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

Predicting Student Performance in an Educational Game Using a Hidden Markov Model

Apr 24, 2019
Manie Tadayon, Greg Pottie

Contributions: Prior studies on education have mostly followed the model of the cross sectional study, namely, examining the pretest and the posttest scores. This paper shows that students' knowledge throughout the intervention can be estimated by time series analysis using a hidden Markov model. Background: Analyzing time series and the interaction between the students and the game data can result in valuable information that cannot be gained by only cross sectional studies of the exams. Research Questions: Can a hidden Markov model be used to analyze the educational games? Can a hidden Markov model be used to make a prediction of the students' performance? Methodology: The study was conducted on (N=854) students who played the Save Patch game. Students were divided into class 1 and class 2. Class 1 students are those who scored lower in the test than class 2 students. The analysis is done by choosing various features of the game as the observations. Findings: The state trajectories can predict the students' performance accurately for both class 1 and class 2.

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Neural CDEs for Long Time Series via the Log-ODE Method

Sep 17, 2020
James Morrill, Patrick Kidger, Cristopher Salvi, James Foster, Terry Lyons

Neural Controlled Differential Equations (Neural CDEs) are the continuous-time analogue of an RNN, just as Neural ODEs are analogous to ResNets. However just like RNNs, training Neural CDEs can be difficult for long time series. Here, we propose to apply a technique drawn from stochastic analysis, namely the log-ODE method. Instead of using the original input sequence, our procedure summarises the information over local time intervals via the log-signature map, and uses the resulting shorter stream of log-signatures as the new input. This represents a length/channel trade-off. In doing so we demonstrate efficacy on problems of length up to 17k observations and observe significant training speed-ups, improvements in model performance, and reduced memory requirements compared to the existing algorithm.

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Towards social pattern characterization in egocentric photo-streams

Jan 09, 2018
Maedeh Aghaei, Mariella Dimiccoli, Cristian Canton Ferrer, Petia Radeva

Following the increasingly popular trend of social interaction analysis in egocentric vision, this manuscript presents a comprehensive study for automatic social pattern characterization of a wearable photo-camera user, by relying on the visual analysis of egocentric photo-streams. The proposed framework consists of three major steps. The first step is to detect social interactions of the user where the impact of several social signals on the task is explored. The detected social events are inspected in the second step for categorization into different social meetings. These two steps act at event-level where each potential social event is modeled as a multi-dimensional time-series, whose dimensions correspond to a set of relevant features for each task, and LSTM is employed to classify the time-series. The last step of the framework is to characterize social patterns, which is essentially to infer the diversity and frequency of the social relations of the user through discovery of recurrences of the same people across the whole set of social events of the user. Experimental evaluation over a dataset acquired by 9 users demonstrates promising results on the task of social pattern characterization from egocentric photo-streams.

* 42 pages, 14 figures. Submitted to Elsevier, Computer Vision and Image Understanding (Under Review) 
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Modeling the Sequence of Brain Volumes by Local Mesh Models for Brain Decoding

Mar 03, 2016
Itir Onal, Mete Ozay, Eda Mizrak, Ilke Oztekin, Fatos T. Yarman Vural

We represent the sequence of fMRI (Functional Magnetic Resonance Imaging) brain volumes recorded during a cognitive stimulus by a graph which consists of a set of local meshes. The corresponding cognitive process, encoded in the brain, is then represented by these meshes each of which is estimated assuming a linear relationship among the voxel time series in a predefined locality. First, we define the concept of locality in two neighborhood systems, namely, the spatial and functional neighborhoods. Then, we construct spatially and functionally local meshes around each voxel, called seed voxel, by connecting it either to its spatial or functional p-nearest neighbors. The mesh formed around a voxel is a directed sub-graph with a star topology, where the direction of the edges is taken towards the seed voxel at the center of the mesh. We represent the time series recorded at each seed voxel in terms of linear combination of the time series of its p-nearest neighbors in the mesh. The relationships between a seed voxel and its neighbors are represented by the edge weights of each mesh, and are estimated by solving a linear regression equation. The estimated mesh edge weights lead to a better representation of information in the brain for encoding and decoding of the cognitive tasks. We test our model on a visual object recognition and emotional memory retrieval experiments using Support Vector Machines that are trained using the mesh edge weights as features. In the experimental analysis, we observe that the edge weights of the spatial and functional meshes perform better than the state-of-the-art brain decoding models.

* 13 pages, 10 figures, submitted to JSTSP Special Issue on Advanced Signal Processing in Brain Networks 
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Dynamical Systems as Temporal Feature Spaces

Jul 15, 2019
Peter Tino

Parameterized state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand the dynamical features of the input driving time series that are formed in the state space. We propose a framework for rigorous analysis of such state representations in vanishing memory state space models such as echo state networks (ESN). In particular, we consider the state space a temporal feature space and the readout mapping from the state space a kernel machine operating in that feature space. We show that: (1) The usual ESN strategy of randomly generating input-to-state, as well as state coupling leads to shallow memory time series representations, corresponding to cross-correlation operator with fast exponentially decaying coefficients; (2) Imposing symmetry on dynamic coupling yields a constrained dynamic kernel matching the input time series with straightforward exponentially decaying motifs or exponentially decaying motifs of the highest frequency; (3) Simple cycle high-dimensional reservoir topology specified only through two free parameters can implement deep memory dynamic kernels with a rich variety of matching motifs. We quantify richness of feature representations imposed by dynamic kernels and demonstrate that for dynamic kernel associated with cycle reservoir topology, the kernel richness undergoes a phase transition close to the edge of stability.

* 45 pages, 17 figures 
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Early Predictions for Medical Crowdfunding: A Deep Learning Approach Using Diverse Inputs

Nov 09, 2019
Tong Wang, Fujie Jin, Yu, Hu, Yuan Cheng

Medical crowdfunding is a popular channel for people needing financial help paying medical bills to collect donations from large numbers of people. However, large heterogeneity exists in donations across cases, and fundraisers face significant uncertainty in whether their crowdfunding campaigns can meet fundraising goals. Therefore, it is important to provide early warnings for fundraisers if such a channel will eventually fail. In this study, we aim to develop novel algorithms to provide accurate and timely predictions of fundraising performance, to better inform fundraisers. In particular, we propose a new approach to combine time-series features and time-invariant features in the deep learning model, to process diverse sources of input data. Compared with baseline models, our model achieves better accuracy and requires a shorter observation window of the time-varying features from the campaign launch to provide robust predictions with high confidence. To extract interpretable insights, we further conduct a multivariate time-series clustering analysis and identify four typical temporal donation patterns. This demonstrates the heterogeneity in the features and how they relate to the fundraising outcome. The prediction model and the interpretable insights can be applied to assist fundraisers with better promoting their fundraising campaigns and can potentially help crowdfunding platforms to provide more timely feedback to all fundraisers. Our proposed framework is also generalizable to other fields where diverse structured and unstructured data are valuable for predictions.

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Crossmatching variable objects with the Gaia data

Feb 14, 2017
Lorenzo Rimoldini, Krzysztof Nienartowicz, Maria Süveges, Jonathan Charnas, Leanne P. Guy, Grégory Jevardat de Fombelle, Berry Holl, Isabelle Lecoeur-Taïbi, Nami Mowlavi, Diego Ordóñez-Blanco, Laurent Eyer

Tens of millions of new variable objects are expected to be identified in over a billion time series from the Gaia mission. Crossmatching known variable sources with those from Gaia is crucial to incorporate current knowledge, understand how these objects appear in the Gaia data, train supervised classifiers to recognise known classes, and validate the results of the Variability Processing and Analysis Coordination Unit (CU7) within the Gaia Data Analysis and Processing Consortium (DPAC). The method employed by CU7 to crossmatch variables for the first Gaia data release includes a binary classifier to take into account positional uncertainties, proper motion, targeted variability signals, and artefacts present in the early calibration of the Gaia data. Crossmatching with a classifier makes it possible to automate all those decisions which are typically made during visual inspection. The classifier can be trained with objects characterized by a variety of attributes to ensure similarity in multiple dimensions (astrometry, photometry, time-series features), with no need for a-priori transformations to compare different photometric bands, or of predictive models of the motion of objects to compare positions. Other advantages as well as some disadvantages of the method are discussed. Implementation steps from the training to the assessment of the crossmatch classifier and selection of results are described.

* 4 pages, 1 figure, in Astronomical Data Analysis Software and Systems XXVI, Astronomical Society of the Pacific Conference Series 
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FinGAT: Financial Graph Attention Networks for Recommending Top-K Profitable Stocks

Jun 18, 2021
Yi-Ling Hsu, Yu-Che Tsai, Cheng-Te Li

Financial technology (FinTech) has drawn much attention among investors and companies. While conventional stock analysis in FinTech targets at predicting stock prices, less effort is made for profitable stock recommendation. Besides, in existing approaches on modeling time series of stock prices, the relationships among stocks and sectors (i.e., categories of stocks) are either neglected or pre-defined. Ignoring stock relationships will miss the information shared between stocks while using pre-defined relationships cannot depict the latent interactions or influence of stock prices between stocks. In this work, we aim at recommending the top-K profitable stocks in terms of return ratio using time series of stock prices and sector information. We propose a novel deep learning-based model, Financial Graph Attention Networks (FinGAT), to tackle the task under the setting that no pre-defined relationships between stocks are given. The idea of FinGAT is three-fold. First, we devise a hierarchical learning component to learn short-term and long-term sequential patterns from stock time series. Second, a fully-connected graph between stocks and a fully-connected graph between sectors are constructed, along with graph attention networks, to learn the latent interactions among stocks and sectors. Third, a multi-task objective is devised to jointly recommend the profitable stocks and predict the stock movement. Experiments conducted on Taiwan Stock, S&P 500, and NASDAQ datasets exhibit remarkable recommendation performance of our FinGAT, comparing to state-of-the-art methods.

* Accepted to IEEE TKDE 2021. The first two authors equally contribute to this work. Code is available at 
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Inference of High-dimensional Autoregressive Generalized Linear Models

Jun 24, 2017
Eric C. Hall, Garvesh Raskutti, Rebecca Willett

Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector could correspond to a different node in a network, and the parameters of an autoregressive model would correspond to the impact of the network structure on the time series evolution. Often these models are used successfully in practice to learn the structure of social, epidemiological, financial, or biological neural networks. However, little is known about statistical guarantees on estimates of such models in non-Gaussian settings. This paper addresses the inference of the autoregressive parameters and associated network structure within a generalized linear model framework that includes Poisson and Bernoulli autoregressive processes. At the heart of this analysis is a sparsity-regularized maximum likelihood estimator. While sparsity-regularization is well-studied in the statistics and machine learning communities, those analysis methods cannot be applied to autoregressive generalized linear models because of the correlations and potential heteroscedasticity inherent in the observations. Sample complexity bounds are derived using a combination of martingale concentration inequalities and modern empirical process techniques for dependent random variables. These bounds, which are supported by several simulation studies, characterize the impact of various network parameters on estimator performance.

* Submitted to IEEE Transactions on Information Theory 
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Clinical Risk Prediction with Temporal Probabilistic Asymmetric Multi-Task Learning

Jun 23, 2020
Tuan A. Nguyen, Hyewon Jeong, Eunho Yang, Sung Ju Hwang

Although recent multi-task learning methods have shown to be effective in improving the generalization of deep neural networks, they should be used with caution for safety-critical applications, such as clinical risk prediction. This is because even if they achieve improved task-average performance, they may still yield degraded performance on individual tasks, which may be critical (e.g., prediction of mortality risk). Existing asymmetric multi-task learning methods tackle this negative transfer problem by performing knowledge transfer from tasks with low loss to tasks with high loss. However, using loss as a measure of reliability is risky since it could be a result of overfitting. In the case of time-series prediction tasks, knowledge learned for one task (e.g., predicting the sepsis onset) at a specific timestep may be useful for learning another task (e.g., prediction of mortality) at a later timestep, but lack of loss at each timestep makes it difficult to measure the reliability at each timestep. To capture such dynamically changing asymmetric relationships between tasks in time-series data, we propose a novel temporal asymmetric multi-task learning model that performs knowledge transfer from certain tasks/timesteps to relevant uncertain tasks, based on feature-level uncertainty. We validate our model on multiple clinical risk prediction tasks against various deep learning models for time-series prediction, which our model significantly outperforms, without any sign of negative transfer. Further qualitative analysis of learned knowledge graphs by clinicians shows that they are helpful in analyzing the predictions of the model. Our final code is available at

* 10 pages, 4 figures, 4 tables 
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