In this paper, we propose a novel mixture of expert architecture for learning polyhedral classifiers. We learn the parameters of the classifierusing an expectation maximization algorithm. Wederive the generalization bounds of the proposedapproach. Through an extensive simulation study, we show that the proposed method performs comparably to other state-of-the-art approaches.

Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying graphical models from data. Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. Useful structured graphs include the multi-component graph, bipartite graph, connected graph, sparse graph, and regular graph. In general, structured graph learning is an NP-hard combinatorial problem, therefore, designing a general tractable optimization method is extremely challenging. In this paper, we introduce a unified graph learning framework lying at the integration of Gaussian graphical models and spectral graph theory. To impose a particular structure on a graph, we first show how to formulate the combinatorial constraints as an analytical property of the graph matrix. Then we develop an optimization framework that leverages graph learning with specific structures via spectral constraints on graph matrices. The proposed algorithms are provably convergent, computationally efficient, and practically amenable for numerous graph-based tasks. Extensive numerical experiments with both synthetic and real data sets illustrate the effectiveness of the proposed algorithms. The code for all the simulations is made available as an open source repository.

Face Anti-spoofing gains increased attentions recently in both academic and industrial fields. With the emergence of various CNN based solutions, the multi-modal(RGB, depth and IR) methods based CNN showed better performance than single modal classifiers. However, there is a need for improving the performance and reducing the complexity. Therefore, an extreme light network architecture(FeatherNet A/B) is proposed with a streaming module which fixes the weakness of Global Average Pooling and uses less parameters. Our single FeatherNet trained by depth image only, provides a higher baseline with 0.00168 ACER, 0.35M parameters and 83M FLOPS. Furthermore, a novel fusion procedure with ``ensemble + cascade'' structure is presented to satisfy the performance preferred use cases. Meanwhile, the MMFD dataset is collected to provide more attacks and diversity to gain better generalization. We use the fusion method in the Face Anti-spoofing Attack Detection Challenge@CVPR2019 and got the result of 0.0013(ACER), 0.999(TPR@FPR=10e-2), 0.998(TPR@FPR=10e-3) and 0.9814(TPR@FPR=10e-4).

Networks are powerful data structures, but are challenging to work with for conventional machine learning methods. Network Embedding (NE) methods attempt to resolve this by learning vector representations for the nodes, for subsequent use in downstream machine learning tasks. Link Prediction (LP) is one such downstream machine learning task that is an important use case and popular benchmark for NE methods. Unfortunately, while NE methods perform exceedingly well at this task, they are lacking in transparency as compared to simpler LP approaches. We introduce ExplaiNE, an approach to offer counterfactual explanations for NE-based LP methods, by identifying existing links in the network that explain the predicted links. ExplaiNE is applicable to a broad class of NE algorithms. An extensive empirical evaluation for the NE method `Conditional Network Embedding' in particular demonstrates its accuracy and scalability.

Previous studies on stochastic primal-dual algorithms for solving min-max problems with faster convergence heavily rely on the bilinear structure of the problem, which restricts their applicability to a narrowed range of problems. The main contribution of this paper is the design and analysis of new stochastic primal-dual algorithms that use a mixture of stochastic gradient updates and a logarithmic number of deterministic dual updates for solving a family of convex-concave problems with no bilinear structure assumed. Faster convergence rates than $O(1/\sqrt{T})$ with $T$ being the number of stochastic gradient updates are established under some mild conditions of involved functions on the primal and the dual variable. For example, for a family of problems that enjoy a weak strong convexity in terms of the primal variable and has a strongly concave function of the dual variable, the convergence rate of the proposed algorithm is $O(1/T)$. We also investigate the effectiveness of the proposed algorithms for learning robust models and empirical AUC maximization.

Most of real-world graphs are {\em dynamic}, i.e., they change over time. However, while the regression problem has been studied for {\em static} graphs, it has not been investigated for {\em dynamic} graphs, yet. In the current paper, first we present the notion of {\em update-efficient matrix embedding} that defines the conditions sufficient for a matrix embedding to be used for the dynamic graph regression problem, efficiently. We also show that some of the standard matrix embeddings, e.g., the (weighted) adjacency matrix, satisfy these conditions. Then, we prove that given an $n \times m$ update-efficient matrix embedding, after an update operation in the graph, the optimal solution of the graph regression problem for the revised graph can be computed in $O(nm)$ time. In particular, using the (weighted) adjacency matrix as the matrix embedding of $G$, it takes $O(n^2)$ time to update the optimal solution, where $n$ is the number of nodes of the revised graph. To the best of our knowledge, this is the first result on updating the solution of the graph regression problem, in a time considerably less than the time of computing the solution from the scratch. Finally, we study a generalization of the dynamic graph regression problem and show that it can be solved in $O(nm + mm')$ space.

Most of the existing recommender systems use the ratings provided by users on individual items. An additional source of preference information is to use the ratings that users provide on sets of items. The advantages of using preferences on sets are two-fold. First, a rating provided on a set conveys some preference information about each of the set's items, which allows us to acquire a user's preferences for more items that the number of ratings that the user provided. Second, due to privacy concerns, users may not be willing to reveal their preferences on individual items explicitly but may be willing to provide a single rating to a set of items, since it provides some level of information hiding. This paper investigates two questions related to using set-level ratings in recommender systems. First, how users' item-level ratings relate to their set-level ratings. Second, how collaborative filtering-based models for item-level rating prediction can take advantage of such set-level ratings. We have collected set-level ratings from active users of Movielens on sets of movies that they have rated in the past. Our analysis of these ratings shows that though the majority of the users provide the average of the ratings on a set's constituent items as the rating on the set, there exists a significant number of users that tend to consistently either under- or over-rate the sets. We have developed collaborative filtering-based methods to explicitly model these user behaviors that can be used to recommend items to users. Experiments on real data and on synthetic data that resembles the under- or over-rating behavior in the real data, demonstrate that these models can recover the overall characteristics of the underlying data and predict the user's ratings on individual items.

Recommender systems are widely used to recommend the most appealing items to users. These recommendations can be generated by applying collaborative filtering methods. The low-rank matrix completion method is the state-of-the-art collaborative filtering method. In this work, we show that the skewed distribution of ratings in the user-item rating matrix of real-world datasets affects the accuracy of matrix-completion-based approaches. Also, we show that the number of ratings that an item or a user has positively correlates with the ability of low-rank matrix-completion-based approaches to predict the ratings for the item or the user accurately. Furthermore, we use these insights to develop four matrix completion-based approaches, i.e., Frequency Adaptive Rating Prediction (FARP), Truncated Matrix Factorization (TMF), Truncated Matrix Factorization with Dropout (TMF + Dropout) and Inverse Frequency Weighted Matrix Factorization (IFWMF), that outperforms traditional matrix-completion-based approaches for the users and the items with few ratings in the user-item rating matrix.

Recommending new items to existing users has remained a challenging problem due to absence of user's past preferences for these items. The user personalized non-collaborative methods based on item features can be used to address this item cold-start problem. These methods rely on similarities between the target item and user's previous preferred items. While computing similarities based on item features, these methods overlook the interactions among the features of the items and consider them independently. Modeling interactions among features can be helpful as some features, when considered together, provide a stronger signal on the relevance of an item when compared to case where features are considered independently. To address this important issue, in this work we introduce the Feature-based factorized Bilinear Similarity Model (FBSM), which learns factorized bilinear similarity model for TOP-n recommendation of new items, given the information about items preferred by users in past as well as the features of these items. We carry out extensive empirical evaluations on benchmark datasets, and we find that the proposed FBSM approach improves upon traditional non-collaborative methods in terms of recommendation performance. Moreover, the proposed approach also learns insightful interactions among item features from data, which lead to deep understanding on how these interactions contribute to personalized recommendation.

In order to help undergraduate students towards successfully completing their degrees, developing tools that can assist students during the course selection process is a significant task in the education domain. The optimal set of courses for each student should include courses that help him/her graduate in a timely fashion and for which he/she is well-prepared for so as to get a good grade in. To this end, we propose two different grade-aware course recommendation approaches to recommend to each student his/her optimal set of courses. The first approach ranks the courses by using an objective function that differentiates between courses that are expected to increase or decrease a student's GPA. The second approach combines the grades predicted by grade prediction methods with the rankings produced by course recommendation methods to improve the final course rankings. To obtain the course rankings in the first approach, we adapt two widely-used representation learning techniques to learn the optimal temporal ordering between courses. Our experiments on a large dataset obtained from the University of Minnesota that includes students from 23 different majors show that the grade-aware course recommendation methods can do better on recommending more courses in which the students are expected to perform well and recommending fewer courses in which they are expected not to perform well in than grade-unaware course recommendation methods.