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Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Joseph Early, Gavin Cheung, Kurt Cutajar, Hanting Xie, Jas Kandola, Niall Twomey

Conventional Time Series Classification (TSC) methods are often black boxes that obscure inherent interpretation of their decision-making processes. In this work, we leverage Multiple Instance Learning (MIL) to overcome this issue, and propose a new framework called MILLET: Multiple Instance Learning for Locally Explainable Time series classification. We apply MILLET to existing deep learning TSC models and show how they become inherently interpretable without compromising (and in some cases, even improving) predictive performance. We evaluate MILLET on 85 UCR TSC datasets and also present a novel synthetic dataset that is specially designed to facilitate interpretability evaluation. On these datasets, we show MILLET produces sparse explanations quickly that are of higher quality than other well-known interpretability methods. To the best of our knowledge, our work with MILLET is the first to develop general MIL methods for TSC and apply them to an extensive variety of domains.

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Lifan Zhao, Yanyan Shen

Recently, channel-independent methods have achieved state-of-the-art performance in multivariate time series (MTS) forecasting. Despite reducing overfitting risks, these methods miss potential opportunities in utilizing channel dependence for accurate predictions. We argue that there exist locally stationary lead-lag relationships between variates, i.e., some lagged variates may follow the leading indicators within a short time period. Exploiting such channel dependence is beneficial since leading indicators offer advance information that can be used to reduce the forecasting difficulty of the lagged variates. In this paper, we propose a new method named LIFT that first efficiently estimates leading indicators and their leading steps at each time step and then judiciously allows the lagged variates to utilize the advance information from leading indicators. LIFT plays as a plugin that can be seamlessly collaborated with arbitrary time series forecasting methods. Extensive experiments on six real-world datasets demonstrate that LIFT improves the state-of-the-art methods by 5.4% in average forecasting performance. Our code is available at https://github.com/SJTU-Quant/LIFT.

Applications · Time Series

Xuan Zhang, Jacob Helwig, Yuchao Lin, Yaochen Xie, Cong Fu, Stephan Wojtowytsch, Shuiwang Ji

We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dynamics. While the U-Net architecture with skip connections is commonly used by prior studies to enable multi-scale processing, our analysis shows that the need for features to evolve across layers results in temporally misaligned features in skip connections, which limits the model’s performance. To address this limitation, we propose SineNet, consisting of multiple sequentially connected U-shaped network blocks, referred to as waves. In SineNet, high-resolution features are evolved progressively through multiple stages, thereby reducing the amount of misalignment within each stage. We furthermore analyze the role of skip connections in enabling both parallel and sequential processing of multi-scale information. Our method is rigorously tested on multiple PDE datasets, including the Navier-Stokes equations and shallow water equations, showcasing the advantages of our proposed approach over conventional U-Nets with a comparable parameter budget. We further demonstrate that increasing the number of waves in SineNet while maintaining the same number of parameters leads to a monotonically improved performance. The results highlight the effectiveness of SineNet and the potential of our approach in advancing the state-of-the-art in neural PDE solver design. Our code is available as part of AIRS (https://github.com/divelab/AIRS).

Miscellaneous Aspects of Machine Learning · Everything Else

Haowei Lin, Yijia Shao, Weinan Qian, Ningxin Pan, Yiduo Guo, Bing Liu

Class incremental learning (CIL) is a challenging setting of continual learning, which learns a series of tasks sequentially. Each task consists of a set of unique classes. The key feature of CIL is that no task identifier (or task-id) is provided at test time. Predicting the task-id for each test sample is a challenging problem. An emerging theory-guided approach (called TIL+OOD) is to train a task-specific model for each task in a shared network for all tasks based on a task-incremental learning (TIL) method to deal with catastrophic forgetting. The model for each task is an out-of-distribution (OOD) detector rather than a conventional classifier. The OOD detector can perform both within-task (in-distribution (IND)) class prediction and OOD detection. The OOD detection capability is the key to task-id prediction during inference. However, this paper argues that using a traditional OOD detector for task-id prediction is sub-optimal because additional information (e.g., the replay data and the learned tasks) available in CIL can be exploited to design a better and principled method for task-id prediction. We call the new method TPL (Task-id Prediction based on Likelihood Ratio). TPL markedly outperforms strong CIL baselines and has negligible catastrophic forgetting. The code of TPL is publicly available at https://github.com/linhaowei1/TPL.

Yu-Hsuan Wu, Jerry Hu, Weijian Li, Bo-Yu Chen, Han Liu

We present **STanHop-Net** (**S**parse **Tan**dem **Hop**field **Net**work) for multivariate time series prediction with memory-enhanced capabilities. At the heart of our approach is **STanHop**, a novel Hopfield-based neural network block, which sparsely learns and stores both temporal and cross-series representations in a data-dependent fashion. In essence, STanHop sequentially learns temporal representation and cross-series representation using two tandem sparse Hopfield layers. Additionally, STanHop incorporates two external memory modules: **Plug-and-Play** and **Tune-and-Play** for train-less and task-aware memory enhancements, respectively. They allow StanHop-Net to swiftly respond to sudden events. Methodologically, we construct the STanHop-Net by stacking STanHop blocks in a hierarchical fashion, enabling multi-resolution feature extraction with resolution-specific sparsity. Theoretically, we introduce a unified construction (**Generalized Sparse Modern Hopfield Model**) for both dense and sparse modern Hopfield models and show that it endows a tighter memory retrieval error compared to the dense counterpart without sacrificing memory capacity. Empirically, we validate the efficacy of STanHop-Net on many settings: time series prediction, fast test-time adaptation, and strongly correlated time series prediction.

Deep Learning · Sequential Models, Time series

Yi Heng Lim, Qi Zhu, Joshua Selfridge, Muhammad Firmansyah

Sequential models, such as Recurrent Neural Networks and Neural Ordinary Differential Equations, have long suffered from slow training due to their inherent sequential nature.For many years this bottleneck has persisted, as many thought sequential models could not be parallelized.We challenge this long-held belief with our parallel algorithm that accelerates GPU evaluation of sequential models by up to 3 orders of magnitude faster without compromising output accuracy.The algorithm does not need any special structure in the sequential models' architecture, making it applicable to a wide range of architectures.Using our method, training sequential models can be more than 10 times faster than the common sequential method without any meaningful difference in the training results.Leveraging this accelerated training, we discovered the efficacy of the Gated Recurrent Unit in a long time series classification problem with 17k time samples.By overcoming the training bottleneck, our work serves as the first step to unlock the potential of non-linear sequential models for long sequence problems.

Deep Learning · Sequential Models, Time series

Xihaier Luo, Wei Xu, Balasubramanya T. Nadiga, Yihui Ren, Shinjae Yoo

Reliably reconstructing physical fields from sparse sensor data is a challenge that frequenty arises in many scientific domains. In practice, the process generating the data is often not known to sufficient accuracy. Therefore, there is a growing interest in the deep neural network route to the problem. In this work, we present a novel approach that learns a continuous representation of the field using implicit neural representations (INR). Specifically, after factorizing spatiotemporal variability into spatial and temporal components using the technique of separation of variables, the method learns relevant basis functions from sparsely sampled irregular data points to thus develop a continuous representation of the data. In experimental evaluations, the proposed model outperforms recent INR methods, offering superior reconstruction quality on simulation data from a state of the art climate model and on a second dataset that comprises of ultra-high resolution satellite-based sea surface temperature field. [Website for the Project: Both data and code are accessible.](https://xihaier.github.io/ICLR-2024-MMGN/)

Miscellaneous Aspects of Machine Learning/Sequential, Network, and Time Series Modeling

Gaetano Romano, Idris A. Eckley, Paul Fearnhead, Guillem Rigaill

Many modern applications of online changepoint detection require the ability to process high-frequency observations, sometimes with limited available computational resources. Online algorithms for detecting a change in mean often involve using a moving window, or specifying the expected size of change. Such choices affect which changes the algorithms have most power to detect. We introduce an algorithm, Functional Online CuSUM (FOCuS), which is equivalent to running these earlier methods simultaneously for all sizes of windows, or all possible values for the size of change. Our theoretical results give tight bounds on the expected computational cost per iteration of FOCuS, with this being logarithmic in the number of observations. We show how FOCuS can be applied to a number of different changes in mean scenarios, and demonstrate its practical utility through its state-of-the-art performance at detecting anomalous behaviour in computer server data.

Miscellaneous Aspects of Machine Learning/Sequential, Network, and Time Series Modeling

Giacomo Meanti, Antoine Chatalic, Vladimir Kostic, Pietro Novelli, Massimiliano Pontil, Lorenzo Rosasco

The theory of Koopman operators allows to deploy non-parametric machine learning algorithms to predict and analyze complex dynamical systems.Estimators such as principal component regression (PCR) or reduced rank regression (RRR) in kernel spaces can be shown to provably learn Koopman operators from finite empirical observations of the system's time evolution. Scaling these approaches to very long trajectories is a challenge and requires introducing suitable approximations to make computations feasible. In this paper, we boost the efficiency of different kernel-based Koopman operator estimators using random projections (sketching).We derive, implement and test the new ``sketched'' estimators with extensive experiments on synthetic and large-scale molecular dynamics datasets. Further, we establish non asymptotic error bounds giving a sharp characterization of the trade-offs between statistical learning rates and computational efficiency.Our empirical and theoretical analysis shows that the proposed estimators provide a sound and efficient way to learn large scale dynamical systems.In particular our experiments indicate that the proposed estimators retain the same accuracy of PCR or RRR, while being much faster.

Probabilistic Methods/Bayesian Models and Methods

Mingxuan Zhang, Yan Sun, Faming Liang

Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research has focused on problems where the observations are independent and identically distributed (i.i.d.), and there has been little work on the problems where the observations are dependent, such as time series data and sequential data in natural language processing. This paper aims to address this gap by studying the theory for sparse deep learning with dependent data. We show that sparse recurrent neural networks (RNNs) can be consistently estimated, and their predictions are asymptotically normally distributed under appropriate assumptions, enabling the prediction uncertainty to be correctly quantified. Our numerical results show that sparse deep learning outperforms state-of-the-art methods, such as conformal predictions, in prediction uncertainty quantification for time series data. Furthermore, our results indicate that the proposed method can consistently identify the autoregressive order for time series data and outperform existing methods in large-scale model compression. Our proposed method has important practical implications in fields such as finance, healthcare, and energy, where both accurate point estimates and prediction uncertainty quantification are of concern.

Deep Learning/Recurrent Networks

Lukas Eisenmann, Zahra Monfared, Niclas Göring, Daniel Durstewitz

Recurrent neural networks (RNNs) are popular machine learning tools for modeling and forecasting sequential data and for inferring dynamical systems (DS) from observed time series. Concepts from DS theory (DST) have variously been used to further our understanding of both, how trained RNNs solve complex tasks, and the training process itself. Bifurcations are particularly important phenomena in DS, including RNNs, that refer to topological (qualitative) changes in a system's dynamical behavior as one or more of its parameters are varied. Knowing the bifurcation structure of an RNN will thus allow to deduce many of its computational and dynamical properties, like its sensitivity to parameter variations or its behavior during training. In particular, bifurcations may account for sudden loss jumps observed in RNN training that could severely impede the training process. Here we first mathematically prove for a particular class of ReLU-based RNNs that certain bifurcations are indeed associated with loss gradients tending toward infinity or zero. We then introduce a novel heuristic algorithm for detecting all fixed points and $k$-cycles in ReLU-based RNNs and their existence and stability regions, hence bifurcation manifolds in parameter space. In contrast to previous numerical algorithms for finding fixed points and common continuation methods, our algorithm provides $\textit{exact}$ results and returns fixed points and cycles up to high orders with surprisingly good scaling behavior. We exemplify the algorithm on the analysis of the training process of RNNs, and find that the recently introduced technique of generalized teacher forcing completely avoids certain types of bifurcations in training. Thus, besides facilitating the DST analysis of trained RNNs, our algorithm provides a powerful instrument for analyzing the training process itself.

Miscellaneous Aspects of Machine Learning/Sequential, Network, and Time Series Modeling

suresh kumar amalapuram, Sumohana Channappayya, Bheemarjuna Reddy Tamma

Intrusion detection is a form of anomalous activity detection in communication network traffic. Continual learning (CL) approaches to the intrusion detection task accumulate old knowledge while adapting to the latest threat knowledge. Previous works have shown the effectiveness of memory replay-based CL approaches for this task. In this work, we present two novel contributions to improve the performance of CL-based network intrusion detection in the context of class imbalance and scalability. First, we extend class balancing reservoir sampling (CBRS), a memory-based CL method, to address the problems of severe class imbalance for large datasets. Second, we propose a novel approach titled perturbation assistance for parameter approximation (PAPA) based on the Gaussian mixture model to reduce the number of \textit{virtual stochastic gradient descent (SGD) parameter} computations needed to discover maximally interfering samples for CL. We demonstrate that the proposed approaches perform remarkably better than the baselines on standard intrusion detection benchmarks created over shorter periods (KDDCUP'99, NSL-KDD, CICIDS-2017/2018, UNSW-NB15, and CTU-13) and a longer period with distribution shift (AnoShift). We also validated proposed approaches on standard continual learning benchmarks (SVHN, CIFAR-10/100, and CLEAR-10/100) and anomaly detection benchmarks (SMAP, SMD, and MSL). Further, the proposed PAPA approach significantly lowers the number of virtual SGD update operations, thus resulting in training time savings in the range of 12 to 40\% compared to the maximally interfered samples retrieval algorithm.

Miscellaneous Aspects of Machine Learning/Sequential, Network, and Time Series Modeling

Xin Liu, Zheng Li, Yifan Gao, Jingfeng Yang, Tianyu Cao, Zhengyang Wang, Bing Yin, Yangqiu Song

The goal of session-based recommendation in E-commerce is to predict the next item that an anonymous user will purchase based on the browsing and purchase history. However, constructing global or local transition graphs to supplement session data can lead to noisy correlations and user intent vanishing. In this work, we propose the Frequent Attribute Pattern Augmented Transformer (FAPAT) that characterizes user intents by building attribute transition graphs and matching attribute patterns. Specifically, the frequent and compact attribute patterns are served as memory to augment session representations, followed by a gate and a transformer block to fuse the whole session information. Through extensive experiments on two public benchmarks and 100 million industrial data in three domains, we demonstrate that FAPAT consistently outperforms state-of-the-art methods by an average of 4.5% across various evaluation metrics (Hits, NDCG, MRR). Besides evaluating the next-item prediction, we estimate the models' capabilities to capture user intents via predicting items' attributes and period-item recommendations.

Reinforcement Learning/Multi-agent

Yiheng Zhu, Yang Zhan, Xuankun Huang, Yuwei Chen, yujie Chen, Jiangwen Wei, Wei Feng, Yinzhi Zhou, Haoyuan Hu, Jieping Ye

The dramatic growth of global e-commerce has led to a surge in demand for efficient and cost-effective order fulfillment which can increase customers' service levels and sellers' competitiveness. However, managing order fulfillment is challenging due to a series of interdependent online sequential decision-making problems. To clear this hurdle, rather than solving the problems separately as attempted in some recent researches, this paper proposes a method based on multi-agent reinforcement learning to integratively solve the series of interconnected problems, encompassing order handling, packing and pickup, storage, order consolidation, and last-mile delivery. In particular, we model the integrated problem as a Markov game, wherein a team of agents learns a joint policy via interacting with a simulated environment. Since no simulated environment supporting the complete order fulfillment problem exists, we devise Order Fulfillment COoperative mUlti-agent Reinforcement learning Scalable Environment (OFCOURSE) in the OpenAI Gym style, which allows reproduction and re-utilization to build customized applications. By constructing the fulfillment system in OFCOURSE, we optimize a joint policy that solves the integrated problem, facilitating sequential order-wise operations across all fulfillment units and minimizing the total cost of fulfilling all orders within the promised time. With OFCOURSE, we also demonstrate that the joint policy learned by multi-agent reinforcement learning outperforms the combination of locally optimal policies. The source code of OFCOURSE is available at: https://github.com/GitYiheng/ofcourse.

Deep Learning/Generative Models and Autoencoders

Hang Lou, Siran Li, Hao Ni

Generating high-fidelity time series data using generative adversarial networks (GANs) remains a challenging task, as it is difficult to capture the temporal dependence of joint probability distributions induced by time-series data. Towards this goal, a key step is the development of an effective discriminator to distinguish between time series distributions. We propose the so-called PCF-GAN, a novel GAN that incorporates the path characteristic function (PCF) as the principled representation of time series distribution into the discriminator to enhance its generative performance. On the one hand, we establish theoretical foundations of the PCF distance by proving its characteristicity, boundedness, differentiability with respect to generator parameters, and weak continuity, which ensure the stability and feasibility of training the PCF-GAN. On the other hand, we design efficient initialisation and optimisation schemes for PCFs to strengthen the discriminative power and accelerate training efficiency. To further boost the capabilities of complex time series generation, we integrate the auto-encoder structure via sequential embedding into the PCF-GAN, which provides additional reconstruction functionality. Extensive numerical experiments on various datasets demonstrate the consistently superior performance of PCF-GAN over state-of-the-art baselines, in both generation and reconstruction quality.

Deep Learning/Sequential Models, Time series

Vinitra Swamy, Malika Satayeva, Jibril Frej, Thierry Bossy, Thijs Vogels, Martin Jaggi, Tanja Käser, Mary-Anne Hartley

Predicting multiple real-world tasks in a single model often requires a particularly diverse feature space. Multimodal (MM) models aim to extract the synergistic predictive potential of multiple data types to create a shared feature space with aligned semantic meaning across inputs of drastically varying sizes (i.e. images, text, sound). Most current MM architectures fuse these representations in parallel, which not only limits their interpretability but also creates a dependency on modality availability. We present MultiModN, a multimodal, modular network that fuses latent representations in a sequence of any number, combination, or type of modality while providing granular real-time predictive feedback on any number or combination of predictive tasks. MultiModN's composable pipeline is interpretable-by-design, as well as innately multi-task and robust to the fundamental issue of biased missingness. We perform four experiments on several benchmark MM datasets across 10 real-world tasks (predicting medical diagnoses, academic performance, and weather), and show that MultiModN's sequential MM fusion does not compromise performance compared with a baseline of parallel fusion. By simulating the challenging bias of missing not-at-random (MNAR), this work shows that, contrary to MultiModN, parallel fusion baselines erroneously learn MNAR and suffer catastrophic failure when faced with different patterns of MNAR at inference. To the best of our knowledge, this is the first inherently MNAR-resistant approach to MM modeling. In conclusion, MultiModN provides granular insights, robustness, and flexibility without compromising performance.

Applications/Neuroscience, Cognitive Science

Qi Xu, Yuyuan Gao, Jiangrong Shen, Yaxin Li, Xuming Ran, Huajin Tang, Gang Pan

Spiking neural networks (SNNs) serve as one type of efficient model to process spatio-temporal patterns in time series, such as the Address-Event Representation data collected from Dynamic Vision Sensor (DVS). Although convolutional SNNs have achieved remarkable performance on these AER datasets, benefiting from the predominant spatial feature extraction ability of convolutional structure, they ignore temporal features related to sequential time points. In this paper, we develop a recurrent spiking neural network (RSNN) model embedded with an advanced spiking convolutional block attention module (SCBAM) component to combine both spatial and temporal features of spatio-temporal patterns. It invokes the history information in spatial and temporal channels adaptively through SCBAM, which brings the advantages of efficient memory calling and history redundancy elimination. The performance of our model was evaluated in DVS128-Gesture dataset and other time-series datasets. The experimental results show that the proposed SRNN-SCBAM model makes better use of the history information in spatial and temporal dimensions with less memory space, and achieves higher accuracy compared to other models.

Miscellaneous Aspects of Machine Learning/Sequential, Network, and Time Series Modeling

Tian Zhou, Peisong Niu, xue wang, Liang Sun, Rong Jin

Although we have witnessed great success of pre-trained models in natural language processing (NLP) and computer vision (CV), limited progress has been made for general time series analysis. Unlike NLP and CV where a unified model can be used to perform different tasks, specially designed approach still dominates in each time series analysis task such as classification, anomaly detection, forecasting, and few-shot learning. The main challenge that blocks the development of pre-trained model for time series analysis is the lack of a large amount of data for training. In this work, we address this challenge by leveraging language or CV models, pre-trained from billions of tokens, for time series analysis. Specifically, we refrain from altering the self-attention and feedforward layers of the residual blocks in the pre-trained language or image model. This model, known as the Frozen Pretrained Transformer (FPT), is evaluated through fine-tuning on all major types of tasks involving time series. Our results demonstrate that pre-trained models on natural language or images can lead to a comparable or state-of-the-art performance in all main time series analysis tasks, as illustrated in Figure1. We also found both theoretically and empirically that the self-attention module behaviors similarly to principle component analysis (PCA), an observation that helps explains how transformer bridges the domain gap and a crucial step towards understanding the universality of a pre-trained transformer. The code is publicly available at https://anonymous.4open.science/r/Pretrained-LM-for-TSForcasting-C561.

Miscellaneous Aspects of Machine Learning/Sequential, Network, and Time Series Modeling

YIXUAN ZHANG, Quyu Kong, Feng Zhou

In this study, we propose a novel deep spatio-temporal point process model, Deep Kernel Mixture Point Processes (DKMPP), that incorporates multimodal covariate information. DKMPP is an enhanced version of Deep Mixture Point Processes (DMPP), which uses a more flexible deep kernel to model complex relationships between events and covariate data, improving the model's expressiveness. To address the intractable training procedure of DKMPP due to the non-integrable deep kernel, we utilize an integration-free method based on score matching, and further improve efficiency by adopting a scalable denoising score matching method. Our experiments demonstrate that DKMPP and its corresponding score-based estimators outperform baseline models, showcasing the advantages of incorporating covariate information, utilizing a deep kernel, and employing score-based estimators.

Miscellaneous Aspects of Machine Learning/Sequential, Network, and Time Series Modeling

Michael Scholkemper, Michael T Schaub

Similar to community detection, partitioning the nodes of a complex network according to their structural roles aims to identify fundamental building blocks of a network, which can be used, e.g., to find simplified descriptions of the network connectivity, to derive reduced order models for dynamical processes unfolding on processes, or as ingredients for various network analysis and graph mining tasks. In this work, we offer a fresh look on the problem of role extraction and its differences to community detection and present a definition of node roles and two associated optimization problems (cost functions) grounded in ideas related to graph-isomorphism tests, the Weisfeiler-Leman algorithm and equitable partitions. We present theoretical guarantees and validate our approach via a novel “role-infused partition benchmark”, a network model from which we can sample networks in which nodes are endowed with different roles in a stochastic way.