The previous support vector machine(SVM) including $0/1$ loss SVM, hinge loss SVM, ramp loss SVM, truncated pinball loss SVM, and others, overlooked the degree of penalty for the correctly classified samples within the margin. This oversight affects the generalization ability of the SVM classifier to some extent. To address this limitation, from the perspective of confidence margin, we propose a novel Slide loss function ($\ell_s$) to construct the support vector machine classifier($\ell_s$-SVM). By introducing the concept of proximal stationary point, and utilizing the property of Lipschitz continuity, we derive the first-order optimality conditions for $\ell_s$-SVM. Based on this, we define the $\ell_s$ support vectors and working set of $\ell_s$-SVM. To efficiently handle $\ell_s$-SVM, we devise a fast alternating direction method of multipliers with the working set ($\ell_s$-ADMM), and provide the convergence analysis. The numerical experiments on real world datasets confirm the robustness and effectiveness of the proposed method.

Despite their simplicity, linear models perform well at time series forecasting, even when pitted against deeper and more expensive models. A number of variations to the linear model have been proposed, often including some form of feature normalisation that improves model generalisation. In this paper we analyse the sets of functions expressible using these linear model architectures. In so doing we show that several popular variants of linear models for time series forecasting are equivalent and functionally indistinguishable from standard, unconstrained linear regression. We characterise the model classes for each linear variant. We demonstrate that each model can be reinterpreted as unconstrained linear regression over a suitably augmented feature set, and therefore admit closed-form solutions when using a mean-squared loss function. We provide experimental evidence that the models under inspection learn nearly identical solutions, and finally demonstrate that the simpler closed form solutions are superior forecasters across 72% of test settings.

This paper addresses the problem of designing reliable prediction models that abstain from predictions when faced with uncertain or out-of-distribution samples - a recently proposed problem known as Selective Classification in the presence of Out-of-Distribution data (SCOD). We make three key contributions to SCOD. Firstly, we demonstrate that the optimal SCOD strategy involves a Bayes classifier for in-distribution (ID) data and a selector represented as a stochastic linear classifier in a 2D space, using i) the conditional risk of the ID classifier, and ii) the likelihood ratio of ID and out-of-distribution (OOD) data as input. This contrasts with suboptimal strategies from current OOD detection methods and the Softmax Information Retaining Combination (SIRC), specifically developed for SCOD. Secondly, we establish that in a distribution-free setting, the SCOD problem is not Probably Approximately Correct learnable when relying solely on an ID data sample. Third, we introduce POSCOD, a simple method for learning a plugin estimate of the optimal SCOD strategy from both an ID data sample and an unlabeled mixture of ID and OOD data. Our empirical results confirm the theoretical findings and demonstrate that our proposed method, POSCOD, out performs existing OOD methods in effectively addressing the SCOD problem.

Learning graph generative models over latent spaces has received less attention compared to models that operate on the original data space and has so far demonstrated lacklustre performance. We present GLAD a latent space graph generative model. Unlike most previous latent space graph generative models, GLAD operates on a discrete latent space that preserves to a significant extent the discrete nature of the graph structures making no unnatural assumptions such as latent space continuity. We learn the prior of our discrete latent space by adapting diffusion bridges to its structure. By operating over an appropriately constructed latent space we avoid relying on decompositions that are often used in models that operate in the original data space. We present experiments on a series of graph benchmark datasets which clearly show the superiority of the discrete latent space and obtain state of the art graph generative performance, making GLAD the first latent space graph generative model with competitive performance. Our source code is published at: \url{https://github.com/v18nguye/GLAD}.

Neural network actor-critic algorithms are one of the most popular methods in deep reinforcement learning. A neural network model is trained to select the policy (the "actor") while another neural network (the "critic") is simultaneously trained to learn the value function given the actor's policy. Specifically, the actor selects an action and, given the action, a new state transition occurs according to a Markov stochastic process and a reward (a measurement of the success/failure) is observed. The critic must learn to approximate the value function - the solution to the Bellman equation - given the actor's policy. Given the critic's estimate for the value function of the current policy, the actor must be updated to improve the value function (i.e., increase the expected reward). Actor-critic algorithms are well-established methods in reinforcement learning [17, 15]; the key recent advance is using (deep) neural networks as the actor/critic and training their parameters using gradient descent methods [26, 10, 25, 2, 29]. Analysis of neural network actor-critic algorithms is challenging due to: (1) the non-convexity of the neural networks, (2) the complex feedback loop between the actor and critic (the actor determines the sequence of data samples which are used to train the critic and the critic is used to train the actor), and (3) the simultaneous online updates of both the actor and critic which lead to (3A) the distribution of the data, which depends upon the actor, constantly evolving in time and (3B) the actor being updated with a noisy, biased estimate of the value function.

This paper studies the truncation method from Alquier [1] to derive high-probability PAC-Bayes bounds for unbounded losses with heavy tails. Assuming that the $p$-th moment is bounded, the resulting bounds interpolate between a slow rate $1 / \sqrt{n}$ when $p=2$, and a fast rate $1 / n$ when $p \to \infty$ and the loss is essentially bounded. Moreover, the paper derives a high-probability PAC-Bayes bound for losses with a bounded variance. This bound has an exponentially better dependence on the confidence parameter and the dependency measure than previous bounds in the literature. Finally, the paper extends all results to guarantees in expectation and single-draw PAC-Bayes. In order to so, it obtains analogues of the PAC-Bayes fast rate bound for bounded losses from [2] in these settings.

In order to adhere to regulatory standards governing individual data privacy and safety, machine learning models must systematically eliminate information derived from specific subsets of a user's training data that can no longer be utilized. The emerging discipline of Machine Unlearning has arisen as a pivotal area of research, facilitating the process of selectively discarding information designated to specific sets or classes of data from a pre-trained model, thereby eliminating the necessity for extensive retraining from scratch. The principal aim of this study is to formulate a methodology tailored for the purposeful elimination of information linked to a specific class of data from a pre-trained classification network. This intentional removal is crafted to degrade the model's performance specifically concerning the unlearned data class while concurrently minimizing any detrimental impacts on the model's performance in other classes. To achieve this goal, we frame the class unlearning problem from a Bayesian perspective, which yields a loss function that minimizes the log-likelihood associated with the unlearned data with a stability regularization in parameter space. This stability regularization incorporates Mohalanobis distance with respect to the Fisher Information matrix and $l_2$ distance from the pre-trained model parameters. Our novel approach, termed \textbf{Partially-Blinded Unlearning (PBU)}, surpasses existing state-of-the-art class unlearning methods, demonstrating superior effectiveness. Notably, PBU achieves this efficacy without requiring awareness of the entire training dataset but only to the unlearned data points, marking a distinctive feature of its performance.

In recent years, complementary recommendation has received extensive attention in the e-commerce domain. In this paper, we comprehensively summarize and compare 34 representative studies conducted between 2009 and 2024. Firstly, we compare the data and methods used for modeling complementary relationships between products, including simple complementarity and more complex scenarios such as asymmetric complementarity, the coexistence of substitution and complementarity relationships between products, and varying degrees of complementarity between different pairs of products. Next, we classify and compare the models based on the research problems of complementary recommendation, such as diversity, personalization, and cold-start. Furthermore, we provide a comparative analysis of experimental results from different studies conducted on the same dataset, which helps identify the strengths and weaknesses of the research. Compared to previous surveys, this paper provides a more updated and comprehensive summary of the research, discusses future research directions, and contributes to the advancement of this field.

Federated learning achieves effective performance in modeling decentralized data. In practice, client data are not well-labeled, which makes it potential for federated unsupervised learning (FUSL) with non-IID data. However, the performance of existing FUSL methods suffers from insufficient representations, i.e., (1) representation collapse entanglement among local and global models, and (2) inconsistent representation spaces among local models. The former indicates that representation collapse in local model will subsequently impact the global model and other local models. The latter means that clients model data representation with inconsistent parameters due to the deficiency of supervision signals. In this work, we propose FedU2 which enhances generating uniform and unified representation in FUSL with non-IID data. Specifically, FedU2 consists of flexible uniform regularizer (FUR) and efficient unified aggregator (EUA). FUR in each client avoids representation collapse via dispersing samples uniformly, and EUA in server promotes unified representation by constraining consistent client model updating. To extensively validate the performance of FedU2, we conduct both cross-device and cross-silo evaluation experiments on two benchmark datasets, i.e., CIFAR10 and CIFAR100.

Graph data, also known as complex network data, is omnipresent across various domains and applications. Prior graph neural network models primarily focused on extracting task-specific structural features through supervised learning objectives, but they fell short in capturing the inherent semantic and structural features of the entire graph. In this paper, we introduce the semantic-structural attention-enhanced graph convolutional network (SSA-GCN), which not only models the graph structure but also extracts generalized unsupervised features to enhance vertex classification performance. The SSA-GCN's key contributions lie in three aspects: firstly, it derives semantic information through unsupervised feature extraction from a knowledge graph perspective; secondly, it obtains structural information through unsupervised feature extraction from a complex network perspective; and finally, it integrates these features through a cross-attention mechanism. By leveraging these features, we augment the graph convolutional network, thereby enhancing the model's generalization capabilities. Our experiments on the Cora and CiteSeer datasets demonstrate the performance improvements achieved by our proposed method. Furthermore, our approach also exhibits excellent accuracy under privacy settings, making it a robust and effective solution for graph data analysis.