Negative sampling has been heavily used to train recommender models on large-scale data, wherein sampling hard examples usually not only accelerates the convergence but also improves the model accuracy. Nevertheless, the reasons for the effectiveness of Hard Negative Sampling (HNS) have not been revealed yet. In this work, we fill the research gap by conducting thorough theoretical analyses on HNS. Firstly, we prove that employing HNS on the Bayesian Personalized Ranking (BPR) learner is equivalent to optimizing One-way Partial AUC (OPAUC). Concretely, the BPR equipped with Dynamic Negative Sampling (DNS) is an exact estimator, while with softmax-based sampling is a soft estimator. Secondly, we prove that OPAUC has a stronger connection with Top-K evaluation metrics than AUC and verify it with simulation experiments. These analyses establish the theoretical foundation of HNS in optimizing Top-K recommendation performance for the first time. On these bases, we offer two insightful guidelines for effective usage of HNS: 1) the sampling hardness should be controllable, e.g., via pre-defined hyper-parameters, to adapt to different Top-K metrics and datasets; 2) the smaller the $K$ we emphasize in Top-K evaluation metrics, the harder the negative samples we should draw. Extensive experiments on three real-world benchmarks verify the two guidelines.

Although much of the success of Deep Learning builds on learning good representations, a rigorous method to evaluate their quality is lacking. In this paper, we treat the evaluation of representations as a model selection problem and propose to use the Minimum Description Length (MDL) principle to devise an evaluation metric. Contrary to the established practice of limiting the capacity of the readout model, we design a hybrid discrete and continuous-valued model space for the readout models and employ a switching strategy to combine their predictions. The MDL score takes model complexity, as well as data efficiency into account. As a result, the most appropriate model for the specific task and representation will be chosen, making it a unified measure for comparison. The proposed metric can be efficiently computed with an online method and we present results for pre-trained vision encoders of various architectures (ResNet and ViT) and objective functions (supervised and self-supervised) on a range of downstream tasks. We compare our methods with accuracy-based approaches and show that the latter are inconsistent when multiple readout models are used. Finally, we discuss important properties revealed by our evaluations such as model scaling, preferred readout model, and data efficiency.

A significant share of political discourse occurs online on social media platforms. Policymakers and researchers try to understand the role of social media design in shaping the quality of political discourse around the globe. In the past decades, scholarship on political discourse theory has produced distinct characteristics of different types of prominent political rhetoric such as deliberative, civic, or demagogic discourse. This study investigates the relationship between social media reaction mechanisms (i.e., upvotes, downvotes) and political rhetoric in user discussions by engaging in an in-depth conceptual analysis of political discourse theory. First, we analyze 155 million user comments in 55 political subforums on Reddit between 2010 and 2018 to explore whether users' style of political discussion aligns with the essential components of deliberative, civic, and demagogic discourse. Second, we perform a quantitative study that combines confirmatory factor analysis with difference in differences models to explore whether different reaction mechanism schemes (e.g., upvotes only, upvotes and downvotes, no reaction mechanisms) correspond with political user discussion that is more or less characteristic of deliberative, civic, or demagogic discourse. We produce three main takeaways. First, despite being "ideal constructs of political rhetoric," we find that political discourse theories describe political discussions on Reddit to a large extent. Second, we find that discussions in subforums with only upvotes, or both up- and downvotes are associated with user discourse that is more deliberate and civic. Third, social media discussions are most demagogic in subreddits with no reaction mechanisms at all. These findings offer valuable contributions for ongoing policy discussions on the relationship between social media interface design and respectful political discussion among users.

Gradient descent-ascent (GDA) is a widely used algorithm for minimax optimization. However, GDA has been proved to converge to stationary points for nonconvex minimax optimization, which are suboptimal compared with local minimax points. In this work, we develop cubic regularization (CR) type algorithms that globally converge to local minimax points in nonconvex-strongly-concave minimax optimization. We first show that local minimax points are equivalent to second-order stationary points of a certain envelope function. Then, inspired by the classic cubic regularization algorithm, we propose an algorithm named Cubic-LocalMinimax for finding local minimax points, and provide a comprehensive convergence analysis by leveraging its intrinsic potential function. Specifically, we establish the global convergence of Cubic-LocalMinimax to a local minimax point at a sublinear convergence rate and characterize its iteration complexity. Also, we propose a GDA-based solver for solving the cubic subproblem involved in Cubic-LocalMinimax up to certain pre-defined accuracy, and analyze the overall gradient and Hessian-vector product computation complexities of such an inexact Cubic-LocalMinimax algorithm. Moreover, we propose a stochastic variant of Cubic-LocalMinimax for large-scale minimax optimization, and characterize its sample complexity under stochastic sub-sampling. Experimental results demonstrate faster convergence of our stochastic Cubic-LocalMinimax than some existing algorithms.

Spatiotemporal data mining plays an important role in air quality monitoring, crowd flow modeling, and climate forecasting. However, the originally collected spatiotemporal data in real-world scenarios is usually incomplete due to sensor failures or transmission loss. Spatiotemporal imputation aims to fill the missing values according to the observed values and the underlying spatiotemporal dependence of them. The previous dominant models impute missing values autoregressively and suffer from the problem of error accumulation. As emerging powerful generative models, the diffusion probabilistic models can be adopted to impute missing values conditioned by observations and avoid inferring missing values from inaccurate historical imputation. However, the construction and utilization of conditional information are inevitable challenges when applying diffusion models to spatiotemporal imputation. To address above issues, we propose a conditional diffusion framework for spatiotemporal imputation with enhanced prior modeling, named PriSTI. Our proposed framework provides a conditional feature extraction module first to extract the coarse yet effective spatiotemporal dependencies from conditional information as the global context prior. Then, a noise estimation module transforms random noise to realistic values, with the spatiotemporal attention weights calculated by the conditional feature, as well as the consideration of geographic relationships. PriSTI outperforms existing imputation methods in various missing patterns of different real-world spatiotemporal data, and effectively handles scenarios such as high missing rates and sensor failure. The implementation code is available at https://github.com/LMZZML/PriSTI.

Learning with noisy labels has become imperative in the Big Data era, which saves expensive human labors on accurate annotations. Previous noise-transition-based methods have achieved theoretically-grounded performance under the Class-Conditional Noise model (CCN). However, these approaches builds upon an ideal but impractical anchor set available to pre-estimate the noise transition. Even though subsequent works adapt the estimation as a neural layer, the ill-posed stochastic learning of its parameters in back-propagation easily falls into undesired local minimums. We solve this problem by introducing a Latent Class-Conditional Noise model (LCCN) to parameterize the noise transition under a Bayesian framework. By projecting the noise transition into the Dirichlet space, the learning is constrained on a simplex characterized by the complete dataset, instead of some ad-hoc parametric space wrapped by the neural layer. We then deduce a dynamic label regression method for LCCN, whose Gibbs sampler allows us efficiently infer the latent true labels to train the classifier and to model the noise. Our approach safeguards the stable update of the noise transition, which avoids previous arbitrarily tuning from a mini-batch of samples. We further generalize LCCN to different counterparts compatible with open-set noisy labels, semi-supervised learning as well as cross-model training. A range of experiments demonstrate the advantages of LCCN and its variants over the current state-of-the-art methods.

Unsupervised meta-learning aims to learn the meta knowledge from unlabeled data and rapidly adapt to novel tasks. However, existing approaches may be misled by the context-bias (e.g. background) from the training data. In this paper, we abstract the unsupervised meta-learning problem into a Structural Causal Model (SCM) and point out that such bias arises due to hidden confounders. To eliminate the confounders, we define the priors are \textit{conditionally} independent, learn the relationships between priors and intervene on them with casual factorization. Furthermore, we propose Causal Meta VAE (CMVAE) that encodes the priors into latent codes in the causal space and learns their relationships simultaneously to achieve the downstream few-shot image classification task. Results on toy datasets and three benchmark datasets demonstrate that our method can remove the context-bias and it outperforms other state-of-the-art unsupervised meta-learning algorithms because of bias-removal. Code is available at \url{https://github.com/GuodongQi/CMVAE}

Federated Learning (FL) is a learning paradigm that protects privacy by keeping client data on edge devices. However, optimizing FL in practice can be difficult due to the diversity and heterogeneity of the learning system. Despite recent research efforts to improve the optimization of heterogeneous data, the impact of time-evolving heterogeneous data in real-world scenarios, such as changing client data or intermittent clients joining or leaving during training, has not been studied well. In this work, we propose Continual Federated Learning (CFL), a flexible framework for capturing the time-evolving heterogeneity of FL. CFL can handle complex and realistic scenarios, which are difficult to evaluate in previous FL formulations, by extracting information from past local data sets and approximating local objective functions. We theoretically demonstrate that CFL methods have a faster convergence rate than FedAvg in time-evolving scenarios, with the benefit depending on approximation quality. Through experiments, we show that our numerical findings match the convergence analysis and that CFL methods significantly outperform other state-of-the-art FL baselines.

In supervised machine learning, we have a labeled dataset that is used to train the model. For example, we train a model to predict the prices of houses based on features like area, number of bedrooms, and location, etc. In unsupervised machine learning, we do not have a labeled dataset. The goal of unsupervised machine learning is to find patterns and relationships in data. Clustering is one of the most popular techniques used in unsupervised machine learning.

The sole aim of this book is to give a self-contained introduction to concepts and mathematical tools in Bayesian matrix decomposition in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning Bayesian matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of variational inference for conducting the optimization. We refer the reader to literature in the field of Bayesian analysis for a more detailed introduction to the related fields. This book is primarily a summary of purpose, significance of important Bayesian matrix decomposition methods, e.g., real-valued decomposition, nonnegative matrix factorization, Bayesian interpolative decomposition, and the origin and complexity of the methods which shed light on their applications. The mathematical prerequisite is a first course in statistics and linear algebra. Other than this modest background, the development is self-contained, with rigorous proof provided throughout.