Distributed learning is indispensable for training large-scale deep models. Asynchronous SGD (ASGD) and its variants are commonly used distributed learning methods in many scenarios where the computing capabilities of workers in the cluster are heterogeneous. Momentum has been acknowledged for its benefits in both optimization and generalization in deep model training. However, existing works have found that naively incorporating momentum into ASGD can impede the convergence. In this paper, we propose a novel method, called ordered momentum (OrMo), for ASGD. In OrMo, momentum is incorporated into ASGD by organizing the gradients in order based on their iteration indexes. We theoretically prove the convergence of OrMo for non-convex problems. To the best of our knowledge, this is the first work to establish the convergence analysis of ASGD with momentum without relying on the bounded delay assumption. Empirical results demonstrate that OrMo can achieve better convergence performance compared with ASGD and other asynchronous methods with momentum.

As data plays an increasingly pivotal role in decision-making, the emergence of data markets underscores the growing importance of data valuation. Within the machine learning landscape, Data Shapley stands out as a widely embraced method for data valuation. However, a limitation of Data Shapley is its assumption of a fixed dataset, contrasting with the dynamic nature of real-world applications where data constantly evolves and expands. This paper establishes the relationship between Data Shapley and infinite-order U-statistics and addresses this limitation by quantifying the uncertainty of Data Shapley with changes in data distribution from the perspective of U-statistics. We make statistical inferences on data valuation to obtain confidence intervals for the estimations. We construct two different algorithms to estimate this uncertainty and provide recommendations for their applicable situations. We also conduct a series of experiments on various datasets to verify asymptotic normality and propose a practical trading scenario enabled by this method.

In this study, we delve into the Structured State Space Model (S4), Change Point Detection methodologies, and the Switching Non-linear Dynamics System (SNLDS). Our central proposition is an enhanced inference technique and long-range dependency method for SNLDS. The cornerstone of our approach is the fusion of S4 and SNLDS, leveraging the strengths of both models to effectively address the intricacies of long-range dependencies in switching time series. Through rigorous testing, we demonstrate that our proposed methodology adeptly segments and reproduces long-range dependencies in both the 1-D Lorenz dataset and the 2-D bouncing ball dataset. Notably, our integrated approach outperforms the standalone SNLDS in these tasks.

Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or multi-layer-perceptrons lack the structure required to explore things like prompting and alignment within models capable of in-context-learning. We propose univariate polynomial regression as a function class that is just rich enough to study prompting and alignment, while allowing us to visualize and understand what is going on clearly.

Graph neural networks (GNNs) have demonstrated remarkable success in numerous graph analytical tasks. Yet, their effectiveness is often compromised in real-world scenarios due to distribution shifts, limiting their capacity for knowledge transfer across changing environments or domains. Recently, Unsupervised Graph Domain Adaptation (UGDA) has been introduced to resolve this issue. UGDA aims to facilitate knowledge transfer from a labeled source graph to an unlabeled target graph. Current UGDA efforts primarily focus on model-centric methods, such as employing domain invariant learning strategies and designing model architectures. However, our critical examination reveals the limitations inherent to these model-centric methods, while a data-centric method allowed to modify the source graph provably demonstrates considerable potential. This insight motivates us to explore UGDA from a data-centric perspective. By revisiting the theoretical generalization bound for UGDA, we identify two data-centric principles for UGDA: alignment principle and rescaling principle. Guided by these principles, we propose GraphAlign, a novel UGDA method that generates a small yet transferable graph. By exclusively training a GNN on this new graph with classic Empirical Risk Minimization (ERM), GraphAlign attains exceptional performance on the target graph. Extensive experiments under various transfer scenarios demonstrate the GraphAlign outperforms the best baselines by an average of 2.16%, training on the generated graph as small as 0.25~1% of the original training graph.

We consider the problem of Bayesian regression with trustworthy uncertainty quantification. We define that the uncertainty quantification is trustworthy if the ground truth can be captured by intervals dependent on the predictive distributions with a pre-specified probability. Furthermore, we propose, Trust-Bayes, a novel optimization framework for Bayesian meta learning which is cognizant of trustworthy uncertainty quantification without explicit assumptions on the prior model/distribution of the functions. We characterize the lower bounds of the probabilities of the ground truth being captured by the specified intervals and analyze the sample complexity with respect to the feasible probability for trustworthy uncertainty quantification. Monte Carlo simulation of a case study using Gaussian process regression is conducted for verification and comparison with the Meta-prior algorithm.

Determining the number of clusters is a fundamental issue in data clustering. Several algorithms have been proposed, including centroid-based algorithms using the Euclidean distance and model-based algorithms using a mixture of probability distributions. Among these, greedy algorithms for searching the number of clusters by repeatedly splitting or merging clusters have advantages in terms of computation time for problems with large sample sizes. However, studies comparing these methods in systematic evaluation experiments still need to be included. This study examines centroid- and model-based cluster search algorithms in various cases that Gaussian mixture models (GMMs) can generate. The cases are generated by combining five factors: dimensionality, sample size, the number of clusters, cluster overlap, and covariance type. The results show that some cluster-splitting criteria based on Euclidean distance make unreasonable decisions when clusters overlap. The results also show that model-based algorithms are insensitive to covariance type and cluster overlap compared to the centroid-based method if the sample size is sufficient. Our cluster search implementation codes are available at https://github.com/lipryou/searchClustK

Models for categorical sequences typically assume exchangeable or first-order dependent sequence elements. These are common assumptions, for example, in models of computer malware traces and protein sequences. Although such simplifying assumptions lead to computational tractability, these models fail to capture long-range, complex dependence structures that may be harnessed for greater predictive power. To this end, a Bayesian modelling framework is proposed to parsimoniously capture rich dependence structures in categorical sequences, with memory efficiency suitable for real-time processing of data streams. Parsimonious Bayesian context trees are introduced as a form of variable-order Markov model with conjugate prior distributions. The novel framework requires fewer parameters than fixed-order Markov models by dropping redundant dependencies and clustering sequential contexts. Approximate inference on the context tree structure is performed via a computationally efficient model-based agglomerative clustering procedure. The proposed framework is tested on synthetic and real-world data examples, and it outperforms existing sequence models when fitted to real protein sequences and honeypot computer terminal sessions.

Representation learning has emerged as a powerful paradigm for extracting valuable latent features from complex, high-dimensional data. In financial domains, learning informative representations for assets can be used for tasks like sector classification, and risk management. However, the complex and stochastic nature of financial markets poses unique challenges. We propose a novel contrastive learning framework to generate asset embeddings from financial time series data. Our approach leverages the similarity of asset returns over many subwindows to generate informative positive and negative samples, using a statistical sampling strategy based on hypothesis testing to address the noisy nature of financial data. We explore various contrastive loss functions that capture the relationships between assets in different ways to learn a discriminative representation space. Experiments on real-world datasets demonstrate the effectiveness of the learned asset embeddings on benchmark industry classification and portfolio optimization tasks. In each case our novel approaches significantly outperform existing baselines highlighting the potential for contrastive learning to capture meaningful and actionable relationships in financial data.

As a new practical and economical solution to the aging problem of overhead line (OHL) assets, the technical policies of most power grid companies in the world experienced a gradual transition from scheduled preventive maintenance to a risk-based approach in asset management. Even though the accumulation of contamination is predictable within a certain degree, there are currently no effective ways to identify the risk of the insulator flashover in order to plan its replacement. This paper presents a novel machine learning (ML) based method for estimating the flashover probability of the cup-and-pin glass insulator string. The proposed method is based on the Extreme Gradient Boosting (XGBoost) supervised ML model, in which the leakage current (LC) features and applied voltage are used as the inputs. The established model can estimate the critical flashover voltage (U50%) for various designs of OHL insulators with different voltage levels. The proposed method is also able to accurately determine the condition of the insulator strings and instruct asset management engineers to take appropriate actions.