Deep Convolutional Mixture Density Networks
The deep convolutional mixture density network (DCMDN) is a feed-forward neural network model, built combining a convolutional neural network (CNN) and a mixture density network (MDN).
The presented software realizes an architecture to extract photometric redshift probability density functions (PDFs) directly from images, without need of pre-classification and pre-processing of the data. Such a model is able to make a better use of the information contained in the data and give superior performance respect to other models commonly used in literature. Moreover, the DCMDN is a very general model, and can be used to solve several regression problems. In fact, the algorithm is highly flexible and the user can define its own architecture, changing number and type of the layers and several hyperparameters, in order to build the structure that is more suitable for the problem considered.
In particular, the proposed model uses by default the continuous rank probability score (CRPS) as loss function, but other functions are available (e.g. the log-likelihood). The estimates are expressed as Gaussian mixture models, representing the probability density functions (PDFs) in the redshift space. In addition to the traditional scores, the continuous ranked probability score (CRPS) and the probability integral transform (PIT) can be calculated as performance criteria.
The code is developed in Python using the library Theano and can run in CPU or GPU (suggested) environments.