Graph-based Sequential Recommender systems (GSRs) have gained significant research attention due to their ability to simultaneously handle user-item interactions and sequential relationships between items. Current GSRs often utilize composite or in-depth structures for graph encoding (e.g., the Graph Transformer). Nevertheless, they have high computational complexity, hindering the deployment on resource-constrained edge devices. Moreover, the relative position encoding in Graph Transformer has difficulty in considering the complicated positional dependencies within sequence. To this end, we propose an External Attentive Graph convolutional network with Positional prompts for Sequential recommendation, namely EA-GPS. Specifically, we first introduce an external attentive graph convolutional network that linearly measures the global associations among nodes via two external memory units. Then, we present a positional prompt-based decoder that explicitly treats the absolute item positions as external prompts. By introducing length-adaptive sequential masking and a soft attention network, such a decoder facilitates the model to capture the long-term positional dependencies and contextual relationships within sequences. Extensive experimental results on five real-world datasets demonstrate that the proposed EA-GPS outperforms the state-of-the-art methods. Remarkably, it achieves the superior performance while maintaining a smaller parameter size and lower training overhead. The implementation of this work is publicly available at https://github.com/ZZY-GraphMiningLab/EA-GPS.

We study the problem of estimating Dynamic Discrete Choice (DDC) models, also known as offline Maximum Entropy-Regularized Inverse Reinforcement Learning (offline MaxEnt-IRL) in machine learning. The objective is to recover reward or $Q^*$ functions that govern agent behavior from offline behavior data. In this paper, we propose a globally convergent gradient-based method for solving these problems without the restrictive assumption of linearly parameterized rewards. The novelty of our approach lies in introducing the Empirical Risk Minimization (ERM) based IRL/DDC framework, which circumvents the need for explicit state transition probability estimation in the Bellman equation. Furthermore, our method is compatible with non-parametric estimation techniques such as neural networks. Therefore, the proposed method has the potential to be scaled to high-dimensional, infinite state spaces. A key theoretical insight underlying our approach is that the Bellman residual satisfies the Polyak-Lojasiewicz (PL) condition -- a property that, while weaker than strong convexity, is sufficient to ensure fast global convergence guarantees. Through a series of synthetic experiments, we demonstrate that our approach consistently outperforms benchmark methods and state-of-the-art alternatives.

To date, the multi-objective optimization literature has mainly focused on conflicting objectives, studying the Pareto front, or requiring users to balance tradeoffs. Yet, in machine learning practice, there are many scenarios where such conflict does not take place. Recent findings from multi-task learning, reinforcement learning, and LLMs training show that diverse related tasks can enhance performance across objectives simultaneously. Despite this evidence, such phenomenon has not been examined from an optimization perspective. This leads to a lack of generic gradient-based methods that can scale to scenarios with a large number of related objectives. To address this gap, we introduce the Aligned Multi-Objective Optimization framework, propose new algorithms for this setting, and provide theoretical guarantees of their superior performance compared to naive approaches.

--This is the third part of a series of studies that model the target trajectory, which describes the target state evolution over continuous time, as a sample path of a stochastic process (SP). By adopting a deterministic-stochastic decomposition framework, we decompose the learning of the trajectory SP into two sequential stages: the first fits the deterministic trend of the trajectory using a curve function of time, while the second estimates the residual stochastic component through parametric learning of either a Gaussian process (GP) or Student's-t process (StP). This leads to a Markov-free data-driven tracking approach that produces the continuous-time trajectory with minimal prior knowledge of the target dynamics. It does not only take advantage of the smooth trend of the target but also makes use of the long-term temporal correlation of both the data noise and the model fitting error . Simulations in four maneuvering target tracking scenarios have demonstrated its effectiveness and superiority in comparison with existing approaches. ARGET tracking that involves the online estimation of the trajectory of a target has been a long-standing research topic and plays a significant role in aerospace, traffic, defense, robotics, etc. [1] In essence, target tracking is more about estimating the continuous-time trajectory of the target rather than merely a finite number of point states. The continuous-time trajectory enables the acquisition of a point estimate of the state at any time in the trajectory period. However, the converse is not true. X, defined in spatio-temporal space, where X denotes the state space. Manuscript created Feb 2025; This work was supported in part by the National Natural Science Foundation of China under Grants 62422117 and 62201316 and in part by the Fundamental Research Funds for the Central Universities.

A similar approach, SMOTE (Synthetic Minority Over-sampling Technique) (Chawla et al., 2002; He et al., 2008; Bunkhumpornpat et al., 2012; Douzas et al., 2018), also leverages interpolated synthetic instances to enhance model performance particularly for imbalanced or long-tail distributions, showcasing the effectiveness of mixup methods. In this paper we place special focus on data synthesis, an important constituent of data augmentation. While there is extensive research on how synthetic data generated by mixup can enhance model performance (Carratino et al., 2022; Zhang et al., 2021), less attention has been given to understanding the fundamental properties of the synthesized data itself; see Sec. 2.1. In fact most mixup methods generate linearly interpolated instances by taking a weighted average where the weights are randomly drawn from distributions within the range of [0, 1], such as the beta or the uniform distribution. However, this interpolation process reduces the variance, which inevitably distorts the statistical structure of the original dataset both marginally and jointly. The net effect is a less dispersed dataset with more emphasis on representative instances and suppressing the others. In this regard, mixup-based synthetic datasets achieve better performance in training machine learning models from sacrificing non-representative instances, such as the tail instances, in the dataset.

We introduce Volume-Sorted Prediction Set ( VSPS), a novel method for uncertainty quantification in multi-target regression that uses conditional normalizing flows with conformal calibration. This approach constructs flexible, non-convex predictive regions with guaranteed coverage probabilities, overcoming limitations of traditional methods. By learning a transformation where the conditional distribution of responses follows a known form, VSPS identifies dense regions in the original space using the Jacobian determinant. This enables the creation of prediction regions that adapt to the true underlying distribution, focusing on areas of high probability density. Experimental results demonstrate that VSPS produces smaller, more informative prediction regions while maintaining robust coverage guarantees, enhancing uncertainty modeling in complex, high-dimensional settings. Introduction In real-world applications, it is often required to estimate more than one response variable [1, 2, 3]. Consider, for example, estimating the effects and side effects of a drug given the patient's demographic information and medical measurements.

This paper proposes an online inference method of the stochastic gradient descent (SGD) with a constant learning rate for quantile loss functions with theoretical guarantees. Since the quantile loss function is neither smooth nor strongly convex, we view such SGD iterates as an irreducible and positive recurrent Markov chain. By leveraging this interpretation, we show the existence of a unique asymptotic stationary distribution, regardless of the arbitrarily fixed initialization. To characterize the exact form of this limiting distribution, we derive bounds for its moment generating function and tail probabilities, controlling over the first and second moments of SGD iterates. By these techniques, we prove that the stationary distribution converges to a Gaussian distribution as the constant learning rate $\eta\rightarrow0$. Our findings provide the first central limit theorem (CLT)-type theoretical guarantees for the last iterate of constant learning-rate SGD in non-smooth and non-strongly convex settings. We further propose a recursive algorithm to construct confidence intervals of SGD iterates in an online manner. Numerical studies demonstrate strong finite-sample performance of our proposed quantile estimator and inference method. The theoretical tools in this study are of independent interest to investigate general transition kernels in Markov chains.

Regularizing neural networks is important for anticipating model behavior in regions of the data space that are not well represented. In this work, we propose a regularization technique for enforcing a level of smoothness in the mapping between the data input space and the loss value. We specify the level of regularity by requiring that the loss of the network satisfies an elliptic operator over the data domain. To do this, we modify the usual empirical risk minimization objective such that we instead minimize a new objective that satisfies an elliptic operator over points within the domain. This allows us to use existing theory on elliptic operators to anticipate the behavior of the error for points outside the training set. We propose a tractable computational method that approximates the behavior of the elliptic operator while being computationally efficient. Finally, we analyze the properties of the proposed regularization to understand the performance on common problems of distribution shift and group imbalance. Numerical experiments confirm the utility of the proposed regularization technique.

We address the problem of zero-order optimization from noisy observations for an objective function satisfying the Polyak-{\L}ojasiewicz or the strong convexity condition. Additionally, we assume that the objective function has an additive structure and satisfies a higher-order smoothness property, characterized by the H\"older family of functions. The additive model for H\"older classes of functions is well-studied in the literature on nonparametric function estimation, where it is shown that such a model benefits from a substantial improvement of the estimation accuracy compared to the H\"older model without additive structure. We study this established framework in the context of gradient-free optimization. We propose a randomized gradient estimator that, when plugged into a gradient descent algorithm, allows one to achieve minimax optimal optimization error of the order $dT^{-(\beta-1)/\beta}$, where $d$ is the dimension of the problem, $T$ is the number of queries and $\beta\ge 2$ is the H\"older degree of smoothness. We conclude that, in contrast to nonparametric estimation problems, no substantial gain of accuracy can be achieved when using additive models in gradient-free optimization.

In this paper, we investigate the effect of data heterogeneity across clients on the performance of distributed learning systems, i.e., one-round Federated Learning, as measured by the associated generalization error. Specifically, \(K\) clients have each \(n\) training samples generated independently according to a possibly different data distribution and their individually chosen models are aggregated by a central server. We study the effect of the discrepancy between the clients' data distributions on the generalization error of the aggregated model. First, we establish in-expectation and tail upper bounds on the generalization error in terms of the distributions. In part, the bounds extend the popular Conditional Mutual Information (CMI) bound which was developed for the centralized learning setting, i.e., \(K=1\), to the distributed learning setting with arbitrary number of clients $K \geq 1$. Then, we use a connection with information theoretic rate-distortion theory to derive possibly tighter \textit{lossy} versions of these bounds. Next, we apply our lossy bounds to study the effect of data heterogeneity across clients on the generalization error for distributed classification problem in which each client uses Support Vector Machines (D-SVM). In this case, we establish explicit generalization error bounds which depend explicitly on the data heterogeneity degree. It is shown that the bound gets smaller as the degree of data heterogeneity across clients gets higher, thereby suggesting that D-SVM generalizes better when the dissimilarity between the clients' training samples is bigger. This finding, which goes beyond D-SVM, is validated experimentally through a number of experiments.