Learning to Recommend with Missing Modalities (LRMM)
Multimodal learning has shown promising performance in content-based recommendation due to the auxiliary user and item information of multiple modalities such as text and images. However, the problem of incomplete and missing modality is rarely explored and most existing methods fail in learning a recommendation model with missing or corrupted modalities. In this paper, we propose LRMM, a novel framework that mitigates not only the problem of missing modalities but also more generally the cold-start problem of recommender systems. We propose modality dropout (m-drop) and a multimodal sequential autoencoder (m-auto) to learn multimodal representations for complementing and imputing missing modalities. Extensive experiments on real-world Amazon data show that LRMM achieves state-of-the-art performance on rating prediction tasks. More importantly, LRMM is more robust to previous methods in alleviating data-sparsity and the cold-start problem. …

Self-weighted Multiview Metric Learning (SM2L)
With the development of multimedia time, one sample can always be described from multiple views which contain compatible and complementary information. Most algorithms cannot take information from multiple views into considerations and fail to achieve desirable performance in most situations. For many applications, such as image retrieval, face recognition, etc., an appropriate distance metric can better reflect the similarities between various samples. Therefore, how to construct a good distance metric learning methods which can deal with multiview data has been an important topic during the last decade. In this paper, we proposed a novel algorithm named Self-weighted Multiview Metric Learning (SM2L) which can finish this task by maximizing the cross correlations between different views. Furthermore, because multiple views have different contributions to the learning procedure of SM2L, we adopt a self-weighted learning framework to assign multiple views with different weights. Various experiments on benchmark datasets can verify the performance of our proposed method. …

Multilevel Networks Analysis
Described in Lazega et al (2008) <doi:10.1016/j.socnet.2008.02.001> and in Lazega and Snijders (2016, ISBN:978-3-319-24520-1). …

Horseshoe Regularization
Feature subset selection arises in many high-dimensional applications in machine learning and statistics, such as compressed sensing and genomics. The $\ell_0$ penalty is ideal for this task, the caveat being it requires the NP-hard combinatorial evaluation of all models. A recent area of considerable interest is to develop efficient algorithms to fit models with a non-convex $\ell_\gamma$ penalty for $\gamma\in (0,1)$, which results in sparser models than the convex $\ell_1$ or lasso penalty, but is harder to fit. We propose an alternative, termed the horseshoe regularization penalty for feature subset selection, and demonstrate its theoretical and computational advantages. The distinguishing feature from existing non-convex optimization approaches is a full probabilistic representation of the penalty as the negative of the logarithm of a suitable prior, which in turn enables an efficient expectation-maximization algorithm for optimization and MCMC for uncertainty quantification. In synthetic and real data, the resulting algorithm provides better statistical performance, and the computation requires a fraction of time of state of the art non-convex solvers. …