Alternating minimization (AltMin) is a generic term for a widely popular approach in non-convex learning: often, it is possible to partition the variables into two (or more) sets, so that the problem is convex/tractable in one set if the other is held fixed (and vice versa). This allows for alternating between optimally updating one set of variables, and then the other. AltMin methods typically do not have associated global consistency guarantees; even though they are empirically observed to perform better than methods (e.g. based on convex optimization) that do have guarantees. In this thesis, we obtain rigorous performance guarantees for AltMin in three statistical learning settings: low rank matrix completion, phase retrieval and learning sparsely-used dictionaries. The overarching theme behind our results consists of two parts: (i) devising new initialization procedures (as opposed to doing so randomly, as is typical), and (ii) establishing exponential local convergence from this initialization. Our work shows that the pursuit of statistical guarantees can yield algorithmic improvements (initialization in our case) that perform better in practice. / text

The two main bottlenecks using deep neural networks are data dependency and training time. This thesis proposes a novel method for weight initialization of the convolutional layers in a convolutional neural network. This thesis introduces the usage of sparse dictionaries. A sparse dictionary optimized on domain specific data can be seen as a set of intelligent feature extracting filters. This thesis investigates the effect of using such filters as kernels in the convolutional layers in the neural network. How do they affect the training time and final performance? The dataset used here is the Cityscapes-dataset which is a library of 25000 labeled road scene images.The sparse dictionary was acquired using the K-SVD method. The filters were added to two different networks whose performance was tested individually. One of the architectures is much deeper than the other. The results have been presented for both networks. The results show that filter initialization is an important aspect which should be taken into consideration while training the deep networks for semantic segmentation.