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Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which can be very informative, especially in high-dimensional settings or when mean information is not available. To extract the information from the dependence structure for clustering, we propose a new latent variable model for the features arranged in matrix form, with some unknown membership matrices representing the clusters for the rows and columns. Under this model, we further propose a class of hierarchical clustering algorithms using the difference of a weighted covariance matrix as the dissimilarity measure. Theoretically, we show that under mild conditions, our algorithm attains clustering consistency in the high-dimensional setting. While this consistency result holds for our algorithm with a broad class of weighted covariance matrices, the conditions for this result depend on the choice of the weight. To investigate how the weight affects the theoretical performance of our algorithm, we establish the minimax lower bound for clustering under our latent variable model in terms of some cluster separation metric. Given these results, we identify the optimal weight in the sense that using this weight guarantees our algorithm to be minimax rate-optimal. The practical implementation of our algorithm with the optimal weight is also discussed. Simulation studies show that our algorithm performs better than existing methods in terms of the adjusted Rand index (ARI). The method is applied to a genomic dataset and yields meaningful interpretations.

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Offline reinforcement learning (RL) is challenged by the distributional shift problem. To address this problem, existing works mainly focus on designing sophisticated policy constraints between the learned policy and the behavior policy. However, these constraints are applied equally to well-performing and inferior actions through uniform sampling, which might negatively affect the learned policy. To alleviate this issue, we propose Offline Prioritized Experience Replay (OPER), featuring a class of priority functions designed to prioritize highly-rewarding transitions, making them more frequently visited during training. Through theoretical analysis, we show that this class of priority functions induce an improved behavior policy, and when constrained to this improved policy, a policy-constrained offline RL algorithm is likely to yield a better solution. We develop two practical strategies to obtain priority weights by estimating advantages based on a fitted value network (OPER-A) or utilizing trajectory returns (OPER-R) for quick computation. OPER is a plug-and-play component for offline RL algorithms. As case studies, we evaluate OPER on five different algorithms, including BC, TD3+BC, Onestep RL, CQL, and IQL. Extensive experiments demonstrate that both OPER-A and OPER-R significantly improve the performance for all baseline methods. Codes and priority weights are availiable at //github.com/sail-sg/OPER.

Additive spatial statistical models with weakly stationary process assumptions have become standard in spatial statistics. However, one disadvantage of such models is the computation time, which rapidly increases with the number of data points. The goal of this article is to apply an existing subsampling strategy to standard spatial additive models and to derive the spatial statistical properties. We call this strategy the "spatial data subset model" (SDSM) approach, which can be applied to big datasets in a computationally feasible way. Our approach has the advantage that one does not require any additional restrictive model assumptions. That is, computational gains increase as model assumptions are removed when using our model framework. This provides one solution to the computational bottlenecks that occur when applying methods such as Kriging to "big data". We provide several properties of this new spatial data subset model approach in terms of moments, sill, nugget, and range under several sampling designs. An advantage of our approach is that it subsamples without throwing away data, and can be implemented using datasets of any size that can be stored. We present the results of the spatial data subset model approach on simulated datasets, and on a large dataset consists of 150,000 observations of daytime land surface temperatures measured by the MODIS instrument onboard the Terra satellite.

Driven by the appealing properties of neural fields for storing and communicating 3D data, the problem of directly processing them to address tasks such as classification and part segmentation has emerged and has been investigated in recent works. Early approaches employ neural fields parameterized by shared networks trained on the whole dataset, achieving good task performance but sacrificing reconstruction quality. To improve the latter, later methods focus on individual neural fields parameterized as large Multi-Layer Perceptrons (MLPs), which are, however, challenging to process due to the high dimensionality of the weight space, intrinsic weight space symmetries, and sensitivity to random initialization. Hence, results turn out significantly inferior to those achieved by processing explicit representations, e.g., point clouds or meshes. In the meantime, hybrid representations, in particular based on tri-planes, have emerged as a more effective and efficient alternative to realize neural fields, but their direct processing has not been investigated yet. In this paper, we show that the tri-plane discrete data structure encodes rich information, which can be effectively processed by standard deep-learning machinery. We define an extensive benchmark covering a diverse set of fields such as occupancy, signed/unsigned distance, and, for the first time, radiance fields. While processing a field with the same reconstruction quality, we achieve task performance far superior to frameworks that process large MLPs and, for the first time, almost on par with architectures handling explicit representations.

Test-time adaptation (TTA) is a task that continually adapts a pre-trained source model to the target domain during inference. One popular approach involves fine-tuning model with cross-entropy loss according to estimated pseudo-labels. However, its performance is significantly affected by noisy pseudo-labels. This study reveals that minimizing the classification error of each sample causes the cross-entropy loss's vulnerability to label noise. To address this issue, we propose a novel Decoupled Prototype Learning (DPL) method that features prototype-centric loss computation. First, we decouple the optimization of class prototypes. For each class prototype, we reduce its distance with positive samples and enlarge its distance with negative samples in a contrastive manner. This strategy prevents the model from overfitting to noisy pseudo-labels. Second, we propose a memory-based strategy to enhance DPL's robustness for the small batch sizes often encountered in TTA. We update each class's pseudo-feature from a memory in a momentum manner and insert an additional DPL loss. Finally, we introduce a consistency regularization-based approach to leverage samples with unconfident pseudo-labels. This approach transfers feature styles of samples with unconfident pseudo-labels to those with confident pseudo-labels. Thus, more reliable samples for TTA are created. The experimental results demonstrate that our methods achieve state-of-the-art performance on domain generalization benchmarks, and reliably improve the performance of self-training-based methods on image corruption benchmarks. The code will be released.

There has been a recent surge of interest in developing generally-capable agents that can adapt to new tasks without additional training in the environment. Learning world models from reward-free exploration is a promising approach, and enables policies to be trained using imagined experience for new tasks. However, achieving a general agent requires robustness across different environments. In this work, we address the novel problem of generating curricula in the reward-free setting to train robust world models. We consider robustness in terms of minimax regret over all environment instantiations and show that the minimax regret can be connected to minimising the maximum error in the world model across environment instances. This result informs our algorithm, WAKER: Weighted Acquisition of Knowledge across Environments for Robustness. WAKER selects environments for data collection based on the estimated error of the world model for each environment. Our experiments demonstrate that WAKER outperforms several baselines, resulting in improved robustness, efficiency, and generalisation.

Transformer models have achieved remarkable results in a wide range of applications. However, their scalability is hampered by the quadratic time and memory complexity of the self-attention mechanism concerning the sequence length. This limitation poses a substantial obstacle when dealing with long documents or high-resolution images. In this work, we study the self-attention mechanism by analyzing the distribution of the attention matrix and its concentration ability. Furthermore, we propose instruments to measure these quantities and introduce a novel self-attention mechanism, Linear Log-Normal Attention, designed to emulate the distribution and concentration behavior of the original self-attention. Our experimental results on popular natural language benchmarks reveal that our proposed Linear Log-Normal Attention outperforms other linearized attention alternatives, offering a promising avenue for enhancing the scalability of transformer models. Our code is available in supplementary materials.

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.

Learning latent representations of nodes in graphs is an important and ubiquitous task with widespread applications such as link prediction, node classification, and graph visualization. Previous methods on graph representation learning mainly focus on static graphs, however, many real-world graphs are dynamic and evolve over time. In this paper, we present Dynamic Self-Attention Network (DySAT), a novel neural architecture that operates on dynamic graphs and learns node representations that capture both structural properties and temporal evolutionary patterns. Specifically, DySAT computes node representations by jointly employing self-attention layers along two dimensions: structural neighborhood and temporal dynamics. We conduct link prediction experiments on two classes of graphs: communication networks and bipartite rating networks. Our experimental results show that DySAT has a significant performance gain over several different state-of-the-art graph embedding baselines.

Collaborative filtering often suffers from sparsity and cold start problems in real recommendation scenarios, therefore, researchers and engineers usually use side information to address the issues and improve the performance of recommender systems. In this paper, we consider knowledge graphs as the source of side information. We propose MKR, a Multi-task feature learning approach for Knowledge graph enhanced Recommendation. MKR is a deep end-to-end framework that utilizes knowledge graph embedding task to assist recommendation task. The two tasks are associated by cross&compress units, which automatically share latent features and learn high-order interactions between items in recommender systems and entities in the knowledge graph. We prove that cross&compress units have sufficient capability of polynomial approximation, and show that MKR is a generalized framework over several representative methods of recommender systems and multi-task learning. Through extensive experiments on real-world datasets, we demonstrate that MKR achieves substantial gains in movie, book, music, and news recommendation, over state-of-the-art baselines. MKR is also shown to be able to maintain a decent performance even if user-item interactions are sparse.

It is always well believed that modeling relationships between objects would be helpful for representing and eventually describing an image. Nevertheless, there has not been evidence in support of the idea on image description generation. In this paper, we introduce a new design to explore the connections between objects for image captioning under the umbrella of attention-based encoder-decoder framework. Specifically, we present Graph Convolutional Networks plus Long Short-Term Memory (dubbed as GCN-LSTM) architecture that novelly integrates both semantic and spatial object relationships into image encoder. Technically, we build graphs over the detected objects in an image based on their spatial and semantic connections. The representations of each region proposed on objects are then refined by leveraging graph structure through GCN. With the learnt region-level features, our GCN-LSTM capitalizes on LSTM-based captioning framework with attention mechanism for sentence generation. Extensive experiments are conducted on COCO image captioning dataset, and superior results are reported when comparing to state-of-the-art approaches. More remarkably, GCN-LSTM increases CIDEr-D performance from 120.1% to 128.7% on COCO testing set.

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