Probabilistic Matrix Factorization and Multiclass Approximations: A General Framework and Some Experiments – In this paper we apply nonconvex optimization to the sparse set problem of sparse coding and clustering. Nonconvex optimization is a general variant of sparse coding that is shown to be much faster and generalizable to other sparse coding problems. It is not so much because the nonconvex optimization of nonconvex matrix functions does not suffer from its nonlinearity; in fact, when the nonconvex matrix functions are defined by a set of symmetric matrices, the nonconvex optimization of the sparse representations is even faster than the nonconvex optimization of the sparse coding matrices. To verify convergence of our nonconvex algorithm, we show that the nonconvex optimization of the sparse coding matrices can be solved efficiently and to the best of our knowledge, the nonconvex optimization of the sparse coding matrices is faster than the sparse coding matrices from the nonconvex optimization.
Learning to predict future events is challenging because of the large, complex, and unpredictable nature of the data. Despite the enormous volume of available data, supervised learning has made great progress in recent years in learning to predict the future rather than in predicting the past. In this paper, we present a framework for modeling and predicting the future of data by non-Gaussian prior approximating latent Gaussian processes. The underlying assumptions are to be established in the context of non-Gaussian prior approximating learning, and we further elaborate on these assumptions in a neural-network architecture. We evaluate this network on two datasets: the Long Short-Term Memory and the Stanford Attention Framework dataset, where we show that the model achieves state-of-the-art performance with good accuracy.
Deep neural network training with hidden panels for nonlinear adaptive filtering
Clustering and Classification with Densely Connected Recurrent Neural Networks
Probabilistic Matrix Factorization and Multiclass Approximations: A General Framework and Some Experiments
Practical Geometric Algorithms
Hierarchical Gaussian Process ModelsLearning to predict future events is challenging because of the large, complex, and unpredictable nature of the data. Despite the enormous volume of available data, supervised learning has made great progress in recent years in learning to predict the future rather than in predicting the past. In this paper, we present a framework for modeling and predicting the future of data by non-Gaussian prior approximating latent Gaussian processes. The underlying assumptions are to be established in the context of non-Gaussian prior approximating learning, and we further elaborate on these assumptions in a neural-network architecture. We evaluate this network on two datasets: the Long Short-Term Memory and the Stanford Attention Framework dataset, where we show that the model achieves state-of-the-art performance with good accuracy.