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Knowledge graphs (KGs) are commonly used as side information to enhance collaborative signals and improve recommendation quality. In the context of knowledge-aware recommendation (KGR), graph neural networks (GNNs) have emerged as promising solutions for modeling factual and semantic information in KGs. However, the long-tail distribution of entities leads to sparsity in supervision signals, which weakens the quality of item representation when utilizing KG enhancement. Additionally, the binary relation representation of KGs simplifies hyper-relational facts, making it challenging to model complex real-world information. Furthermore, the over-smoothing phenomenon results in indistinguishable representations and information loss. To address these challenges, we propose the SDK (Self-Supervised Dynamic Hypergraph Recommendation based on Hyper-Relational Knowledge Graph) framework. This framework establishes a cross-view hypergraph self-supervised learning mechanism for KG enhancement. Specifically, we model hyper-relational facts in KGs to capture interdependencies between entities under complete semantic conditions. With the refined representation, a hypergraph is dynamically constructed to preserve features in the deep vector space, thereby alleviating the over-smoothing problem. Furthermore, we mine external supervision signals from both the global perspective of the hypergraph and the local perspective of collaborative filtering (CF) to guide the model prediction process. Extensive experiments conducted on different datasets demonstrate the superiority of the SDK framework over state-of-the-art models. The results showcase its ability to alleviate the effects of over-smoothing and supervision signal sparsity.

Causal regularization was introduced as a stable causal inference strategy in a two-environment setting in Kania and Wit [2022] for linear structural equations models (SEMs). We start with observing that causal regularizer can be extended to several shifted environments and non-linear SEMs. We derive the multi-environment casual regularizer in the population setting. We propose its plug-in estimator, and study its concentration in measure behavior. Although the variance of the plug-in estimator is not well-defined in general, we instead study its conditional variance both with respect to a natural filtration of the empirical as well as conditioning with respect to certain events. We also study generalizations where we consider conditional expectations of higher central absolute moments of the estimator. The results presented here are also new in the prior setting of Kania and Wit [2022] as well as in Rothenhausler et al. [2021].

In this paper, we study the problem of estimating the autocovariance sequence resulting from a reversible Markov chain. A motivating application for studying this problem is the estimation of the asymptotic variance in central limit theorems for Markov chains. We propose a novel shape-constrained estimator of the autocovariance sequence, which is based on the key observation that the representability of the autocovariance sequence as a moment sequence imposes certain shape constraints. We examine the theoretical properties of the proposed estimator and provide strong consistency guarantees for our estimator. In particular, for geometrically ergodic reversible Markov chains, we show that our estimator is strongly consistent for the true autocovariance sequence with respect to an $\ell_2$ distance, and that our estimator leads to strongly consistent estimates of the asymptotic variance. Finally, we perform empirical studies to illustrate the theoretical properties of the proposed estimator as well as to demonstrate the effectiveness of our estimator in comparison with other current state-of-the-art methods for Markov chain Monte Carlo variance estimation, including batch means, spectral variance estimators, and the initial convex sequence estimator.

We describe a new dependent-rounding algorithmic framework for bipartite graphs. Given a fractional assignment $y$ of values to edges of graph $G = (U \cup V, E)$, the algorithms return an integral solution $Y$ such that each right-node $v \in V$ has at most one neighboring edge $f$ with $Y_f = 1$, and where the variables $Y_e$ also satisfy broad nonpositive-correlation properties. In particular, for any edges $e_1, e_2$ sharing a left-node $u \in U$, the variables $Y_{e_1}, Y_{e_2}$ have strong negative-correlation properties, i.e. the expectation of $Y_{e_1} Y_{e_2}$ is significantly below $y_{e_1} y_{e_2}$. This algorithm is a refinement of a dependent-rounding algorithm of Im \& Shadloo (2020) based on simulation of Poisson processes. Our algorithm allows greater flexibility, in particular, it allows ``irregular'' fractional assignments, and it gives more refined bounds on the negative correlation. Dependent rounding schemes with negative correlation properties have been used for approximation algorithms for job-scheduling on unrelated machines to minimize weighted completion times (Bansal, Srinivasan, & Svensson (2021), Im & Shadloo (2020), Im & Li (2023)). Using our new dependent-rounding algorithm, among other improvements, we obtain a $1.407$-approximation for this problem. This significantly improves over the prior $1.45$-approximation ratio of Im & Li (2023).

The work of Kalman and Bucy has established a duality between filtering and optimal estimation in the context of time-continuous linear systems. This duality has recently been extended to time-continuous nonlinear systems in terms of an optimization problem constrained by a backward stochastic partial differential equation. Here we revisit this problem from the perspective of appropriate forward-backward stochastic differential equations. This approach sheds new light on the estimation problem and provides a unifying perspective. It is also demonstrated that certain formulations of the estimation problem lead to deterministic formulations similar to the linear Gaussian case as originally investigated by Kalman and Bucy. Finally, optimal control of partially observed diffusion processes is discussed as an application of the proposed estimators.

Recently, instruction-following Large Language Models (LLMs) , represented by ChatGPT, have exhibited exceptional performance in general Natural Language Processing (NLP) tasks. However, the unique characteristics of E-commerce data pose significant challenges to general LLMs. An LLM tailored specifically for E-commerce scenarios, possessing robust cross-dataset/task generalization capabilities, is a pressing necessity. To solve this issue, in this work, we proposed the first e-commerce instruction dataset EcomInstruct, with a total of 2.5 million instruction data. EcomInstruct scales up the data size and task diversity by constructing atomic tasks with E-commerce basic data types, such as product information, user reviews. Atomic tasks are defined as intermediate tasks implicitly involved in solving a final task, which we also call Chain-of-Task tasks. We developed EcomGPT with different parameter scales by training the backbone model BLOOMZ with the EcomInstruct. Benefiting from the fundamental semantic understanding capabilities acquired from the Chain-of-Task tasks, EcomGPT exhibits excellent zero-shot generalization capabilities. Extensive experiments and human evaluations demonstrate that EcomGPT outperforms ChatGPT in term of cross-dataset/task generalization on E-commerce tasks.

Delaunay Triangulation(DT) is one of the important geometric problems that is used in various branches of knowledge such as computer vision, terrain modeling, spatial clustering and networking. Kinetic data structures have become very important in computational geometry for dealing with moving objects. However, when dealing with moving points, maintaining a dynamically changing Delaunay triangulation can be challenging. So, In this case, we have to update triangulation repeatedly. If points move so far, it is better to rebuild the triangulation. One approach to handle moving points is to use an incremental algorithm. For the case that points move slowly, we can give a faster algorithm than rebuilding it. Furthermore, sequential algorithms can be computationally expensive for large datasets. So, one way to compute as fast as possible is parallelism. In this paper, we propose a parallel algorithm for moving points. we propose an algorithm that divides datasets into equal partitions and give every partition to one block. Each block satisfay the Delaunay constraints after each time step and uses delete and insert algorithms to do this. We show this algorithm works faster than serial algorithms.

The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that validation of XAI must be done empirically, on a case-by-case basis, which prevents systematic theory-building in XAI. We propose a psychological theory of how humans draw conclusions from saliency maps, the most common form of XAI explanation, which for the first time allows for precise prediction of explainee inference conditioned on explanation. Our theory posits that absent explanation humans expect the AI to make similar decisions to themselves, and that they interpret an explanation by comparison to the explanations they themselves would give. Comparison is formalized via Shepard's universal law of generalization in a similarity space, a classic theory from cognitive science. A pre-registered user study on AI image classifications with saliency map explanations demonstrate that our theory quantitatively matches participants' predictions of the AI.

The core of information retrieval (IR) is to identify relevant information from large-scale resources and return it as a ranked list to respond to user's information need. Recently, the resurgence of deep learning has greatly advanced this field and leads to a hot topic named NeuIR (i.e., neural information retrieval), especially the paradigm of pre-training methods (PTMs). Owing to sophisticated pre-training objectives and huge model size, pre-trained models can learn universal language representations from massive textual data, which are beneficial to the ranking task of IR. Since there have been a large number of works dedicating to the application of PTMs in IR, we believe it is the right time to summarize the current status, learn from existing methods, and gain some insights for future development. In this survey, we present an overview of PTMs applied in different components of IR system, including the retrieval component, the re-ranking component, and other components. In addition, we also introduce PTMs specifically designed for IR, and summarize available datasets as well as benchmark leaderboards. Moreover, we discuss some open challenges and envision some promising directions, with the hope of inspiring more works on these topics for future research.

Recommender systems are widely used in big information-based companies such as Google, Twitter, LinkedIn, and Netflix. A recommender system deals with the problem of information overload by filtering important information fragments according to users' preferences. In light of the increasing success of deep learning, recent studies have proved the benefits of using deep learning in various recommendation tasks. However, most proposed techniques only aim to target individuals, which cannot be efficiently applied in group recommendation. In this paper, we propose a deep learning architecture to solve the group recommendation problem. On the one hand, as different individual preferences in a group necessitate preference trade-offs in making group recommendations, it is essential that the recommendation model can discover substitutes among user behaviors. On the other hand, it has been observed that a user as an individual and as a group member behaves differently. To tackle such problems, we propose using an attention mechanism to capture the impact of each user in a group. Specifically, our model automatically learns the influence weight of each user in a group and recommends items to the group based on its members' weighted preferences. We conduct extensive experiments on four datasets. Our model significantly outperforms baseline methods and shows promising results in applying deep learning to the group recommendation problem.