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Vector Error Correction Model (VECM) is a classic method to analyse cointegration relationships amongst multivariate non-stationary time series. In this paper, we focus on high dimensional setting and seek for sample-size-efficient methodology to determine the level of cointegration. Our investigation centres at a Bayesian approach to analyse the cointegration matrix, henceforth determining the cointegration rank. We design two algorithms and implement them on simulated examples, yielding promising results particularly when dealing with high number of variables and relatively low number of observations. Furthermore, we extend this methodology to empirically investigate the constituents of the S&P 500 index, where low-volatility portfolios can be found during both in-sample training and out-of-sample testing periods.

We introduce Clifford Group Equivariant Simplicial Message Passing Networks, a method for steerable E(n)-equivariant message passing on simplicial complexes. Our method integrates the expressivity of Clifford group-equivariant layers with simplicial message passing, which is topologically more intricate than regular graph message passing. Clifford algebras include higher-order objects such as bivectors and trivectors, which express geometric features (e.g., areas, volumes) derived from vectors. Using this knowledge, we represent simplex features through geometric products of their vertices. To achieve efficient simplicial message passing, we share the parameters of the message network across different dimensions. Additionally, we restrict the final message to an aggregation of the incoming messages from different dimensions, leading to what we term shared simplicial message passing. Experimental results show that our method is able to outperform both equivariant and simplicial graph neural networks on a variety of geometric tasks.

Automatic Differentiation Variational Inference (ADVI) is efficient in learning probabilistic models. Classic ADVI relies on the parametric approach to approximate the posterior. In this paper, we develop a spline-based nonparametric approximation approach that enables flexible posterior approximation for distributions with complicated structures, such as skewness, multimodality, and bounded support. Compared with widely-used nonparametric variational inference methods, the proposed method is easy to implement and adaptive to various data structures. By adopting the spline approximation, we derive a lower bound of the importance weighted autoencoder and establish the asymptotic consistency. Experiments demonstrate the efficiency of the proposed method in approximating complex posterior distributions and improving the performance of generative models with incomplete data.

Semantic Communication (SC) is a novel paradigm for data transmission in 6G. However, there are several challenges posed when performing SC in 3D scenarios: 1) 3D semantic extraction; 2) Latent semantic redundancy; and 3) Uncertain channel estimation. To address these issues, we propose a Generative AI Model assisted 3D SC (GAM-3DSC) system. Firstly, we introduce a 3D Semantic Extractor (3DSE), which employs generative AI models, including Segment Anything Model (SAM) and Neural Radiance Field (NeRF), to extract key semantics from a 3D scenario based on user requirements. The extracted 3D semantics are represented as multi-perspective images of the goal-oriented 3D object. Then, we present an Adaptive Semantic Compression Model (ASCM) for encoding these multi-perspective images, in which we use a semantic encoder with two output heads to perform semantic encoding and mask redundant semantics in the latent semantic space, respectively. Next, we design a conditional Generative adversarial network and Diffusion model aided-Channel Estimation (GDCE) to estimate and refine the Channel State Information (CSI) of physical channels. Finally, simulation results demonstrate the advantages of the proposed GAM-3DSC system in effectively transmitting the goal-oriented 3D scenario.

Recent advances in machine learning have significantly impacted the field of information extraction, with Large Language Models (LLMs) playing a pivotal role in extracting structured information from unstructured text. This paper explores the challenges and limitations of current methodologies in structured entity extraction and introduces a novel approach to address these issues. We contribute to the field by first introducing and formalizing the task of Structured Entity Extraction (SEE), followed by proposing Approximate Entity Set OverlaP (AESOP) Metric designed to appropriately assess model performance on this task. Later, we propose a new model that harnesses the power of LLMs for enhanced effectiveness and efficiency through decomposing the entire extraction task into multiple stages. Quantitative evaluation and human side-by-side evaluation confirm that our model outperforms baselines, offering promising directions for future advancements in structured entity extraction.

Multimodal Sentiment Analysis (MSA) aims to understand human intentions by integrating emotion-related clues from diverse modalities, such as visual, language, and audio. Unfortunately, the current MSA task invariably suffers from unplanned dataset biases, particularly multimodal utterance-level label bias and word-level context bias. These harmful biases potentially mislead models to focus on statistical shortcuts and spurious correlations, causing severe performance bottlenecks. To alleviate these issues, we present a Multimodal Counterfactual Inference Sentiment (MCIS) analysis framework based on causality rather than conventional likelihood. Concretely, we first formulate a causal graph to discover harmful biases from already-trained vanilla models. In the inference phase, given a factual multimodal input, MCIS imagines two counterfactual scenarios to purify and mitigate these biases. Then, MCIS can make unbiased decisions from biased observations by comparing factual and counterfactual outcomes. We conduct extensive experiments on several standard MSA benchmarks. Qualitative and quantitative results show the effectiveness of the proposed framework.

2D-based Industrial Anomaly Detection has been widely discussed, however, multimodal industrial anomaly detection based on 3D point clouds and RGB images still has many untouched fields. Existing multimodal industrial anomaly detection methods directly concatenate the multimodal features, which leads to a strong disturbance between features and harms the detection performance. In this paper, we propose Multi-3D-Memory (M3DM), a novel multimodal anomaly detection method with hybrid fusion scheme: firstly, we design an unsupervised feature fusion with patch-wise contrastive learning to encourage the interaction of different modal features; secondly, we use a decision layer fusion with multiple memory banks to avoid loss of information and additional novelty classifiers to make the final decision. We further propose a point feature alignment operation to better align the point cloud and RGB features. Extensive experiments show that our multimodal industrial anomaly detection model outperforms the state-of-the-art (SOTA) methods on both detection and segmentation precision on MVTec-3D AD dataset. Code is available at //github.com/nomewang/M3DM.

Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.

Graph Neural Networks (GNN) is an emerging field for learning on non-Euclidean data. Recently, there has been increased interest in designing GNN that scales to large graphs. Most existing methods use "graph sampling" or "layer-wise sampling" techniques to reduce training time. However, these methods still suffer from degrading performance and scalability problems when applying to graphs with billions of edges. This paper presents GBP, a scalable GNN that utilizes a localized bidirectional propagation process from both the feature vectors and the training/testing nodes. Theoretical analysis shows that GBP is the first method that achieves sub-linear time complexity for both the precomputation and the training phases. An extensive empirical study demonstrates that GBP achieves state-of-the-art performance with significantly less training/testing time. Most notably, GBP can deliver superior performance on a graph with over 60 million nodes and 1.8 billion edges in less than half an hour on a single machine.

We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.