In this paper, we study the following problem. Consider a setting where a proposal is offered to the vertices of a given network $G$, and the vertices must conduct a vote and decide whether to accept the proposal or reject it. Each vertex $v$ has its own valuation of the proposal; we say that $v$ is ``happy'' if its valuation is positive (i.e., it expects to gain from adopting the proposal) and ``sad'' if its valuation is negative. However, vertices do not base their vote merely on their own valuation. Rather, a vertex $v$ is a \emph{proponent} of the proposal if a majority of its neighbors are happy with it and an \emph{opponent} in the opposite case. At the end of the vote, the network collectively accepts the proposal whenever a majority of its vertices are proponents. We study this problem on regular graphs with loops. Specifically, we consider the class ${\mathcal G}_{n|d|h}$ of $d$-regular graphs of odd order $n$ with all $n$ loops and $h$ happy vertices. We are interested in establishing necessary and sufficient conditions for the class ${\mathcal G}_{n|d|h}$ to contain a labeled graph accepting the proposal, as well as conditions to contain a graph rejecting the proposal. We also discuss connections to the existing literature, including that on majority domination, and investigate the properties of the obtained conditions.
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In this paper, we explore the role of matrix scaling on a matrix of counts when building a topic model using non-negative matrix factorization. We present a scaling inspired by the normalized Laplacian (NL) for graphs that can greatly improve the quality of a non-negative matrix factorization. The results parallel those in the spectral graph clustering work of \cite{Priebe:2019}, where the authors proved adjacency spectral embedding (ASE) spectral clustering was more likely to discover core-periphery partitions and Laplacian Spectral Embedding (LSE) was more likely to discover affinity partitions. In text analysis non-negative matrix factorization (NMF) is typically used on a matrix of co-occurrence ``contexts'' and ``terms" counts. The matrix scaling inspired by LSE gives significant improvement for text topic models in a variety of datasets. We illustrate the dramatic difference a matrix scalings in NMF can greatly improve the quality of a topic model on three datasets where human annotation is available. Using the adjusted Rand index (ARI), a measure cluster similarity we see an increase of 50\% for Twitter data and over 200\% for a newsgroup dataset versus using counts, which is the analogue of ASE. For clean data, such as those from the Document Understanding Conference, NL gives over 40\% improvement over ASE. We conclude with some analysis of this phenomenon and some connections of this scaling with other matrix scaling methods.
Link prediction task is vital to automatically understanding the structure of large knowledge bases. In this paper, we present our system to solve this task at the Data Science and Advanced Analytics 2023 Competition "Efficient and Effective Link Prediction" (DSAA-2023 Competition) with a corpus containing 948,233 training and 238,265 for public testing. This paper introduces an approach to link prediction in Wikipedia articles by formulating it as a natural language inference (NLI) task. Drawing inspiration from recent advancements in natural language processing and understanding, we cast link prediction as an NLI task, wherein the presence of a link between two articles is treated as a premise, and the task is to determine whether this premise holds based on the information presented in the articles. We implemented our system based on the Sentence Pair Classification for Link Prediction for the Wikipedia Articles task. Our system achieved 0.99996 Macro F1-score and 1.00000 Macro F1-score for the public and private test sets, respectively. Our team UIT-NLP ranked 3rd in performance on the private test set, equal to the scores of the first and second places. Our code is publicly for research purposes.
In this paper we study the dynamic behavior of threshold networks on undirected signed graphs. While much attention has been given to the convergence and long-term behavior of this model, an open question remains: How does the underlying graph structure influence network dynamics? While similar papers have been carried out for threshold networks (as well as for other networks) these have largely focused on unsigned networks. However, the signed graph model finds applications in various real-world domains like gene regulation and social networks. By studying a graph parameter that we call "stability index," we search to establish a connection between the structure and the dynamics of threshold network. Interestingly, this parameter is related to the concepts of frustration and balance in signed graphs. We show that graphs that present negative stability index exhibit stable dynamics, meaning that the dynamics converges to fixed points regardless of threshold parameters. Conversely, if at least one subgraph has positive stability index, oscillations in long term behavior may appear. Finally, we generalize the analysis to network dynamics under periodic update schemes and we explore the case in which the stability index is positive for some subgraph finding that attractors with superpolynomial period on the size of the network may appear.
In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model with oblique projections. This model partitions the measurement space into a dynamic subspace and a static subspace that do not need to be orthogonal. The partition allows us to apply an oblique projection to extract dynamic latent variables (DLVs) from high-dimensional data with maximized predictability. We develop an alternating iterative PredVAR algorithm that exploits the interaction between updating the latent VAR dynamics and estimating the oblique projection, using expectation maximization (EM) and a statistical constraint. In addition, the noise covariance matrices are estimated as a natural outcome of the EM method. A simulation case study of the nonlinear Lorenz oscillation system illustrates the advantages of the proposed approach over two alternatives.
In this work, we propose a novel framework for achieving robotic autonomy in orchards. It consists of two key steps: perception and semantic mapping. In the perception step, we introduce a 3D detection method that accurately identifies objects directly on point cloud maps. In the semantic mapping step, we develop a mapping module that constructs a visibility graph map by incorporating object-level information and terrain analysis. By combining these two steps, our framework improves the autonomy of agricultural robots in orchard environments. The accurate detection of objects and the construction of a semantic map enable the robot to navigate autonomously, perform tasks such as fruit harvesting, and acquire actionable information for efficient agricultural production.
In this paper, we study systems where each job or request can be split into a flexible number of sub-jobs up to a maximum limit. The number of sub-jobs a job is split into depends on the number of available servers found upon its arrival. All sub-jobs of a job are then processed in parallel at different servers leading to a linear speed-up of the job. We refer to such jobs as {\em adaptive multi-server jobs}. We study the problem of optimal assignment of such jobs when each server can process at most one sub-job at any given instant and there is no waiting room in the system. We assume that, upon arrival, a job can only access a randomly sampled subset of $k(n)$ servers from a total of $n$ servers, and the number of sub-jobs is determined based on the number of idle servers within the sampled subset. We analyze the steady-state performance of the system when system load varies according to $\lambda(n) =1 - \beta n^{-\alpha}$ for $\alpha \in [0,1)$, and $\beta \geq 0$. Our interest is to find how large the subset $k(n)$ should be in order to have zero blocking and maximum speed-up in the limit as $n \to \infty$. We first characterize the system's performance when the jobs have access to the full system, i.e., $k(n)=n$. In this setting, we show that the blocking probability approaches to zero at the rate $O(1/\sqrt{n})$ and the mean response time of accepted jobs approaches to its minimum achievable value at rate $O(1/n)$. We then consider the case where the jobs only have access to subset of servers, i.e., $k(n) < n$. We show that as long as $k(n)=\omega(n^\alpha)$, the same asymptotic performance can be achieved as in the case with full system access. In particular, for $k(n)=\Theta(n^\alpha \log n)$, we show that both the blocking probability and the mean response time approach to their desired limits at rate $O(n^{-(1-\alpha)/2})$.
In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.
We propose a novel method for automatic reasoning on knowledge graphs based on debate dynamics. The main idea is to frame the task of triple classification as a debate game between two reinforcement learning agents which extract arguments -- paths in the knowledge graph -- with the goal to promote the fact being true (thesis) or the fact being false (antithesis), respectively. Based on these arguments, a binary classifier, called the judge, decides whether the fact is true or false. The two agents can be considered as sparse, adversarial feature generators that present interpretable evidence for either the thesis or the antithesis. In contrast to other black-box methods, the arguments allow users to get an understanding of the decision of the judge. Since the focus of this work is to create an explainable method that maintains a competitive predictive accuracy, we benchmark our method on the triple classification and link prediction task. Thereby, we find that our method outperforms several baselines on the benchmark datasets FB15k-237, WN18RR, and Hetionet. We also conduct a survey and find that the extracted arguments are informative for users.
Machine learning techniques have deeply rooted in our everyday life. However, since it is knowledge- and labor-intensive to pursue good learning performance, human experts are heavily involved in every aspect of machine learning. In order to make machine learning techniques easier to apply and reduce the demand for experienced human experts, automated machine learning (AutoML) has emerged as a hot topic with both industrial and academic interest. In this paper, we provide an up to date survey on AutoML. First, we introduce and define the AutoML problem, with inspiration from both realms of automation and machine learning. Then, we propose a general AutoML framework that not only covers most existing approaches to date but also can guide the design for new methods. Subsequently, we categorize and review the existing works from two aspects, i.e., the problem setup and the employed techniques. Finally, we provide a detailed analysis of AutoML approaches and explain the reasons underneath their successful applications. We hope this survey can serve as not only an insightful guideline for AutoML beginners but also an inspiration for future research.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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