Learning from Multi-View Multi-Way Data via Structural Factorization Machines

Real-world relations among entities can often be observed and determined by different perspectives/views. For example, the decision made by a user on whether to adopt an item relies on multiple aspects such as the contextual information of the decision, the item's attributes, the user's profile and the reviews given by other users. Different views may exhibit multi-way interactions among entities and provide complementary information. In this paper, we introduce a multi-tensor-based approach that can preserve the underlying structure of multi-view data in a generic predictive model. Specifically, we propose structural factorization machines (SFMs) that learn the common latent spaces shared by multi-view tensors and automatically adjust the importance of each view in the predictive model. Furthermore, the complexity of SFMs is linear in the number of parameters, which make SFMs suitable to large-scale problems. Extensive experiments on real-world datasets demonstrate that the proposed SFMs outperform several state-of-the-art methods in terms of prediction accuracy and computational cost.Comment: 10 page

IceCube Non-detection of GRBs: Constraints on the Fireball Properties

The increasingly deep limit on the neutrino emission from gamma-ray bursts (GRBs) with IceCube observations has reached the level that could put useful constraints on the fireball properties. We first present a revised analytic calculation of the neutrino flux, which predicts a flux an order of magnitude lower than that obtained by the IceCube collaboration. For benchmark model parameters (e.g. the bulk Lorentz factor is \Gamma=10^{2.5}, the observed variability time for long GRBs is t_v=0.01 s and the ratio between the energy in accelerated protons and in radiation is \eta_p=10 for every burst) in the standard internal shock scenario, the predicted neutrino flux from 215 bursts during the period of the 40-string and 59-string configurations is found to be a factor of ~3 below the IceCube sensitivity. However, if we accept the recently found inherent relation between the bulk Lorentz factor and burst energy, the expected neutrino flux increases significantly and the spectral peak shifts to lower energy. In this case, the non-detection then implies that the baryon loading ratio should be \eta_p<10 if the variability time of long GRBs is fixed to t_v=0.01 s. Instead, if we relax the standard internal shock scenario but keep to assume \eta_p=10, the non-detection constrains the dissipation radius to be R>4x10^{12} cm assuming the same dissipation radius for every burst and benchmark parameters for fireballs. We also calculate the diffuse neutrino flux from GRBs for different luminosity functions existing in the literature. The expected flux exceeds the current IceCube limit for some luminosity functions, and thus the non-detection constrains \eta_p<10 in such cases when the variability time of long GRBs is fixed to t_v=0.01 s.Comment: Accepted by ApJ, 14 pages, 5 figures, typos corrected, scheduled for the June 10, 2012, v752 - 1 issu