Machine Learning (cs.LG)

Abstract: We propose a node clustering method for time-varying graphs based on the assumption that the cluster labels are changed smoothly over time. Clustering is one of the fundamental tasks in many science and engineering fields including signal processing, machine learning, and data mining. Although most existing studies focus on the clustering of nodes in static graphs, we often encounter time-varying graphs for time-series data, e.g., social networks, brain functional connectivity, and point clouds. In this paper, we formulate a node clustering of time-varying graphs as an optimization problem based on spectral clustering, with a smoothness constraint of the node labels. We solve the problem with a primal-dual splitting algorithm. Experiments on synthetic and real-world time-varying graphs are performed to validate the effectiveness of the proposed approach.

Abstract: We develop the first active learning method in the predict-then-optimize framework. Specifically, we develop a learning method that sequentially decides whether to request the "labels" of feature samples from an unlabeled data stream, where the labels correspond to the parameters of an optimization model for decision-making. Our active learning method is the first to be directly informed by the decision error induced by the predicted parameters, which is referred to as the Smart Predict-then-Optimize (SPO) loss. Motivated by the structure of the SPO loss, our algorithm adopts a margin-based criterion utilizing the concept of distance to degeneracy and minimizes a tractable surrogate of the SPO loss on the collected data. In particular, we develop an efficient active learning algorithm with both hard and soft rejection variants, each with theoretical excess risk (i.e., generalization) guarantees. We further derive bounds on the label complexity, which refers to the number of samples whose labels are acquired to achieve a desired small level of SPO risk. Under some natural low-noise conditions, we show that these bounds can be better than the naive supervised learning approach that labels all samples. Furthermore, when using the SPO+ loss function, a specialized surrogate of the SPO loss, we derive a significantly smaller label complexity under separability conditions. We also present numerical evidence showing the practical value of our proposed algorithms in the settings of personalized pricing and the shortest path problem.

Abstract: Spectral-temporal graph neural network is a promising abstraction underlying most time series forecasting models that are based on graph neural networks (GNNs). However, more is needed to know about the underpinnings of this branch of methods. In this paper, we establish a theoretical framework that unravels the expressive power of spectral-temporal GNNs. Our results show that linear spectral-temporal GNNs are universal under mild assumptions, and their expressive power is bounded by our extended first-order Weisfeiler-Leman algorithm on discrete-time dynamic graphs. To make our findings useful in practice on valid instantiations, we discuss related constraints in detail and outline a theoretical blueprint for designing spatial and temporal modules in spectral domains. Building on these insights and to demonstrate how powerful spectral-temporal GNNs are based on our framework, we propose a simple instantiation named Temporal Graph GegenConv (TGC), which significantly outperforms most existing models with only linear components and shows better model efficiency.

Abstract: Tropical semiring has proven successful in several research areas, including optimal control, bioinformatics, discrete event systems, or solving a decision problem. In previous studies, a matrix two-factorization algorithm based on the tropical semiring has been applied to investigate bipartite and tripartite networks. Tri-factorization algorithms based on standard linear algebra are used for solving tasks such as data fusion, co-clustering, matrix completion, community detection, and more. However, there is currently no tropical matrix tri-factorization approach, which would allow for the analysis of multipartite networks with a high number of parts. To address this, we propose the triFastSTMF algorithm, which performs tri-factorization over the tropical semiring. We apply it to analyze a four-partition network structure and recover the edge lengths of the network. We show that triFastSTMF performs similarly to Fast-NMTF in terms of approximation and prediction performance when fitted on the whole network. When trained on a specific subnetwork and used to predict the whole network, triFastSTMF outperforms Fast-NMTF by several orders of magnitude smaller error. The robustness of triFastSTMF is due to tropical operations, which are less prone to predict large values compared to standard operations.

Abstract: A change point detection (CPD) framework assisted by a predictive machine learning model called ''Predict and Compare'' is introduced and characterised in relation to other state-of-the-art online CPD routines which it outperforms in terms of false positive rate and out-of-control average run length. The method's focus is on improving standard methods from sequential analysis such as the CUSUM rule in terms of these quality measures. This is achieved by replacing typically used trend estimation functionals such as the running mean with more sophisticated predictive models (Predict step), and comparing their prognosis with actual data (Compare step). The two models used in the Predict step are the ARIMA model and the LSTM recursive neural network. However, the framework is formulated in general terms, so as to allow the use of other prediction or comparison methods than those tested here. The power of the method is demonstrated in a tribological case study in which change points separating the run-in, steady-state, and divergent wear phases are detected in the regime of very few false positives.

Abstract: Robust reinforcement learning (RL) aims at learning a policy that optimizes the worst-case performance over an uncertainty set. Given nominal Markov decision process (N-MDP) that generates samples for training, the set contains MDPs obtained by some perturbations from N-MDP. In this paper, we introduce a new uncertainty set containing more realistic MDPs in practice than the existing sets. Using this uncertainty set, we present a robust RL, named ARQ-Learning, for tabular cases. Also, we characterize the finite-time error bounds and prove that it converges as fast as Q-Learning and robust Q-Learning (i.e., the state-of-the-art robust RL method) while providing better robustness for real applications. We propose {\em pessimistic agent} that efficiently tackles the key bottleneck for the extension of ARQ-Learning into large or continuous state spaces. Using this technique, we first propose PRQ-Learning. To the next, combining this with DQN and DDPG, we develop PR-DQN and PR-DDPG, respectively. We emphasize that our technique can be easily combined with the other popular model-free methods. Via experiments, we demonstrate the superiority of the proposed methods in various RL applications with model uncertainties.

Abstract: When fitting the learning data of an individual to algorithm-like learning models, the observations are so dependent and non-stationary that one may wonder what the classical Maximum Likelihood Estimator (MLE) could do, even if it is the usual tool applied to experimental cognition. Our objective in this work is to show that the estimation of the learning rate cannot be efficient if the learning rate is constant in the classical Exp3 (Exponential weights for Exploration and Exploitation) algorithm. Secondly, we show that if the learning rate decreases polynomially with the sample size, then the prediction error and in some cases the estimation error of the MLE satisfy bounds in probability that decrease at a polynomial rate.

Abstract: Time-to-event modelling, known as survival analysis, differs from standard regression as it addresses censoring in patients who do not experience the event of interest. Despite competitive performances in tackling this problem, machine learning methods often ignore other competing risks that preclude the event of interest. This practice biases the survival estimation. Extensions to address this challenge often rely on parametric assumptions or numerical estimations leading to sub-optimal survival approximations. This paper leverages constrained monotonic neural networks to model each competing survival distribution. This modelling choice ensures the exact likelihood maximisation at a reduced computational cost by using automatic differentiation. The effectiveness of the solution is demonstrated on one synthetic and three medical datasets. Finally, we discuss the implications of considering competing risks when developing risk scores for medical practice.

Abstract: NUBO, short for Newcastle University Bayesian Optimisation, is a Bayesian optimisation framework for the optimisation of expensive-to-evaluate black-box functions, such as physical experiments and computer simulators. Bayesian optimisation is a cost-efficient optimisation strategy that uses surrogate modelling via Gaussian processes to represent an objective function and acquisition functions to guide the selection of candidate points to approximate the global optimum of the objective function. NUBO itself focuses on transparency and user experience to make Bayesian optimisation easily accessible to researchers from all disciplines. Clean and understandable code, precise references, and thorough documentation ensure transparency, while user experience is ensured by a modular and flexible design, easy-to-write syntax, and careful selection of Bayesian optimisation algorithms. NUBO allows users to tailor Bayesian optimisation to their specific problem by writing the optimisation loop themselves using the provided building blocks. It supports sequential single-point, parallel multi-point, and asynchronous optimisation of bounded, constrained, and/or mixed (discrete and continuous) parameter input spaces. Only algorithms and methods that are extensively tested and validated to perform well are included in NUBO. This ensures that the package remains compact and does not overwhelm the user with an unnecessarily large number of options. The package is written in Python but does not require expert knowledge of Python to optimise your simulators and experiments. NUBO is distributed as open-source software under the BSD 3-Clause licence.

Abstract: Continuous-time models such as Neural ODEs and Neural Flows have shown promising results in analyzing irregularly sampled time series frequently encountered in electronic health records. Based on these models, time series are typically processed with a hybrid of an initial value problem (IVP) solver and a recurrent neural network within the variational autoencoder architecture. Sequentially solving IVPs makes such models computationally less efficient. In this paper, we propose to model time series purely with continuous processes whose state evolution can be approximated directly by IVPs. This eliminates the need for recurrent computation and enables multiple states to evolve in parallel. We further fuse the encoder and decoder with one IVP solver based on its invertibility, which leads to fewer parameters and faster convergence. Experiments on three real-world datasets show that the proposed approach achieves comparable extrapolation and classification performance while gaining more than one order of magnitude speedup over other continuous-time counterparts.

Abstract: Implicitly Normalized Forecaster (online mirror descent with Tsallis entropy as prox-function) is known to be an optimal algorithm for adversarial multi-armed problems (MAB). However, most of the complexity results rely on bounded rewards or other restrictive assumptions. Recently closely related best-of-both-worlds algorithm were proposed for both adversarial and stochastic heavy-tailed MAB settings. This algorithm is known to be optimal in both settings, but fails to exploit data fully. In this paper, we propose Implicitly Normalized Forecaster with clipping for MAB problems with heavy-tailed distribution on rewards. We derive convergence results under mild assumptions on rewards distribution and show that the proposed method is optimal for both linear and non-linear heavy-tailed stochastic MAB problems. Also we show that algorithm usually performs better compared to best-of-two-worlds algorithm.

Abstract: Vibration-based condition monitoring systems are receiving increasing attention due to their ability to accurately identify different conditions by capturing dynamic features over a broad frequency range. However, there is little research on clustering approaches in vibration data and the resulting solutions are often optimized for a single data set. In this work, we present an extensive comparison of the clustering algorithms K-means clustering, OPTICS, and Gaussian mixture model clustering (GMM) applied to statistical features extracted from the time and frequency domains of vibration data sets. Furthermore, we investigate the influence of feature combinations, feature selection using principal component analysis (PCA), and the specified number of clusters on the performance of the clustering algorithms. We conducted this comparison in terms of a grid search using three different benchmark data sets. Our work showed that averaging (Mean, Median) and variance-based features (Standard Deviation, Interquartile Range) performed significantly better than shape-based features (Skewness, Kurtosis). In addition, K-means outperformed GMM slightly for these data sets, whereas OPTICS performed significantly worse. We were also able to show that feature combinations as well as PCA feature selection did not result in any significant performance improvements. With an increase in the specified number of clusters, clustering algorithms performed better, although there were some specific algorithmic restrictions.

Abstract: Auction-based Federated Learning (AFL) has attracted extensive research interest due to its ability to motivate data owners to join FL through economic means. Existing works assume that only one data consumer and multiple data owners exist in an AFL marketplace (i.e., a monopoly market). Therefore, data owners bid to join the data consumer for FL. However, this assumption is not realistic in practical AFL marketplaces in which multiple data consumers can compete to attract data owners to join their respective FL tasks. In this paper, we bridge this gap by proposing a first-of-its-kind utility-maximizing bidding strategy for data consumers in federated learning (Fed-Bidder). It enables multiple FL data consumers to compete for data owners via AFL effectively and efficiently by providing with utility estimation capabilities which can accommodate diverse forms of winning functions, each reflecting different market dynamics. Extensive experiments based on six commonly adopted benchmark datasets show that Fed-Bidder is significantly more advantageous compared to four state-of-the-art approaches.

Abstract: This paper presents an approach for data-driven policy refinement in reinforcement learning, specifically designed for safety-critical applications. Our methodology leverages the strengths of data-driven optimization and reinforcement learning to enhance policy safety and optimality through iterative refinement. Our principal contribution lies in the mathematical formulation of this data-driven policy refinement concept. This framework systematically improves reinforcement learning policies by learning from counterexamples surfaced during data-driven verification. Furthermore, we present a series of theorems elucidating key theoretical properties of our approach, including convergence, robustness bounds, generalization error, and resilience to model mismatch. These results not only validate the effectiveness of our methodology but also contribute to a deeper understanding of its behavior in different environments and scenarios.

Abstract: Self-awareness is the key capability of autonomous systems, e.g., autonomous driving network, which relies on highly efficient time series forecasting algorithm to enable the system to reason about the future state of the environment, as well as its effect on the system behavior as time progresses. Recently, a large number of forecasting algorithms using either convolutional neural networks or graph neural networks have been developed to exploit the complex temporal and spatial dependencies present in the time series. While these solutions have shown significant advantages over statistical approaches, one open question is to effectively incorporate the global information which represents the seasonality patterns via the time component of time series into the forecasting models to improve their accuracy. This paper presents a general approach to integrating the time component into forecasting models. The main idea is to employ conditional neural fields to represent the auxiliary features extracted from the time component to obtain the global information, which will be effectively combined with the local information extracted from autoregressive neural networks through a layer-wise gated fusion module. Extensive experiments on road traffic and cellular network traffic datasets prove the effectiveness of the proposed approach.

Abstract: Direct policy optimization in reinforcement learning is usually solved with policy-gradient algorithms, which optimize policy parameters via stochastic gradient ascent. This paper provides a new theoretical interpretation and justification of these algorithms. First, we formulate direct policy optimization in the optimization by continuation framework. The latter is a framework for optimizing nonconvex functions where a sequence of surrogate objective functions, called continuations, are locally optimized. Second, we show that optimizing affine Gaussian policies and performing entropy regularization can be interpreted as implicitly optimizing deterministic policies by continuation. Based on these theoretical results, we argue that exploration in policy-gradient algorithms consists in computing a continuation of the return of the policy at hand, and that the variance of policies should be history-dependent functions adapted to avoid local extrema rather than to maximize the return of the policy.

Abstract: Federated learning (FL), which addresses data privacy issues by training models on resource-constrained mobile devices in a distributed manner, has attracted significant research attention. However, the problem of optimizing FL client selection in mobile federated learning networks (MFLNs), where devices move in and out of each others' coverage and no FL server knows all the data owners, remains open. To bridge this gap, we propose a first-of-its-kind \underline{Soc}ially-aware \underline{Fed}erated \underline{C}lient \underline{S}election (SocFedCS) approach to minimize costs and train high-quality FL models. SocFedCS enriches the candidate FL client pool by enabling data owners to propagate FL task information through their local networks of trust, even as devices are moving into and out of each others' coverage. Based on Lyapunov optimization, we first transform this time-coupled problem into a step-by-step optimization problem. Then, we design a method based on alternating minimization and self-adaptive global best harmony search to solve this mixed-integer optimization problem. Extensive experiments comparing SocFedCS against five state-of-the-art approaches based on four real-world multimedia datasets demonstrate that it achieves 2.06\% higher test accuracy and 12.24\% lower cost on average than the best-performing baseline.

Abstract: Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more theoretical research is needed to fully understand the defining properties of disentanglement and how different definitions relate to each other. This paper presents a meta-analysis of existing definitions of disentanglement, using category theory as a unifying and rigorous framework. We propose that the concepts of the cartesian and monoidal products should serve as the core of disentanglement. With these core concepts, we show the similarities and crucial differences in dealing with (i) functions, (ii) equivariant maps, (iii) relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our understanding of disentanglement and its various formulations and can help researchers navigate different definitions and choose the most appropriate one for their specific context.

Abstract: We consider alternating gradient descent (AGD) with fixed step size $\eta > 0$, applied to the asymmetric matrix factorization objective. We show that, for a rank-$r$ matrix $\mathbf{A} \in \mathbb{R}^{m \times n}$, $T = \left( \left(\frac{\sigma_1(\mathbf{A})}{\sigma_r(\mathbf{A})}\right)^2 \log(1/\epsilon)\right)$ iterations of alternating gradient descent suffice to reach an $\epsilon$-optimal factorization $\| \mathbf{A} - \mathbf{X}_T^{\vphantom{\intercal}} \mathbf{Y}_T^{\intercal} \|_{\rm F}^2 \leq \epsilon \| \mathbf{A} \|_{\rm F}^2$ with high probability starting from an atypical random initialization. The factors have rank $d>r$ so that $\mathbf{X}_T\in\mathbb{R}^{m \times d}$ and $\mathbf{Y}_T \in\mathbb{R}^{n \times d}$. Experiments suggest that our proposed initialization is not merely of theoretical benefit, but rather significantly improves convergence of gradient descent in practice. Our proof is conceptually simple: a uniform PL-inequality and uniform Lipschitz smoothness constant are guaranteed for a sufficient number of iterations, starting from our random initialization. Our proof method should be useful for extending and simplifying convergence analyses for a broader class of nonconvex low-rank factorization problems.

Abstract: Deep multi-view subspace clustering (DMVSC) has recently attracted increasing attention due to its promising performance. However, existing DMVSC methods still have two issues: (1) they mainly focus on using autoencoders to nonlinearly embed the data, while the embedding may be suboptimal for clustering because the clustering objective is rarely considered in autoencoders, and (2) existing methods typically have a quadratic or even cubic complexity, which makes it challenging to deal with large-scale data. To address these issues, in this paper we propose a novel deep multi-view subspace clustering method with anchor graph (DMCAG). To be specific, DMCAG firstly learns the embedded features for each view independently, which are used to obtain the subspace representations. To significantly reduce the complexity, we construct an anchor graph with small size for each view. Then, spectral clustering is performed on an integrated anchor graph to obtain pseudo-labels. To overcome the negative impact caused by suboptimal embedded features, we use pseudo-labels to refine the embedding process to make it more suitable for the clustering task. Pseudo-labels and embedded features are updated alternately. Furthermore, we design a strategy to keep the consistency of the labels based on contrastive learning to enhance the clustering performance. Empirical studies on real-world datasets show that our method achieves superior clustering performance over other state-of-the-art methods.

Abstract: The widespread adoption of Machine Learning systems, especially in more decision-critical applications such as criminal sentencing and bank loans, has led to increased concerns about fairness implications. Algorithms and metrics have been developed to mitigate and measure these discriminations. More recently, works have identified a more challenging form of bias called intersectional bias, which encompasses multiple sensitive attributes, such as race and gender, together. In this survey, we review the state-of-the-art in intersectional fairness. We present a taxonomy for intersectional notions of fairness and mitigation. Finally, we identify the key challenges and provide researchers with guidelines for future directions.

Abstract: One of the central questions in the theory of deep learning is to understand how neural networks learn hierarchical features. The ability of deep networks to extract salient features is crucial to both their outstanding generalization ability and the modern deep learning paradigm of pretraining and finetuneing. However, this feature learning process remains poorly understood from a theoretical perspective, with existing analyses largely restricted to two-layer networks. In this work we show that three-layer neural networks have provably richer feature learning capabilities than two-layer networks. We analyze the features learned by a three-layer network trained with layer-wise gradient descent, and present a general purpose theorem which upper bounds the sample complexity and width needed to achieve low test error when the target has specific hierarchical structure. We instantiate our framework in specific statistical learning settings -- single-index models and functions of quadratic features -- and show that in the latter setting three-layer networks obtain a sample complexity improvement over all existing guarantees for two-layer networks. Crucially, this sample complexity improvement relies on the ability of three-layer networks to efficiently learn nonlinear features. We then establish a concrete optimization-based depth separation by constructing a function which is efficiently learnable via gradient descent on a three-layer network, yet cannot be learned efficiently by a two-layer network. Our work makes progress towards understanding the provable benefit of three-layer neural networks over two-layer networks in the feature learning regime.

Abstract: The use of machine learning models in decision support systems with high societal impact raised concerns about unfair (disparate) results for different groups of people. When evaluating such unfair decisions, one generally relies on predefined groups that are determined by a set of features that are considered sensitive. However, such an approach is subjective and does not guarantee that these features are the only ones to be considered as sensitive nor that they entail unfair (disparate) outcomes. In this paper, we propose a preprocessing step to address the task of automatically recognizing sensitive features that does not require a trained model to verify unfair results. Our proposal is based on the Hilber-Schmidt independence criterion, which measures the statistical dependence of variable distributions. We hypothesize that if the dependence between the label vector and a candidate is high for a sensitive feature, then the information provided by this feature will entail disparate performance measures between groups. Our empirical results attest our hypothesis and show that several features considered as sensitive in the literature do not necessarily entail disparate (unfair) results.