Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive forward models, posterior covariance knowledge must be relaxed to deterministic or stochastic approximations. In the carbon flux inversion literature, Chevallier et al. proposed a stochastic method capable of approximating posterior variances of linear functionals of the model parameters that is particularly well-suited for large-scale Earth-system data assimilation tasks. This note formalizes this algorithm and clarifies its properties. We provide a formal statement of the algorithm, demonstrate why it converges to the desired posterior variance quantity of interest, and provide additional uncertainty quantification allowing incorporation of the Monte Carlo sampling uncertainty into the method's Bayesian credible intervals. The methodology is demonstrated using toy simulations and a realistic carbon flux inversion observing system simulation experiment.
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Optimal transport is a fundamental topic that has attracted a great amount of attention from the optimization community in the past decades. In this paper, we consider an interesting discrete dynamic optimal transport problem: can we efficiently update the optimal transport plan when the weights or the locations of the data points change? This problem is naturally motivated by several applications in machine learning. For example, we often need to compute the optimal transport cost between two different data sets; if some changes happen to a few data points, should we re-compute the high complexity cost function or update the cost by some efficient dynamic data structure? We are aware that several dynamic maximum flow algorithms have been proposed before, however, the research on dynamic minimum cost flow problem is still quite limited, to the best of our knowledge. We propose a novel 2D Skip Orthogonal List together with some dynamic tree techniques. Although our algorithm is based on the conventional simplex method, it can efficiently find the variable to pivot within expected $O(1)$ time, and complete each pivoting operation within expected $O(|V|)$ time where $V$ is the set of all supply and demand nodes. Since dynamic modifications typically do not introduce significant changes, our algorithm requires only a few simplex iterations in practice. So our algorithm is more efficient than re-computing the optimal transport cost that needs at least one traversal over all $|E| = O(|V|^2)$ variables, where $|E|$ denotes the number of edges in the network. Our experiments demonstrate that our algorithm significantly outperforms existing algorithms in the dynamic scenarios.
Pioneering efforts have verified the effectiveness of the diffusion models in exploring the informative uncertainty for recommendation. Considering the difference between recommendation and image synthesis tasks, existing methods have undertaken tailored refinements to the diffusion and reverse process. However, these approaches typically use the highest-score item in corpus for user interest prediction, leading to the ignorance of the user's generalized preference contained within other items, thereby remaining constrained by the data sparsity issue. To address this issue, this paper presents a novel Plug-in Diffusion Model for Recommendation (PDRec) framework, which employs the diffusion model as a flexible plugin to jointly take full advantage of the diffusion-generating user preferences on all items. Specifically, PDRec first infers the users' dynamic preferences on all items via a time-interval diffusion model and proposes a Historical Behavior Reweighting (HBR) mechanism to identify the high-quality behaviors and suppress noisy behaviors. In addition to the observed items, PDRec proposes a Diffusion-based Positive Augmentation (DPA) strategy to leverage the top-ranked unobserved items as the potential positive samples, bringing in informative and diverse soft signals to alleviate data sparsity. To alleviate the false negative sampling issue, PDRec employs Noise-free Negative Sampling (NNS) to select stable negative samples for ensuring effective model optimization. Extensive experiments and analyses on four datasets have verified the superiority of the proposed PDRec over the state-of-the-art baselines and showcased the universality of PDRec as a flexible plugin for commonly-used sequential encoders in different recommendation scenarios. The code is available in //github.com/hulkima/PDRec.
Semantic communication is a promising communication paradigm that utilizes Deep Neural Networks (DNNs) to extract the information relevant to downstream tasks, hence significantly reducing the amount of transmitted data. In current practice, the semantic communication transmitter for a specific task is typically pre-trained and shared by all users. However, due to user heterogeneity, it is desirable to use different transmitters according to the available computational and communication resources of users. In this paper, we first show that it is possible to dynamically adjust the computational and communication overhead of DNN-based transmitters, thereby achieving adaptive semantic communication. After that, we investigate the user association and resource allocation problem in a multi-cell network where users are equipped with adaptive semantic communication transmitters. To solve this problem, we decompose it into three subproblems involving the scheduling of each user, the resource allocation of each base station (BS), and the user association between users and BSs. Then we solve each problem progressively based on the solution of the previous subproblem. The final algorithm can obtain near-optimal solutions in polynomial time. Numerical results show that our algorithm outperforms benchmarks under various situations.
This study introduces an innovative approach that integrates community detection algorithms with Graph Neural Network (GNN) models to enhance link prediction in scientific literature networks. We specifically focus on the utilization of the Louvain community detection algorithm to uncover latent community structures within these networks, which are then incorporated into GNN architectures to predict potential links. Our methodology demonstrates the importance of understanding community dynamics in complex networks and leverages the strengths of both community detection and GNNs to improve predictive accuracy. Through extensive experiments on bipartite graphs representing scientific collaborations and citations, our approach not only highlights the synergy between community detection and GNNs but also addresses some of the prevalent challenges in link prediction, such as scalability and resolution limits. The results suggest that incorporating community-level information can significantly enhance the performance of GNNs in link prediction tasks. This work contributes to the evolving field of network science by offering a novel perspective on integrating advanced machine learning techniques with traditional network analysis methods to better understand and predict the intricate patterns of scientific collaborations.
Nonnegative tensor factorization (NTF) has become an important tool for feature extraction and part-based representation with preserved intrinsic structure information from nonnegative high-order data. However, the original NTF methods utilize Euclidean or Kullback-Leibler divergence as the loss function which treats each feature equally leading to the neglect of the side-information of features. To utilize correlation information of features and manifold information of samples, we introduce Wasserstein manifold nonnegative tensor factorization (WMNTF), which minimizes the Wasserstein distance between the distribution of input tensorial data and the distribution of reconstruction. Although some researches about Wasserstein distance have been proposed in nonnegative matrix factorization (NMF), they ignore the spatial structure information of higher-order data. We use Wasserstein distance (a.k.a Earth Mover's distance or Optimal Transport distance) as a metric and add a graph regularizer to a latent factor. Experimental results demonstrate the effectiveness of the proposed method compared with other NMF and NTF methods.
Quantization is of significance for compressing the over-parameterized deep neural models and deploying them on resource-limited devices. Fixed-precision quantization suffers from performance drop due to the limited numerical representation ability. Conversely, mixed-precision quantization (MPQ) is advocated to compress the model effectively by allocating heterogeneous bit-width for layers. MPQ is typically organized into a searching-retraining two-stage process. Previous works only focus on determining the optimal bit-width configuration in the first stage efficiently, while ignoring the considerable time costs in the second stage. However, retraining always consumes hundreds of GPU-hours on the cutting-edge GPUs, thus hindering deployment efficiency significantly. In this paper, we devise a one-shot training-searching paradigm for mixed-precision model compression. Specifically, in the first stage, all potential bit-width configurations are coupled and thus optimized simultaneously within a set of shared weights. However, our observations reveal a previously unseen and severe bit-width interference phenomenon among highly coupled weights during optimization, leading to considerable performance degradation under a high compression ratio. To tackle this problem, we first design a bit-width scheduler to dynamically freeze the most turbulent bit-width of layers during training, to ensure the rest bit-widths converged properly. Then, taking inspiration from information theory, we present an information distortion mitigation technique to align the behaviour of the bad-performing bit-widths to the well-performing ones.
Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the distributions of given graphs and generating more novel graphs. Owing to their wide range of applications, generative models for graphs, which have a rich history, however, are traditionally hand-crafted and only capable of modeling a few statistical properties of graphs. Recent advances in deep generative models for graph generation is an important step towards improving the fidelity of generated graphs and paves the way for new kinds of applications. This article provides an extensive overview of the literature in the field of deep generative models for graph generation. Firstly, the formal definition of deep generative models for the graph generation and the preliminary knowledge are provided. Secondly, taxonomies of deep generative models for both unconditional and conditional graph generation are proposed respectively; the existing works of each are compared and analyzed. After that, an overview of the evaluation metrics in this specific domain is provided. Finally, the applications that deep graph generation enables are summarized and five promising future research directions are highlighted.
Recently, graph neural networks (GNNs) have been widely used for document classification. However, most existing methods are based on static word co-occurrence graphs without sentence-level information, which poses three challenges:(1) word ambiguity, (2) word synonymity, and (3) dynamic contextual dependency. To address these challenges, we propose a novel GNN-based sparse structure learning model for inductive document classification. Specifically, a document-level graph is initially generated by a disjoint union of sentence-level word co-occurrence graphs. Our model collects a set of trainable edges connecting disjoint words between sentences and employs structure learning to sparsely select edges with dynamic contextual dependencies. Graphs with sparse structures can jointly exploit local and global contextual information in documents through GNNs. For inductive learning, the refined document graph is further fed into a general readout function for graph-level classification and optimization in an end-to-end manner. Extensive experiments on several real-world datasets demonstrate that the proposed model outperforms most state-of-the-art results, and reveal the necessity to learn sparse structures for each document.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
Image segmentation is an important component of many image understanding systems. It aims to group pixels in a spatially and perceptually coherent manner. Typically, these algorithms have a collection of parameters that control the degree of over-segmentation produced. It still remains a challenge to properly select such parameters for human-like perceptual grouping. In this work, we exploit the diversity of segments produced by different choices of parameters. We scan the segmentation parameter space and generate a collection of image segmentation hypotheses (from highly over-segmented to under-segmented). These are fed into a cost minimization framework that produces the final segmentation by selecting segments that: (1) better describe the natural contours of the image, and (2) are more stable and persistent among all the segmentation hypotheses. We compare our algorithm's performance with state-of-the-art algorithms, showing that we can achieve improved results. We also show that our framework is robust to the choice of segmentation kernel that produces the initial set of hypotheses.
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