The selection of essential variables in logistic regression is vital because of its extensive use in medical studies, finance, economics and related fields. In this paper, we explore four main typologies (test-based, penalty-based, screening-based, and tree-based) of frequentist variable selection methods in logistic regression setup. Primary objective of this work is to give a comprehensive overview of the existing literature for practitioners. Underlying assumptions and theory, along with the specifics of their implementations, are detailed as well. Next, we conduct a thorough simulation study to explore the performances of fifteen different methods in terms of variable selection, estimation of coefficients, prediction accuracy as well as time complexity under various settings. We take low, moderate and high dimensional setups and consider different correlation structures for the covariates. A real-life application, using a high-dimensional gene expression data, is also included in this study to further understand the efficacy and consistency of the methods. Finally, based on our findings in the simulated data and in the real data, we provide recommendations for practitioners on the choice of variable selection methods under various contexts.
The design of effective online caching policies is an increasingly important problem for content distribution networks, online social networks and edge computing services, among other areas. This paper proposes a new algorithmic toolbox for tackling this problem through the lens of optimistic online learning. We build upon the Follow-the-Regularized-Leader (FTRL) framework, which is developed further here to include predictions for the file requests, and we design online caching algorithms for bipartite networks with fixed-size caches or elastic leased caches subject to time-average budget constraints. The predictions are provided by a content recommendation system that influences the users viewing activity and hence can naturally reduce the caching network's uncertainty about future requests. We also extend the framework to learn and utilize the best request predictor in cases where many are available. We prove that the proposed {optimistic} learning caching policies can achieve sub-zero performance loss (regret) for perfect predictions, and maintain the sub-linear regret bound $O(\sqrt T)$, which is the best achievable bound for policies that do not use predictions, even for arbitrary-bad predictions. The performance of the proposed algorithms is evaluated with detailed trace-driven numerical tests.
In this work, we aim to consider the application of contrastive learning in the scenario of the recommendation system adequately, making it more suitable for recommendation task. We propose a learning paradigm called supervised contrastive learning(SCL) to support the graph convolutional neural network. Specifically, we will calculate the similarity between different nodes in user side and item side respectively during data preprocessing, and then when applying contrastive learning, not only will the augmented views be regarded as the positive samples, but also a certain number of similar samples will be regarded as the positive samples, which is different with SimCLR that treats other samples in a batch as negative samples. We apply SCL on the most advanced LightGCN. In addition, in order to consider the uncertainty of node interaction, we also propose a new data augment method called node replication. Empirical research and ablation study on Gowalla, Yelp2018, Amazon-Book datasets prove the effectiveness of SCL and node replication, which improve the accuracy of recommendations and robustness to interactive noise.
Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.
Binary pointwise labels (aka implicit feedback) are heavily leveraged by deep learning based recommendation algorithms nowadays. In this paper we discuss the limited expressiveness of these labels may fail to accommodate varying degrees of user preference, and thus lead to conflicts during model training, which we call annotation bias. To solve this issue, we find the soft-labeling property of pairwise labels could be utilized to alleviate the bias of pointwise labels. To this end, we propose a momentum contrast framework (MP2) that combines pointwise and pairwise learning for recommendation. MP2 has a three-tower network structure: one user network and two item networks. The two item networks are used for computing pointwise and pairwise loss respectively. To alleviate the influence of the annotation bias, we perform a momentum update to ensure a consistent item representation. Extensive experiments on real-world datasets demonstrate the superiority of our method against state-of-the-art recommendation algorithms.
Despite the recent progress, the existing multi-view unsupervised feature selection methods mostly suffer from two limitations. First, they generally utilize either cluster structure or similarity structure to guide the feature selection, neglecting the possibility of a joint formulation with mutual benefits. Second, they often learn the similarity structure by either global structure learning or local structure learning, lacking the capability of graph learning with both global and local structural awareness. In light of this, this paper presents a joint multi-view unsupervised feature selection and graph learning (JMVFG) approach. Particularly, we formulate the multi-view feature selection with orthogonal decomposition, where each target matrix is decomposed into a view-specific basis matrix and a view-consistent cluster indicator. Cross-space locality preservation is incorporated to bridge the cluster structure learning in the projected space and the similarity learning (i.e., graph learning) in the original space. Further, a unified objective function is presented to enable the simultaneous learning of the cluster structure, the global and local similarity structures, and the multi-view consistency and inconsistency, upon which an alternating optimization algorithm is developed with theoretically proved convergence. Extensive experiments demonstrate the superiority of our approach for both multi-view feature selection and graph learning tasks.
The best neural architecture for a given machine learning problem depends on many factors: not only the complexity and structure of the dataset, but also on resource constraints including latency, compute, energy consumption, etc. Neural architecture search (NAS) for tabular datasets is an important but under-explored problem. Previous NAS algorithms designed for image search spaces incorporate resource constraints directly into the reinforcement learning rewards. In this paper, we argue that search spaces for tabular NAS pose considerable challenges for these existing reward-shaping methods, and propose a new reinforcement learning (RL) controller to address these challenges. Motivated by rejection sampling, when we sample candidate architectures during a search, we immediately discard any architecture that violates our resource constraints. We use a Monte-Carlo-based correction to our RL policy gradient update to account for this extra filtering step. Results on several tabular datasets show TabNAS, the proposed approach, efficiently finds high-quality models that satisfy the given resource constraints.
In variable selection, a selection rule that prescribes the permissible sets of selected variables (called a "selection dictionary") is desirable due to the inherent structural constraints among the candidate variables. The methods that can incorporate such restrictions can improve model interpretability and prediction accuracy. Penalized regression can integrate selection rules by assigning the coefficients to different groups and then applying penalties to the groups. However, no general framework has been proposed to formalize selection rules and their applications. In this work, we establish a framework for structured variable selection that can incorporate universal structural constraints. We develop a mathematical language for constructing arbitrary selection rules, where the selection dictionary is formally defined. We show that all selection rules can be represented as a combination of operations on constructs, which can be used to identify the related selection dictionary. One may then apply some criteria to select the best model. We show that the theoretical framework can help to identify the grouping structure in existing penalized regression methods. In addition, we formulate structured variable selection into mixed-integer optimization problems which can be solved by existing software. Finally, we discuss the significance of the framework in the context of statistics.
Recommender system is one of the most important information services on today's Internet. Recently, graph neural networks have become the new state-of-the-art approach of recommender systems. In this survey, we conduct a comprehensive review of the literature in graph neural network-based recommender systems. We first introduce the background and the history of the development of both recommender systems and graph neural networks. For recommender systems, in general, there are four aspects for categorizing existing works: stage, scenario, objective, and application. For graph neural networks, the existing methods consist of two categories, spectral models and spatial ones. We then discuss the motivation of applying graph neural networks into recommender systems, mainly consisting of the high-order connectivity, the structural property of data, and the enhanced supervision signal. We then systematically analyze the challenges in graph construction, embedding propagation/aggregation, model optimization, and computation efficiency. Afterward and primarily, we provide a comprehensive overview of a multitude of existing works of graph neural network-based recommender systems, following the taxonomy above. Finally, we raise discussions on the open problems and promising future directions of this area. We summarize the representative papers along with their codes repositories in //github.com/tsinghua-fib-lab/GNN-Recommender-Systems.
Many current applications use recommendations in order to modify the natural user behavior, such as to increase the number of sales or the time spent on a website. This results in a gap between the final recommendation objective and the classical setup where recommendation candidates are evaluated by their coherence with past user behavior, by predicting either the missing entries in the user-item matrix, or the most likely next event. To bridge this gap, we optimize a recommendation policy for the task of increasing the desired outcome versus the organic user behavior. We show this is equivalent to learning to predict recommendation outcomes under a fully random recommendation policy. To this end, we propose a new domain adaptation algorithm that learns from logged data containing outcomes from a biased recommendation policy and predicts recommendation outcomes according to random exposure. We compare our method against state-of-the-art factorization methods, in addition to new approaches of causal recommendation and show significant improvements.
State-of-the-art recommendation algorithms -- especially the collaborative filtering (CF) based approaches with shallow or deep models -- usually work with various unstructured information sources for recommendation, such as textual reviews, visual images, and various implicit or explicit feedbacks. Though structured knowledge bases were considered in content-based approaches, they have been largely neglected recently due to the availability of vast amount of data, and the learning power of many complex models. However, structured knowledge bases exhibit unique advantages in personalized recommendation systems. When the explicit knowledge about users and items is considered for recommendation, the system could provide highly customized recommendations based on users' historical behaviors. A great challenge for using knowledge bases for recommendation is how to integrated large-scale structured and unstructured data, while taking advantage of collaborative filtering for highly accurate performance. Recent achievements on knowledge base embedding sheds light on this problem, which makes it possible to learn user and item representations while preserving the structure of their relationship with external knowledge. In this work, we propose to reason over knowledge base embeddings for personalized recommendation. Specifically, we propose a knowledge base representation learning approach to embed heterogeneous entities for recommendation. Experimental results on real-world dataset verified the superior performance of our approach compared with state-of-the-art baselines.