The strategy for selecting candidate sets -- the set of items that the recommendation system is expected to rank for each user -- is an important decision in carrying out an offline top-$N$ recommender system evaluation. The set of candidates is composed of the union of the user's test items and an arbitrary number of non-relevant items that we refer to as decoys. Previous studies have aimed to understand the effect of different candidate set sizes and selection strategies on evaluation. In this paper, we extend this knowledge by studying the specific interaction of candidate set selection strategies with popularity bias, and use simulation to assess whether sampled candidate sets result in metric estimates that are less biased with respect to the true metric values under complete data that is typically unavailable in ordinary experiments.
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Regularized linear regression is a promising approach for binary classification problems in which the training set has noisy labels since the regularization term can help to avoid interpolating the mislabeled data points. In this paper we provide a systematic study of the effects of the regularization strength on the performance of linear classifiers that are trained to solve binary classification problems by minimizing a regularized least-squares objective. We consider the over-parametrized regime and assume that the classes are generated from a Gaussian Mixture Model (GMM) where a fraction $c<\frac{1}{2}$ of the training data is mislabeled. Under these assumptions, we rigorously analyze the classification errors resulting from the application of ridge, $\ell_1$, and $\ell_\infty$ regression. In particular, we demonstrate that ridge regression invariably improves the classification error. We prove that $\ell_1$ regularization induces sparsity and observe that in many cases one can sparsify the solution by up to two orders of magnitude without any considerable loss of performance, even though the GMM has no underlying sparsity structure. For $\ell_\infty$ regularization we show that, for large enough regularization strength, the optimal weights concentrate around two values of opposite sign. We observe that in many cases the corresponding "compression" of each weight to a single bit leads to very little loss in performance. These latter observations can have significant practical ramifications.
Modern detection transformers (DETRs) use a set of object queries to predict a list of bounding boxes, sort them by their classification confidence scores, and select the top-ranked predictions as the final detection results for the given input image. A highly performant object detector requires accurate ranking for the bounding box predictions. For DETR-based detectors, the top-ranked bounding boxes suffer from less accurate localization quality due to the misalignment between classification scores and localization accuracy, thus impeding the construction of high-quality detectors. In this work, we introduce a simple and highly performant DETR-based object detector by proposing a series of rank-oriented designs, combinedly called Rank-DETR. Our key contributions include: (i) a rank-oriented architecture design that can prompt positive predictions and suppress the negative ones to ensure lower false positive rates, as well as (ii) a rank-oriented loss function and matching cost design that prioritizes predictions of more accurate localization accuracy during ranking to boost the AP under high IoU thresholds. We apply our method to improve the recent SOTA methods (e.g., H-DETR and DINO-DETR) and report strong COCO object detection results when using different backbones such as ResNet-$50$, Swin-T, and Swin-L, demonstrating the effectiveness of our approach. Code is available at \url{//github.com/LeapLabTHU/Rank-DETR}.
Submodular maximization under various constraints is a fundamental problem studied continuously, in both computer science and operations research, since the late $1970$'s. A central technique in this field is to approximately optimize the multilinear extension of the submodular objective, and then round the solution. The use of this technique requires a solver able to approximately maximize multilinear extensions. Following a long line of work, Buchbinder and Feldman (2019) described such a solver guaranteeing $0.385$-approximation for down-closed constraints, while Oveis Gharan and Vondr\'ak (2011) showed that no solver can guarantee better than $0.478$-approximation. In this paper, we present a solver guaranteeing $0.401$-approximation, which significantly reduces the gap between the best known solver and the inapproximability result. The design and analysis of our solver are based on a novel bound that we prove for DR-submodular functions. This bound improves over a previous bound due to Feldman et al. (2011) that is used by essentially all state-of-the-art results for constrained maximization of general submodular/DR-submodular functions. Hence, we believe that our new bound is likely to find many additional applications in related problems, and to be a key component for further improvement.
A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite norm can be properly designed to promote such exclusive group sparsity patterns. The resulting norm lends itself to efficient and flexible regularized optimization algorithms for support recovery, like the proximal algorithm. Moreover, an active set algorithm is proposed that builds the solution by successively including structure atoms into the estimated support. It is also shown that such an algorithm can be tailored to match more rigid structures than plain exclusive group sparsity. Asymptotic consistency analysis (with both the number of parameters as well as the number of groups growing with the observation size) establishes the effectiveness of the proposed solution in terms of signed support recovery under conventional assumptions. Finally, a set of numerical simulations further corroborates the results.
Decentralized generalized approximate message-passing (GAMP) is proposed for compressed sensing from distributed generalized linear measurements in a tree-structured network. Consensus propagation is used to realize average consensus required in GAMP via local communications between adjacent nodes. Decentralized GAMP is applicable to all tree-structured networks that do not necessarily have central nodes connected to all other nodes. State evolution is used to analyze the asymptotic dynamics of decentralized GAMP for zero-mean independent and identically distributed Gaussian sensing matrices. The state evolution recursion for decentralized GAMP is proved to have the same fixed points as that for centralized GAMP when homogeneous measurements with an identical dimension in all nodes are considered. Furthermore, existing long-memory proof strategy is used to prove that the state evolution recursion for decentralized GAMP with the Bayes-optimal denoisers converges to a fixed point. These results imply that the state evolution recursion for decentralized GAMP with the Bayes-optimal denoisers converges to the Bayes-optimal fixed point for the homogeneous measurements when the fixed point is unique. Numerical results for decentralized GAMP are presented in the cases of linear measurements and clipping. As examples of tree-structured networks, a one-dimensional chain and a tree with no central nodes are considered.
Social relations are often used to improve recommendation quality when user-item interaction data is sparse in recommender systems. Most existing social recommendation models exploit pairwise relations to mine potential user preferences. However, real-life interactions among users are very complicated and user relations can be high-order. Hypergraph provides a natural way to model complex high-order relations, while its potentials for improving social recommendation are under-explored. In this paper, we fill this gap and propose a multi-channel hypergraph convolutional network to enhance social recommendation by leveraging high-order user relations. Technically, each channel in the network encodes a hypergraph that depicts a common high-order user relation pattern via hypergraph convolution. By aggregating the embeddings learned through multiple channels, we obtain comprehensive user representations to generate recommendation results. However, the aggregation operation might also obscure the inherent characteristics of different types of high-order connectivity information. To compensate for the aggregating loss, we innovatively integrate self-supervised learning into the training of the hypergraph convolutional network to regain the connectivity information with hierarchical mutual information maximization. The experimental results on multiple real-world datasets show that the proposed model outperforms the SOTA methods, and the ablation study verifies the effectiveness of the multi-channel setting and the self-supervised task. The implementation of our model is available via //github.com/Coder-Yu/RecQ.
Generative commonsense reasoning which aims to empower machines to generate sentences with the capacity of reasoning over a set of concepts is a critical bottleneck for text generation. Even the state-of-the-art pre-trained language generation models struggle at this task and often produce implausible and anomalous sentences. One reason is that they rarely consider incorporating the knowledge graph which can provide rich relational information among the commonsense concepts. To promote the ability of commonsense reasoning for text generation, we propose a novel knowledge graph augmented pre-trained language generation model KG-BART, which encompasses the complex relations of concepts through the knowledge graph and produces more logical and natural sentences as output. Moreover, KG-BART can leverage the graph attention to aggregate the rich concept semantics that enhances the model generalization on unseen concept sets. Experiments on benchmark CommonGen dataset verify the effectiveness of our proposed approach by comparing with several strong pre-trained language generation models, particularly KG-BART outperforms BART by 5.80, 4.60, in terms of BLEU-3, 4. Moreover, we also show that the generated context by our model can work as background scenarios to benefit downstream commonsense QA tasks.
The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.
To provide more accurate, diverse, and explainable recommendation, it is compulsory to go beyond modeling user-item interactions and take side information into account. Traditional methods like factorization machine (FM) cast it as a supervised learning problem, which assumes each interaction as an independent instance with side information encoded. Due to the overlook of the relations among instances or items (e.g., the director of a movie is also an actor of another movie), these methods are insufficient to distill the collaborative signal from the collective behaviors of users. In this work, we investigate the utility of knowledge graph (KG), which breaks down the independent interaction assumption by linking items with their attributes. We argue that in such a hybrid structure of KG and user-item graph, high-order relations --- which connect two items with one or multiple linked attributes --- are an essential factor for successful recommendation. We propose a new method named Knowledge Graph Attention Network (KGAT) which explicitly models the high-order connectivities in KG in an end-to-end fashion. It recursively propagates the embeddings from a node's neighbors (which can be users, items, or attributes) to refine the node's embedding, and employs an attention mechanism to discriminate the importance of the neighbors. Our KGAT is conceptually advantageous to existing KG-based recommendation methods, which either exploit high-order relations by extracting paths or implicitly modeling them with regularization. Empirical results on three public benchmarks show that KGAT significantly outperforms state-of-the-art methods like Neural FM and RippleNet. Further studies verify the efficacy of embedding propagation for high-order relation modeling and the interpretability benefits brought by the attention mechanism.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.
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