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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.

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.

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.

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

Abdullah Alomar, Munther Dahleh, Sean Mann, Devavrat Shah

The well-established practice of time series analysis involves estimating deterministic, non-stationary trend and seasonality components followed by learning the residual stochastic, stationary components. Recently, it has been shown that one can learn the deterministic non-stationary components accurately using multivariate Singular Spectrum Analysis (mSSA) in the absence of a correlated stationary component; meanwhile, in the absence of deterministic non-stationary components, the Autoregressive (AR) stationary component can also be learnt readily, e.g. via Ordinary Least Squares (OLS). However, a theoretical underpinning of multi-stage learning algorithms involving both deterministic and stationary components has been absent in the literature despite its pervasiveness. We resolve this open question by establishing desirable theoretical guarantees for a natural two-stage algorithm, where mSSA is first applied to estimate the non-stationary components despite the presence of a correlated stationary AR component, which is subsequently learned from the residual time series. We provide a finite-sample forecasting consistency bound for the proposed algorithm, SAMoSSA, which is data-driven and thus requires minimal parameter tuning. To establish theoretical guarantees, we overcome three hurdles: (i) we characterize the spectra of Page matrices of stable AR processes, thus extending the analysis of mSSA; (ii) we extend the analysis of AR process identification in the presence of arbitrary bounded perturbations; (iii) we characterize the out-of-sample or forecasting error, as opposed to solely considering model identification. Through representative empirical studies, we validate the superior performance of SAMoSSA compared to existing baselines. Notably, SAMoSSA's ability to account for AR noise structure yields improvements ranging from 5% to 37% across various benchmark datasets.

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

Giovanni De Felice, John Goulermas, Vladimir Gusev

Kernel design is a pivotal but challenging aspect of time series analysis, especially in the context of small datasets. In recent years, Reservoir Computing (RC) has emerged as a powerful tool to compare time series based on the underlying dynamics of the generating process rather than the observed data. However, the performance of RC highly depends on the hyperparameter setting, which is hard to interpret and costly to optimize because of the recurrent nature of RC. Here, we present a new kernel for time series based on the recently established equivalence between reservoir dynamics and Nonlinear Vector AutoRegressive (NVAR) processes. The kernel is non-recurrent and depends on a small set of meaningful hyperparameters, for which we suggest an effective heuristic. We demonstrate excellent performance on a wide range of real-world classification tasks, both in terms of accuracy and speed. This further advances the understanding of RC representation learning models and extends the typical use of the NVAR framework to kernel design and representation of real-world time series data.