The project requires familiarity with basic notions of machine learning, as well as Python.