Metric $k$-center clustering is a fundamental unsupervised learning primitive. Although widely used, this primitive is heavily affected by noise in the data, so that a more sensible variant seeks for the best solution that disregards a given number $z$ of points of the dataset, called outliers. We provide efficient algorithms for this important variant in the streaming model under the sliding window setting, where, at each time step, the dataset to be clustered is the window $W$ of the most recent data items. Our algorithms achieve $O(1)$ approximation and, remarkably, require a working memory linear in $k+z$ and only logarithmic in $|W|$. As a by-product, we show how to estimate the effective diameter of the window $W$, which is a measure of the spread of the window points, disregarding a given fraction of noisy distances. We also provide experimental evidence of the practical viability of our theoretical results.
As one of the most well-known artificial feature sampler, the sliding window is widely used in scenarios where spatial and temporal information exists, such as computer vision, natural language process, data stream, and time series. Among which time series is common in many scenarios like credit card payment, user behavior, and sensors. General feature selection for features extracted by sliding window aggregate calls for time-consuming iteration to generate features, and then traditional feature selection methods are employed to rank them. The decision of key parameter, i.e. the period of sli…
Department of Mathematics, The Ohio State University（俄亥俄州立大学数学系）；Translational Data Analytics Institute, The Ohio State University（俄亥俄州立大学转化数据分析研究所）；Department of Mathematics and Statistics, San José State University（圣何塞州立大学数学与统计系）
University of Edinburgh（爱丁堡大学）；University of Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）
Bedside monitors in Intensive Care Units (ICUs) frequently sound incorrectly, slowing response times and desensitising nurses to alarms (Chambrin, 2001), causing true alarms to be missed (Hug et al., 2011). We compare sliding window predictors with recurrent predictors to classify patient state-of-health from ICU multivariate time series; we report slightly improved performance for the RNN for three out of four targets.
We consider reinforcement learning in changing Markov Decision Processes where both the state-transition probabilities and the reward functions may vary over time. For this problem setting, we propose an algorithm using a sliding window approach and provide performance guarantees for the regret evaluated against the optimal non-stationary policy. We also characterize the optimal window size suitable for our algorithm. These results are complemented by a sample complexity bound on the number of sub-optimal steps taken by the algorithm. Finally, we present some experimental results to support ou…
National University of Singapore（新加坡国立大学）；Singapore Management University（新加坡管理大学）
\emph{Coresets} are important tools to generate concise summaries of massive datasets for approximate analysis. A coreset is a small subset of points extracted from the original point set such that certain geometric properties are preserved with provable guarantees. This paper investigates the problem of maintaining a coreset to preserve the minimum enclosing ball (MEB) for a sliding window of points that are continuously updated in a data stream. Although the problem has been extensively studied in batch and append-only streaming settings, no efficient sliding-window solution is available yet…
Renmin University of China（中国人民大学）；Gaoling School of Artificial Intelligence（高瓴人工智能学院）；Pazhou Laboratory (Huangpu)（琶洲实验室（黄埔））；Fudan University（复旦大学）；Alibaba Group（阿里巴巴集团）
University of Edinburgh（爱丁堡大学）；University of Cambridge（剑桥大学）
It is difficult to continually update private machine learning models with new data while maintaining privacy. Data incur increasing privacy loss -- as measured by differential privacy -- when they are used in repeated computations. In this paper, we describe regularized empirical risk minimization algorithms that continually release models for a recent window of data. One version of the algorithm uses the entire data history to improve the model for the recent window. The second version uses a sliding window of constant size to improve the model, ensuring more relevant models in case of evolv…
National University of Singapore（新加坡国立大学）；Singapore Management University（新加坡管理大学）
Representative subset selection (RSS) is an important tool for users to draw insights from massive datasets. Existing literature models RSS as the submodular maximization problem to capture the "diminishing returns" property of the representativeness of selected subsets, but often only has a single constraint (e.g., cardinality), which limits its applications in many real-world problems. To capture the data recency issue and support different types of constraints, we formulate dynamic RSS in data streams as maximizing submodular functions subject to general $d$-knapsack constraints (SMDK) over…
In many applications, monitoring area under the ROC curve (AUC) in a sliding window over a data stream is a natural way of detecting changes in the system. The drawback is that computing AUC in a sliding window is expensive, especially if the window size is large and the data flow is significant. In this paper we propose a scheme for maintaining an approximate AUC in a sliding window of length $k$. More specifically, we propose an algorithm that, given $ε$, estimates AUC within $ε/ 2$, and can maintain this estimate in $O((\log k) / ε)$ time, per update, as the window slides. This provides a s…
Designing Adaptive Algorithms Based on Reinforcement Learning for Dynamic Optimization of Sliding Window Size in Multi-Dimensional Data Streams
Department of Computer Engineering, Ferdowsi University of Mashhad（法尔多西大学马什哈德分校计算机工程系）；Department of Computer Engineering, University of Tehran（德黑兰大学计算机工程系）
This paper provides a framework to analyze stochastic gradient algorithms in a mean squared error (MSE) sense using the asymptotic normality result of the stochastic gradient descent (SGD) iterates. We perform this analysis by taking the asymptotic normality result and applying it to the finite iteration case. Specifically, we look at problems where the gradient estimators are biased and have reduced variance and compare the iterates generated by these gradient estimators to the iterates generated by the SGD algorithm. We use the work of Fabian to characterize the mean and the variance of the …
Sliding-Window Reordering with Overlap Averaging: A Simple Time-Domain Augmentation for Multivariate Forecasting
Data Science Group, University of Hildesheim（希尔德斯海姆大学数据科学组）；Information Systems and Machine Learning Lab (ISMLL), University of Hildesheim（希尔德斯海姆大学信息系统与机器学习实验室）
The literature on provable robustness in machine learning has primarily focused on static prediction problems, such as image classification, in which input samples are assumed to be independent and model performance is measured as an expectation over the input distribution. Robustness certificates are derived for individual input instances with the assumption that the model is evaluated on each instance separately. However, in many deep learning applications such as online content recommendation and stock market analysis, models use historical data to make predictions. Robustness certificates …
