Tensor clustering has become an important topic, specifically in spatio-temporal modeling, due to its ability to cluster spatial modes (e.g., stations or road segments) and temporal modes (e.g., time of the day or day of the week). Our motivating example is from subway passenger flow modeling, where similarities between stations are commonly found. However, the challenges lie in the innate high-dimensionality of tensors and also the potential existence of anomalies. This is because the three tasks, i.e., dimension reduction, clustering, and anomaly decomposition, are inter-correlated to each other, and treating them in a separate manner will render a suboptimal performance. Thus, in this work, we design a tensor-based subspace clustering and anomaly decomposition technique for simultaneously outlier-robust dimension reduction and clustering for high-dimensional tensors. To achieve this, a novel low-rank robust subspace clustering decomposition model is proposed by combining Tucker decomposition, sparse anomaly decomposition, and subspace clustering. An effective algorithm based on Block Coordinate Descent is proposed to update the parameters. Prudent experiments prove the effectiveness of the proposed framework via the simulation study, with a gain of +25% clustering accuracy than benchmark methods in a hard case. The interrelations of the three tasks are also analyzed via ablation studies, validating the interrelation assumption. Moreover, a case study in the station clustering based on real passenger flow data is conducted, with quite valuable insights discovered.
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Conventional methods for student modeling, which involve predicting grades based on measured activities, struggle to provide accurate results for minority/underrepresented student groups due to data availability biases. In this paper, we propose a Multi-Layer Personalized Federated Learning (MLPFL) methodology that optimizes inference accuracy over different layers of student grouping criteria, such as by course and by demographic subgroups within each course. In our approach, personalized models for individual student subgroups are derived from a global model, which is trained in a distributed fashion via meta-gradient updates that account for subgroup heterogeneity while preserving modeling commonalities that exist across the full dataset. The evaluation of the proposed methodology considers case studies of two popular downstream student modeling tasks, knowledge tracing and outcome prediction, which leverage multiple modalities of student behavior (e.g., visits to lecture videos and participation on forums) in model training. Experiments on three real-world online course datasets show significant improvements achieved by our approach over existing student modeling benchmarks, as evidenced by an increased average prediction quality and decreased variance across different student subgroups. Visual analysis of the resulting students' knowledge state embeddings confirm that our personalization methodology extracts activity patterns clustered into different student subgroups, consistent with the performance enhancements we obtain over the baselines.
Microcanonical gradient descent is a sampling procedure for energy-based models allowing for efficient sampling of distributions in high dimension. It works by transporting samples from a high-entropy distribution, such as Gaussian white noise, to a low-energy region using gradient descent. We put this model in the framework of normalizing flows, showing how it can often overfit by losing an unnecessary amount of entropy in the descent. As a remedy, we propose a mean-field microcanonical gradient descent that samples several weakly coupled data points simultaneously, allowing for better control of the entropy loss while paying little in terms of likelihood fit. We study these models in the context of financial time series, illustrating the improvements on both synthetic and real data.
Optimal transport (OT) barycenters are a mathematically grounded way of averaging probability distributions while capturing their geometric properties. In short, the barycenter task is to take the average of a collection of probability distributions w.r.t. given OT discrepancies. We propose a novel algorithm for approximating the continuous Entropic OT (EOT) barycenter for arbitrary OT cost functions. Our approach is built upon the dual reformulation of the EOT problem based on weak OT, which has recently gained the attention of the ML community. Beyond its novelty, our method enjoys several advantageous properties: (i) we establish quality bounds for the recovered solution; (ii) this approach seamlessly interconnects with the Energy-Based Models (EBMs) learning procedure enabling the use of well-tuned algorithms for the problem of interest; (iii) it provides an intuitive optimization scheme avoiding min-max, reinforce and other intricate technical tricks. For validation, we consider several low-dimensional scenarios and image-space setups, including non-Euclidean cost functions. Furthermore, we investigate the practical task of learning the barycenter on an image manifold generated by a pretrained generative model, opening up new directions for real-world applications.
Electromagnetic information theory (EIT) is one of the emerging topics for 6G communication due to its potential to reveal the performance limit of wireless communication systems. For EIT, the research foundation is reasonable and accurate channel modeling. Existing channel modeling works for EIT in non-line-of-sight (NLoS) scenario focus on far-field modeling, which can not accurately capture the characteristics of the channel in near-field. In this paper, we propose the near-field channel model for EIT based on electromagnetic scattering theory. We model the channel by using non-stationary Gaussian random fields and derive the analytical expression of the correlation function of the fields. Furthermore, we analyze the characteristics of the proposed channel model, e.g., channel degrees of freedom (DoF). Finally, we design a channel estimation scheme for near-field scenario by integrating the electromagnetic prior information of the proposed model. Numerical analysis verifies the correctness of the proposed scheme and shows that it can outperform existing schemes like least square (LS) and orthogonal matching pursuit (OMP).
Grounding the reasoning ability of large language models (LLMs) for embodied tasks is challenging due to the complexity of the physical world. Especially, LLM planning for multi-agent collaboration requires communication of agents or credit assignment as the feedback to re-adjust the proposed plans and achieve effective coordination. However, existing methods that overly rely on physical verification or self-reflection suffer from excessive and inefficient querying of LLMs. In this paper, we propose a novel framework for multi-agent collaboration that introduces Reinforced Advantage feedback (ReAd) for efficient self-refinement of plans. Specifically, we perform critic regression to learn a sequential advantage function from LLM-planned data, and then treat the LLM planner as an optimizer to generate actions that maximize the advantage function. It endows the LLM with the foresight to discern whether the action contributes to accomplishing the final task. We provide theoretical analysis by extending advantage-weighted regression in reinforcement learning to multi-agent systems. Experiments on Overcooked-AI and a difficult variant of RoCoBench show that ReAd surpasses baselines in success rate, and also significantly decreases the interaction steps of agents and query rounds of LLMs, demonstrating its high efficiency for grounding LLMs. More results are given at //read-llm.github.io/.
We perform detailed theoretical analysis of an expectation-maximization-based algorithm recently proposed in for solving a variation of the 3D registration problem, named multi-model 3D registration. Despite having shown superior empirical results, did not theoretically justify the conditions under which the EM approach converges to the ground truth. In this project, we aim to close this gap by establishing such conditions. In particular, the analysis revolves around the usage of probabilistic tail bounds that are developed and applied in various instances throughout the course. The problem studied in this project stands as another example, different from those seen in the course, in which tail-bounds help advance our algorithmic understanding in a probabilistic way. We provide self-contained background materials on 3D Registration
Standard common factor models, such as the linear normal factor model, rely on strict parametric assumptions, which require rigorous model-data fit assessment to prevent fallacious inferences. However, overall goodness-of-fit diagnostics conventionally used in factor analysis do not offer diagnostic information on where the misfit originates. In the current work, we propose a new fit assessment framework for common factor models by extending the theory of generalized residuals (Haberman & Sinharay, 2013). This framework allows for the flexible adaptation of test statistics to identify various sources of misfit. In addition, the resulting goodness-of-fit tests provide more informative diagnostics, as the evaluation is performed conditionally on latent variables. Several examples of test statistics suitable for assessing various model assumptions are presented within this framework, and their performance is evaluated by simulation studies and a real data example.
Deep cooperative multi-agent reinforcement learning has demonstrated its remarkable success over a wide spectrum of complex control tasks. However, recent advances in multi-agent learning mainly focus on value decomposition while leaving entity interactions still intertwined, which easily leads to over-fitting on noisy interactions between entities. In this work, we introduce a novel interactiOn Pattern disenTangling (OPT) method, to disentangle the entity interactions into interaction prototypes, each of which represents an underlying interaction pattern within a subgroup of the entities. OPT facilitates filtering the noisy interactions between irrelevant entities and thus significantly improves generalizability as well as interpretability. Specifically, OPT introduces a sparse disagreement mechanism to encourage sparsity and diversity among discovered interaction prototypes. Then the model selectively restructures these prototypes into a compact interaction pattern by an aggregator with learnable weights. To alleviate the training instability issue caused by partial observability, we propose to maximize the mutual information between the aggregation weights and the history behaviors of each agent. Experiments on single-task, multi-task and zero-shot benchmarks demonstrate that the proposed method yields results superior to the state-of-the-art counterparts. Our code is available at //github.com/liushunyu/OPT.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
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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