Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence of optimization errors, while the generalization analysis of stochastic optimization is much lagging behind. This is especially the case for nonconvex and nonsmooth problems often encountered in practice. In this paper, we initialize a systematic stability and generalization analysis of stochastic optimization on nonconvex and nonsmooth problems. We introduce novel algorithmic stability measures and establish their quantitative connection on the gap between population gradients and empirical gradients, which is then further extended to study the gap between the Moreau envelope of the empirical risk and that of the population risk. To our knowledge, these quantitative connection between stability and generalization in terms of either gradients or Moreau envelopes have not been studied in the literature. We introduce a class of sampling-determined algorithms, for which we develop bounds for three stability measures. Finally, we apply these discussions to derive error bounds for stochastic gradient descent and its adaptive variant, where we show how to achieve an implicit regularization by tuning the step sizes and the number of iterations.
The ability to interpret machine learning models has become increasingly important as their usage in data science continues to rise. Most current interpretability methods are optimized to work on either (\textit{i}) a global scale, where the goal is to rank features based on their contributions to overall variation in an observed population, or (\textit{ii}) the local level, which aims to detail on how important a feature is to a particular individual in the data set. In this work, a new operator is proposed called the "GlObal And Local Score" (GOALS): a simple \textit{post hoc} approach to simultaneously assess local and global feature variable importance in nonlinear models. Motivated by problems in biomedicine, the approach is demonstrated using Gaussian process regression where the task of understanding how genetic markers are associated with disease progression both within individuals and across populations is of high interest. Detailed simulations and real data analyses illustrate the flexible and efficient utility of GOALS over state-of-the-art variable importance strategies.
In the growing domain of scientific machine learning, in-context operator learning has demonstrated notable potential in learning operators from prompted data during inference stage without weight updates. However, the current model's overdependence on sensor data, may inadvertently overlook the invaluable human insight into the operator. To address this, we present a transformation of in-context operator learning into a multi-modal paradigm. We propose the use of "captions" to integrate human knowledge about the operator, expressed through natural language descriptions and equations. We illustrate how this method not only broadens the flexibility and generality of physics-informed learning, but also significantly boosts learning performance and reduces data needs. Furthermore, we introduce a more efficient neural network architecture for multi-modal in-context operator learning, referred to as "ICON-LM", based on a language-model-like architecture. We demonstrate the viability of "ICON-LM" for scientific machine learning tasks, which creates a new path for the application of language models.
Even though the analysis of unsteady 2D flow fields is challenging, fluid mechanics experts generally have an intuition on where in the simulation domain specific features are expected. Using this intuition, showing similar regions enables the user to discover flow patterns within the simulation data. When focusing on similarity, a solid mathematical framework for a specific flow pattern is not required. We propose a technique that visualizes similar and dissimilar regions with respect to a region selected by the user. Using infinitesimal strain theory, we capture the strain and rotation progression and therefore the dynamics of fluid parcels along pathlines, which we encode as distributions. We then apply the Jensen-Shannon divergence to compute the (dis)similarity between pathline dynamics originating in a user-defined flow region and the pathline dynamics of the flow field. We validate our method by applying it to two simulation datasets of two-dimensional unsteady flows. Our results show that our approach is suitable for analyzing the similarity of time-dependent flow fields.
Maximum mean discrepancy (MMD) has enjoyed a lot of success in many machine learning and statistical applications, including non-parametric hypothesis testing, because of its ability to handle non-Euclidean data. Recently, it has been demonstrated in Balasubramanian et al.(2021) that the goodness-of-fit test based on MMD is not minimax optimal while a Tikhonov regularized version of it is, for an appropriate choice of the regularization parameter. However, the results in Balasubramanian et al. (2021) are obtained under the restrictive assumptions of the mean element being zero, and the uniform boundedness condition on the eigenfunctions of the integral operator. Moreover, the test proposed in Balasubramanian et al. (2021) is not practical as it is not computable for many kernels. In this paper, we address these shortcomings and extend the results to general spectral regularizers that include Tikhonov regularization.
It has been a hot research topic to enable machines to understand human emotions in multimodal contexts under dialogue scenarios, which is tasked with multimodal emotion analysis in conversation (MM-ERC). MM-ERC has received consistent attention in recent years, where a diverse range of methods has been proposed for securing better task performance. Most existing works treat MM-ERC as a standard multimodal classification problem and perform multimodal feature disentanglement and fusion for maximizing feature utility. Yet after revisiting the characteristic of MM-ERC, we argue that both the feature multimodality and conversational contextualization should be properly modeled simultaneously during the feature disentanglement and fusion steps. In this work, we target further pushing the task performance by taking full consideration of the above insights. On the one hand, during feature disentanglement, based on the contrastive learning technique, we devise a Dual-level Disentanglement Mechanism (DDM) to decouple the features into both the modality space and utterance space. On the other hand, during the feature fusion stage, we propose a Contribution-aware Fusion Mechanism (CFM) and a Context Refusion Mechanism (CRM) for multimodal and context integration, respectively. They together schedule the proper integrations of multimodal and context features. Specifically, CFM explicitly manages the multimodal feature contributions dynamically, while CRM flexibly coordinates the introduction of dialogue contexts. On two public MM-ERC datasets, our system achieves new state-of-the-art performance consistently. Further analyses demonstrate that all our proposed mechanisms greatly facilitate the MM-ERC task by making full use of the multimodal and context features adaptively. Note that our proposed methods have the great potential to facilitate a broader range of other conversational multimodal tasks.
While deep reinforcement learning (RL) has fueled multiple high-profile successes in machine learning, it is held back from more widespread adoption by its often poor data efficiency and the limited generality of the policies it produces. A promising approach for alleviating these limitations is to cast the development of better RL algorithms as a machine learning problem itself in a process called meta-RL. Meta-RL is most commonly studied in a problem setting where, given a distribution of tasks, the goal is to learn a policy that is capable of adapting to any new task from the task distribution with as little data as possible. In this survey, we describe the meta-RL problem setting in detail as well as its major variations. We discuss how, at a high level, meta-RL research can be clustered based on the presence of a task distribution and the learning budget available for each individual task. Using these clusters, we then survey meta-RL algorithms and applications. We conclude by presenting the open problems on the path to making meta-RL part of the standard toolbox for a deep RL practitioner.
It has been a long time that computer architecture and systems are optimized to enable efficient execution of machine learning (ML) algorithms or models. Now, it is time to reconsider the relationship between ML and systems, and let ML transform the way that computer architecture and systems are designed. This embraces a twofold meaning: the improvement of designers' productivity, and the completion of the virtuous cycle. In this paper, we present a comprehensive review of work that applies ML for system design, which can be grouped into two major categories, ML-based modelling that involves predictions of performance metrics or some other criteria of interest, and ML-based design methodology that directly leverages ML as the design tool. For ML-based modelling, we discuss existing studies based on their target level of system, ranging from the circuit level to the architecture/system level. For ML-based design methodology, we follow a bottom-up path to review current work, with a scope of (micro-)architecture design (memory, branch prediction, NoC), coordination between architecture/system and workload (resource allocation and management, data center management, and security), compiler, and design automation. We further provide a future vision of opportunities and potential directions, and envision that applying ML for computer architecture and systems would thrive in the community.
Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.
The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular.
While existing machine learning models have achieved great success for sentiment classification, they typically do not explicitly capture sentiment-oriented word interaction, which can lead to poor results for fine-grained analysis at the snippet level (a phrase or sentence). Factorization Machine provides a possible approach to learning element-wise interaction for recommender systems, but they are not directly applicable to our task due to the inability to model contexts and word sequences. In this work, we develop two Position-aware Factorization Machines which consider word interaction, context and position information. Such information is jointly encoded in a set of sentiment-oriented word interaction vectors. Compared to traditional word embeddings, SWI vectors explicitly capture sentiment-oriented word interaction and simplify the parameter learning. Experimental results show that while they have comparable performance with state-of-the-art methods for document-level classification, they benefit the snippet/sentence-level sentiment analysis.