The paper deals with a linear regression model. The EM algorithm is popular tool for maximum likelihood estimation of the parameters of regression model. It provides a method of robust regression under the assumption that the disturbances are independent and have identical multivariate t distribution. Previous work focused on the method of maximum likelihood estimation via the EM algorithm under the assumption that the degrees of freedom parameter of the t distribution is a scalar. In this paper, a broader assumption is employed, namely, that the disturbances have a multivariate t distribution with a vector of degrees of freedom. Missing values from the EM algorithm are random matrices. The theoretical results are illustrated in a simulation experiment using several distributions for the error process. Robust procedures are shown to be superior to the method of least squares.
In this paper we consider the Shape Boltzmann Machine(SBM) and its multi-label version MSBM. We present an algorithm for training MSBM using only binary masks of objects and the seeds which approximately correspond to the locations of objects parts.
The Shape Boltzmann Machine (SBM) and its multilabel version MSBM have been recently introduced as deep generative models that capture the variations of an object shape. While being more flexible MSBM requires datasets with labeled parts of the objects for training. In the paper we present an algorithm for training MSBM using binary masks of objects and the seeds which approximately correspond to the locations of objects parts. The latter can be obtained from part-based detectors in an unsupervised manner. We derive a latent variable model and an EM-like training procedure for adjusting the weights of MSBM using a deep learning framework. We show that the model trained by our method outperforms SBM in the tasks related to binary shapes and is very close to the original MSBM in terms of quality of multilabel shapes.