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"Time Series Analysis": models, code, and papers

Temporal Registration in Application to In-utero MRI Time Series

Mar 06, 2019
Ruizhi Liao, Esra A. Turk, Miaomiao Zhang, Jie Luo, Elfar Adalsteinsson, P. Ellen Grant, Polina Golland

We present a robust method to correct for motion in volumetric in-utero MRI time series. Time-course analysis for in-utero volumetric MRI time series often suffers from substantial and unpredictable fetal motion. Registration provides voxel correspondences between images and is commonly employed for motion correction. Current registration methods often fail when aligning images that are substantially different from a template (reference image). To achieve accurate and robust alignment, we make a Markov assumption on the nature of motion and take advantage of the temporal smoothness in the image data. Forward message passing in the corresponding hidden Markov model (HMM) yields an estimation algorithm that only has to account for relatively small motion between consecutive frames. We evaluate the utility of the temporal model in the context of in-utero MRI time series alignment by examining the accuracy of propagated segmentation label maps. Our results suggest that the proposed model captures accurately the temporal dynamics of transformations in in-utero MRI time series.

* arXiv admin note: text overlap with arXiv:1608.03907 
  
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A Worrying Analysis of Probabilistic Time-series Models for Sales Forecasting

Nov 21, 2020
Seungjae Jung, Kyung-Min Kim, Hanock Kwak, Young-Jin Park

Probabilistic time-series models become popular in the forecasting field as they help to make optimal decisions under uncertainty. Despite the growing interest, a lack of thorough analysis hinders choosing what is worth applying for the desired task. In this paper, we analyze the performance of three prominent probabilistic time-series models for sales forecasting. To remove the role of random chance in architecture's performance, we make two experimental principles; 1) Large-scale dataset with various cross-validation sets. 2) A standardized training and hyperparameter selection. The experimental results show that a simple Multi-layer Perceptron and Linear Regression outperform the probabilistic models on RMSE without any feature engineering. Overall, the probabilistic models fail to achieve better performance on point estimation, such as RMSE and MAPE, than comparably simple baselines. We analyze and discuss the performances of probabilistic time-series models.

* NeurIPS 2020 workshop (I Can't Believe It's Not Better, [email protected] 2020). All authors contributed equally to this research 
  
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Neural Decomposition of Time-Series Data for Effective Generalization

Jun 05, 2017
Luke B. Godfrey, Michael S. Gashler

We present a neural network technique for the analysis and extrapolation of time-series data called Neural Decomposition (ND). Units with a sinusoidal activation function are used to perform a Fourier-like decomposition of training samples into a sum of sinusoids, augmented by units with nonperiodic activation functions to capture linear trends and other nonperiodic components. We show how careful weight initialization can be combined with regularization to form a simple model that generalizes well. Our method generalizes effectively on the Mackey-Glass series, a dataset of unemployment rates as reported by the U.S. Department of Labor Statistics, a time-series of monthly international airline passengers, the monthly ozone concentration in downtown Los Angeles, and an unevenly sampled time-series of oxygen isotope measurements from a cave in north India. We find that ND outperforms popular time-series forecasting techniques including LSTM, echo state networks, ARIMA, SARIMA, SVR with a radial basis function, and Gashler and Ashmore's model.

* IEEE Transactions on Neural Networks and Learning Systems 29.7 (2018) 2973-2985 
* 13 pages, 11 figures, IEEE TNNLS Preprint 
  
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Warped-Linear Models for Time Series Classification

Nov 24, 2017
Brijnesh J. Jain

This article proposes and studies warped-linear models for time series classification. The proposed models are time-warp invariant analogues of linear models. Their construction is in line with time series averaging and extensions of k-means and learning vector quantization to dynamic time warping (DTW) spaces. The main theoretical result is that warped-linear models correspond to polyhedral classifiers in Euclidean spaces. This result simplifies the analysis of time-warp invariant models by reducing to max-linear functions. We exploit this relationship and derive solutions to the label-dependency problem and the problem of learning warped-linear models. Empirical results on time series classification suggest that warped-linear functions better trade solution quality against computation time than nearest-neighbor and prototype-based methods.

  
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Particle swarm optimization for time series motif discovery

Jan 29, 2015
Joan Serrà, Josep Lluis Arcos

Efficiently finding similar segments or motifs in time series data is a fundamental task that, due to the ubiquity of these data, is present in a wide range of domains and situations. Because of this, countless solutions have been devised but, to date, none of them seems to be fully satisfactory and flexible. In this article, we propose an innovative standpoint and present a solution coming from it: an anytime multimodal optimization algorithm for time series motif discovery based on particle swarms. By considering data from a variety of domains, we show that this solution is extremely competitive when compared to the state-of-the-art, obtaining comparable motifs in considerably less time using minimal memory. In addition, we show that it is robust to different implementation choices and see that it offers an unprecedented degree of flexibility with regard to the task. All these qualities make the presented solution stand out as one of the most prominent candidates for motif discovery in long time series streams. Besides, we believe the proposed standpoint can be exploited in further time series analysis and mining tasks, widening the scope of research and potentially yielding novel effective solutions.

* Knowledge-Based Systems 92: 127-137. Jan 2016 
* 12 pages, 9 figures, 2 tables 
  
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Time series model selection with a meta-learning approach; evidence from a pool of forecasting algorithms

Aug 22, 2019
Sasan Barak, Mahdi Nasiri, Mehrdad Rostamzadeh

One of the challenging questions in time series forecasting is how to find the best algorithm. In recent years, a recommender system scheme has been developed for time series analysis using a meta-learning approach. This system selects the best forecasting method with consideration of the time series characteristics. In this paper, we propose a novel approach to focusing on some of the unanswered questions resulting from the use of meta-learning in time series forecasting. Therefore, three main gaps in previous works are addressed including, analyzing various subsets of top forecasters as inputs for meta-learners; evaluating the effect of forecasting error measures; and assessing the role of the dimensionality of the feature space on the forecasting errors of meta-learners. All of these objectives are achieved with the help of a diverse state-of-the-art pool of forecasters and meta-learners. For this purpose, first, a pool of forecasting algorithms is implemented on the NN5 competition dataset and ranked based on the two error measures. Then, six machine-learning classifiers known as meta-learners, are trained on the extracted features of the time series in order to assign the most suitable forecasting method for the various subsets of the pool of forecasters. Furthermore, two-dimensionality reduction methods are implemented in order to investigate the role of feature space dimension on the performance of meta-learners. In general, it was found that meta-learners were able to defeat all of the individual benchmark forecasters; this performance was improved even after applying the feature selection method.

* 30 pages, 10 tables, and 7 figures 
  
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Forecasting Nonnegative Time Series via Sliding Mask Method (SMM) and Latent Clustered Forecast (LCF)

Feb 10, 2021
Yohann de Castro, Luca Mencarelli

We consider nonnegative time series forecasting framework. Based on recent advances in Nonnegative Matrix Factorization (NMF) and Archetypal Analysis, we introduce two procedures referred to as Sliding Mask Method (SMM) and Latent Clustered Forecast (LCF). SMM is a simple and powerful method based on time window prediction using Completion of Nonnegative Matrices. This new procedure combines low nonnegative rank decomposition and matrix completion where the hidden values are to be forecasted. LCF is two stage: it leverages archetypal analysis for dimension reduction and clustering of time series, then it uses any black-box supervised forecast solver on the clustered latent representation. Theoretical guarantees on uniqueness and robustness of the solution of NMF Completion-type problems are also provided for the first time. Finally, numerical experiments on real-world and synthetic data-set confirms forecasting accuracy for both the methodologies.

  
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Explainable Machine Learning-driven Strategy for Automated Trading Pattern Extraction

Apr 13, 2021
Artur Sokolovsky, Luca Arnaboldi, Jaume Bacardit, Thomas Gross

Financial markets are a source of non-stationary multidimensional time series which has been drawing attention for decades. Each financial instrument has its specific changing over time properties, making their analysis a complex task. Improvement of understanding and development of methods for financial time series analysis is essential for successful operation on financial markets. In this study we propose a volume-based data pre-processing method for making financial time series more suitable for machine learning pipelines. We use a statistical approach for assessing the performance of the method. Namely, we formally state the hypotheses, set up associated classification tasks, compute effect sizes with confidence intervals, and run statistical tests to validate the hypotheses. We additionally assess the trading performance of the proposed method on historical data and compare it to a previously published approach. Our analysis shows that the proposed volume-based method allows successful classification of the financial time series patterns, and also leads to better classification performance than a price action-based method, excelling specifically on more liquid financial instruments. Finally, we propose an approach for obtaining feature interactions directly from tree-based models on example of CatBoost estimator, as well as formally assess the relatedness of the proposed approach and SHAP feature interactions with a positive outcome.

  
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Interpretable ML-driven Strategy for Automated Trading Pattern Extraction

Mar 23, 2021
Artur Sokolovsky, Luca Arnaboldi, Jaume Bacardit, Thomas Gross

Financial markets are a source of non-stationary multidimensional time series which has been drawing attention for decades. Each financial instrument has its specific changing over time properties, making their analysis a complex task. Improvement of understanding and development of methods for financial time series analysis is essential for successful operation on financial markets. In this study we propose a volume-based data pre-processing method for making financial time series more suitable for machine learning pipelines. We use a statistical approach for assessing the performance of the method. Namely, we formally state the hypotheses, set up associated classification tasks, compute effect sizes with confidence intervals, and run statistical tests to validate the hypotheses. We additionally assess the trading performance of the proposed method on historical data and compare it to a previously published approach. Our analysis shows that the proposed volume-based method allows successful classification of the financial time series patterns, and also leads to better classification performance than a price action-based method, excelling specifically on more liquid financial instruments. Finally, we propose an approach for obtaining feature interactions directly from tree-based models on example of CatBoost estimator, as well as formally assess the relatedness of the proposed approach and SHAP feature interactions with a positive outcome.

  
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Graph Learning from Multivariate Dependent Time Series via a Multi-Attribute Formulation

Apr 29, 2022
Jitendra K Tugnait

We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node, and associations between components are represented by edges between the corresponding nodes. We formulate the problem as one of multi-attribute graph estimation for random vectors where a vector is associated with each node of the graph. At each node, the associated random vector consists of a time series component and its delayed copies. We present an alternating direction method of multipliers (ADMM) solution to minimize a sparse-group lasso penalized negative pseudo log-likelihood objective function to estimate the precision matrix of the random vector associated with the entire multi-attribute graph. The time series CIG is then inferred from the estimated precision matrix. A theoretical analysis is provided. Numerical results illustrate the proposed approach which outperforms existing frequency-domain approaches in correctly detecting the graph edges.

* 5 pages, 2 figures, accepted to 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2022), Singapore, May 22-27, 2022. arXiv admin note: text overlap with arXiv:2111.07897 
  
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