The Dog Walking Theory: Rethinking Convergence in Federated Learning

Federated learning (FL) is a collaborative learning paradigm that allows different clients to train one powerful global model without sharing their private data. Although FL has demonstrated promising results in various applications, it is known to suffer from convergence issues caused by the data distribution shift across different clients, especially on non-independent and identically distributed (non-IID) data. In this paper, we study the convergence of FL on non-IID data and propose a novel \emph{Dog Walking Theory} to formulate and identify the missing element in existing research. The Dog Walking Theory describes the process of a dog walker leash walking multiple dogs from one side of the park to the other. The goal of the dog walker is to arrive at the right destination while giving the dogs enough exercise (i.e., space exploration). In FL, the server is analogous to the dog walker while the clients are analogous to the dogs. This analogy allows us to identify one crucial yet missing element in existing FL algorithms: the leash that guides the exploration of the clients. To address this gap, we propose a novel FL algorithm \emph{FedWalk} that leverages an external easy-to-converge task at the server side as a \emph{leash task} to guide the local training of the clients. We theoretically analyze the convergence of FedWalk with respect to data heterogeneity (between server and clients) and task discrepancy (between the leash and the original tasks). Experiments on multiple benchmark datasets demonstrate the superiority of FedWalk over state-of-the-art FL methods under both IID and non-IID settings.

Efficient High-Resolution Time Series Classification via Attention Kronecker Decomposition

The high-resolution time series classification problem is essential due to the increasing availability of detailed temporal data in various domains. To tackle this challenge effectively, it is imperative that the state-of-the-art attention model is scalable to accommodate the growing sequence lengths typically encountered in high-resolution time series data, while also demonstrating robustness in handling the inherent noise prevalent in such datasets. To address this, we propose to hierarchically encode the long time series into multiple levels based on the interaction ranges. By capturing relationships at different levels, we can build more robust, expressive, and efficient models that are capable of capturing both short-term fluctuations and long-term trends in the data. We then propose a new time series transformer backbone (KronTime) by introducing Kronecker-decomposed attention to process such multi-level time series, which sequentially calculates attention from the lower level to the upper level. Experiments on four long time series datasets demonstrate superior classification results with improved efficiency compared to baseline methods.

PMP: Privacy-Aware Matrix Profile against Sensitive Pattern Inference for Time Series

Recent rapid development of sensor technology has allowed massive fine-grained time series (TS) data to be collected and set the foundation for the development of data-driven services and applications. During the process, data sharing is often involved to allow the third-party modelers to perform specific time series data mining (TSDM) tasks based on the need of data owner. The high resolution of TS brings new challenges in protecting privacy. While meaningful information in high-resolution TS shifts from concrete point values to local shape-based segments, numerous research have found that long shape-based patterns could contain more sensitive information and may potentially be extracted and misused by a malicious third party. However, the privacy issue for TS patterns is surprisingly seldom explored in privacy-preserving literature. In this work, we consider a new privacy-preserving problem: preventing malicious inference on long shape-based patterns while preserving short segment information for the utility task performance. To mitigate the challenge, we investigate an alternative approach by sharing Matrix Profile (MP), which is a non-linear transformation of original data and a versatile data structure that supports many data mining tasks. We found that while MP can prevent concrete shape leakage, the canonical correlation in MP index can still reveal the location of sensitive long pattern. Based on this observation, we design two attacks named Location Attack and Entropy Attack to extract the pattern location from MP. To further protect MP from these two attacks, we propose a Privacy-Aware Matrix Profile (PMP) via perturbing the local correlation and breaking the canonical correlation in MP index vector. We evaluate our proposed PMP against baseline noise-adding methods through quantitative analysis and real-world case studies to show the effectiveness of the proposed method.

Robust Time Series Chain Discovery with Incremental Nearest Neighbors

Time series motif discovery has been a fundamental task to identify meaningful repeated patterns in time series. Recently, time series chains were introduced as an expansion of time series motifs to identify the continuous evolving patterns in time series data. Informally, a time series chain (TSC) is a temporally ordered set of time series subsequences, in which every subsequence is similar to the one that precedes it, but the last and the first can be arbitrarily dissimilar. TSCs are shown to be able to reveal latent continuous evolving trends in the time series, and identify precursors of unusual events in complex systems. Despite its promising interpretability, unfortunately, we have observed that existing TSC definitions lack the ability to accurately cover the evolving part of a time series: the discovered chains can be easily cut by noise and can include non-evolving patterns, making them impractical in real-world applications. Inspired by a recent work that tracks how the nearest neighbor of a time series subsequence changes over time, we introduce a new TSC definition which is much more robust to noise in the data, in the sense that they can better locate the evolving patterns while excluding the non-evolving ones. We further propose two new quality metrics to rank the discovered chains. With extensive empirical evaluations, we demonstrate that the proposed TSC definition is significantly more robust to noise than the state of the art, and the top ranked chains discovered can reveal meaningful regularities in a variety of real world datasets.

Federated Learning with Erroneous Communication Links

In this paper, we consider the federated learning (FL) problem in the presence of communication errors. We model the link between the devices and the central node (CN) by a packet erasure channel, where the local parameters from devices are either erased or received correctly by CN with probability $e$ and $1-e$, respectively. We provide mathematical proof for the convergence of the FL algorithm in the presence of communication errors, where the CN uses past local updates when the fresh updates are not received from some devices. We show via simulations that by using the past local updates, the FL algorithm can converge in the presence of communication errors. We also show that when the dataset is uniformly distributed among devices, the FL algorithm that only uses fresh updates and discards missing updates might converge faster than the FL algorithm that uses past local updates.

Semantic Discord: Finding Unusual Local Patterns for Time Series

Finding anomalous subsequence in a long time series is a very important but difficult problem. Existing state-of-the-art methods have been focusing on searching for the subsequence that is the most dissimilar to the rest of the subsequences; however, they do not take into account the background patterns that contain the anomalous candidates. As a result, such approaches are likely to miss local anomalies. We introduce a new definition named \textit{semantic discord}, which incorporates the context information from larger subsequences containing the anomaly candidates. We propose an efficient algorithm with a derived lower bound that is up to 3 orders of magnitude faster than the brute force algorithm in real world data. We demonstrate that our method significantly outperforms the state-of-the-art methods in locating anomalies by extensive experiments. We further explain the interpretability of semantic discord.

Ensemble Grammar Induction For Detecting Anomalies in Time Series

Time series anomaly detection is an important task, with applications in a broad variety of domains. Many approaches have been proposed in recent years, but often they require that the length of the anomalies be known in advance and provided as an input parameter. This limits the practicality of the algorithms, as such information is often unknown in advance, or anomalies with different lengths might co-exist in the data. To address this limitation, previously, a linear time anomaly detection algorithm based on grammar induction has been proposed. While the algorithm can find variable-length patterns, it still requires preselecting values for at least two parameters at the discretization step. How to choose these parameter values properly is still an open problem. In this paper, we introduce a grammar-induction-based anomaly detection method utilizing ensemble learning. Instead of using a particular choice of parameter values for anomaly detection, the method generates the final result based on a set of results obtained using different parameter values. We demonstrate that the proposed ensemble approach can outperform existing grammar-induction-based approaches with different criteria for selection of parameter values. We also show that the proposed approach can achieve performance similar to that of the state-of-the-art distance-based anomaly detection algorithm.

Discovering Subdimensional Motifs of Different Lengths in Large-Scale Multivariate Time Series

Detecting repeating patterns of different lengths in time series, also called variable-length motifs, has received a great amount of attention by researchers and practitioners. Despite the significant progress that has been made in recent single dimensional variable-length motif discovery work, detecting variable-length \textit{subdimensional motifs}---patterns that are simultaneously occurring only in a subset of dimensions in multivariate time series---remains a difficult task. The main challenge is scalability. On the one hand, the brute-force enumeration solution, which searches for motifs of all possible lengths, is very time consuming even in single dimensional time series. On the other hand, previous work show that index-based fixed-length approximate motif discovery algorithms such as random projection are not suitable for detecting variable-length motifs due to memory requirement. In this paper, we introduce an approximate variable-length subdimensional motif discovery algorithm called \textbf{C}ollaborative \textbf{HI}erarchy based \textbf{M}otif \textbf{E}numeration (CHIME) to efficiently detect variable-length subdimensional motifs given a minimum motif length in large-scale multivariate time series. We show that the memory cost of the approach is significantly smaller than that of random projection. Moreover, the speed of the proposed algorithm is significantly faster than that of the state-of-the-art algorithms. We demonstrate that CHIME can efficiently detect meaningful variable-length subdimensional motifs in large real world multivariate time series datasets.

A Novel and Robust Evolution Algorithm for Optimizing Complicated Functions

In this paper, a novel mutation operator of differential evolution algorithm is proposed. A new algorithm called divergence differential evolution algorithm (DDEA) is developed by combining the new mutation operator with divergence operator and assimilation operator (divergence operator divides population, and, assimilation operator combines population), which can detect multiple solutions and robustness in noisy environment. The new algorithm is applied to optimize Michalewicz Function and to track changing of rain-induced-attenuation process. The results based on DDEA are compared with those based on Differential Evolution Algorithm (DEA). It shows that DDEA algorithm gets better results than DEA does in the same premise. The new algorithm is significant for optimizing and tracking the characteristics of MIMO (Multiple Input Multiple Output) channel at millimeter waves.