Analyzing time series data is important to predict future events and changes in finance, manufacturing, and administrative decisions. In time series analysis, Gaussian Process (GP) regression methods recently demonstrate competitive performance by decomposing temporal covariance structures. The covariance structure decomposition allows exploiting shared parameters over a set of multiple, selected time series. In this paper, we present two novel GP models which naturally handle multiple time series by placing an Indian Buffet Process (IBP) prior on the presence of shared kernels. We also investigate the well-definedness of the models when infinite latent components are introduced. We present a pragmatic search algorithm which explores a larger structure space efficiently than the existing search algorithm. Experiments are conducted on both synthetic data sets and real-world data sets, showing improved results in term of structure discoveries and predictive performances. We further provide a promising application generating comparison reports from our model results.
Training deep neural networks often requires careful hyper-parameter tuning and significant computational resources. In this paper, we propose ConvTimeNet (CTN): an off-the-shelf deep convolutional neural network (CNN) trained on diverse univariate time series classification (TSC) source tasks. Once trained, CTN can be easily adapted to new TSC target tasks via a small amount of fine-tuning using labeled instances from the target tasks. We note that the length of convolutional filters is a key aspect when building a pre-trained model that can generalize to time series of different lengths across datasets. To achieve this, we incorporate filters of multiple lengths in all convolutional layers of CTN to capture temporal features at multiple time scales. We consider all 65 datasets with time series of lengths up to 512 points from the UCR TSC Benchmark for training and testing transferability of CTN: We train CTN on a randomly chosen subset of 24 datasets using a multi-head approach with a different softmax layer for each training dataset, and study generalizability and transferability of the learned filters on the remaining 41 TSC datasets. We observe significant gains in classification accuracy as well as computational efficiency when using pre-trained CTN as a starting point for subsequent task-specific fine-tuning compared to existing state-of-the-art TSC approaches. We also provide qualitative insights into the working of CTN by: i) analyzing the activations and filters of first convolution layer suggesting the filters in CTN are generically useful, ii) analyzing the impact of the design decision to incorporate multiple length decisions, and iii) finding regions of time series that affect the final classification decision via occlusion sensitivity analysis.
Time series with long-term structure arise in a variety of contexts and capturing this temporal structure is a critical challenge in time series analysis for both inference and forecasting settings. Traditionally, state space models have been successful in providing uncertainty estimates of trajectories in the latent space. More recently, deep learning, attention-based approaches have achieved state of the art performance for sequence modeling, though often require large amounts of data and parameters to do so. We propose Stanza, a nonlinear, non-stationary state space model as an intermediate approach to fill the gap between traditional models and modern deep learning approaches for complex time series. Stanza strikes a balance between competitive forecasting accuracy and probabilistic, interpretable inference for highly structured time series. In particular, Stanza achieves forecasting accuracy competitive with deep LSTMs on real-world datasets, especially for multi-step ahead forecasting.
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among brain regions. In this paper, we develop a non-asymptotic theory for regularized estimation of high-dimensional spectral density matrices of Gaussian and linear processes using thresholded versions of averaged periodograms. Our theoretical analysis ensures that consistent estimation of spectral density matrix of a $p$-dimensional time series using $n$ samples is possible under high-dimensional regime $\log p / n \rightarrow 0$ as long as the true spectral density is approximately sparse. A key technical component of our analysis is a new concentration inequality of average periodogram around its expectation, which is of independent interest. Our estimation consistency results complement existing results for shrinkage based estimators of multivariate spectral density, which require no assumption on sparsity but only ensure consistent estimation in a regime $p^2/n \rightarrow 0$. In addition, our proposed thresholding based estimators perform consistent and automatic edge selection when learning coherence networks among the components of a multivariate time series. We demonstrate the advantage of our estimators using simulation studies and a real data application on functional connectivity analysis with fMRI data.
Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting time series. However, modeling statistical dependencies can improve accuracy and enable analysis of interaction effects. Deep learning methods are well suited for this problem, but multi-variate models often assume a simple parametric distribution and do not scale to high dimensions. In this work we model the multi-variate temporal dynamics of time series via an autoregressive deep learning model, where the data distribution is represented by a conditioned normalizing flow. This combination retains the power of autoregressive models, such as good performance in extrapolation into the future, with the flexibility of flows as a general purpose high-dimensional distribution model, while remaining computationally tractable. We show that it improves over the state-of-the-art for standard metrics on many real-world data sets with several thousand interacting time-series.
Heterogeneity and irregularity of multi-source data sets present a significant challenge to time-series analysis. In the literature, the fusion of multi-source time-series has been achieved either by using ensemble learning models which ignore temporal patterns and correlation within features or by defining a fixed-size window to select specific parts of the data sets. On the other hand, many studies have shown major improvement to handle the irregularity of time-series, yet none of these studies has been applied to multi-source data. In this work, we design a novel architecture, PIETS, to model heterogeneous time-series. PIETS has the following characteristics: (1) irregularity encoders for multi-source samples that can leverage all available information and accelerate the convergence of the model; (2) parallelised neural networks to enable flexibility and avoid information overwhelming; and (3) attention mechanism that highlights different information and gives high importance to the most related data. Through extensive experiments on real-world data sets related to COVID-19, we show that the proposed architecture is able to effectively model heterogeneous temporal data and outperforms other state-of-the-art approaches in the prediction task.
Modern time series datasets are often high-dimensional, incomplete/sparse, and nonstationary. These properties hinder the development of scalable and efficient solutions for time series forecasting and analysis. To address these challenges, we propose a Nonstationary Temporal Matrix Factorization (NoTMF) model, in which matrix factorization is used to reconstruct the whole time series matrix and vector autoregressive (VAR) process is imposed on a properly differenced copy of the temporal factor matrix. This approach not only preserves the low-rank property of the data but also offers consistent temporal dynamics. The learning process of NoTMF involves the optimization of two factor matrices and a collection of VAR coefficient matrices. To efficiently solve the optimization problem, we derive an alternating minimization framework, in which subproblems are solved using conjugate gradient and least squares methods. In particular, the use of conjugate gradient method offers an efficient routine and allows us to apply NoTMF on large-scale problems. Through extensive experiments on Uber movement speed dataset, we demonstrate the superior accuracy and effectiveness of NoTMF over other baseline models. Our results also confirm the importance of addressing the nonstationarity of real-world time series data such as spatiotemporal traffic flow/speed.
Estimating causal relations is vital in understanding the complex interactions in multivariate time series. Non-linear coupling of variables is one of the major challenges inaccurate estimation of cause-effect relations. In this paper, we propose to use deep autoregressive networks (DeepAR) in tandem with counterfactual analysis to infer nonlinear causal relations in multivariate time series. We extend the concept of Granger causality using probabilistic forecasting with DeepAR. Since deep networks can neither handle missing input nor out-of-distribution intervention, we propose to use the Knockoffs framework (Barberand Cand`es, 2015) for generating intervention variables and consequently counterfactual probabilistic forecasting. Knockoff samples are independent of their output given the observed variables and exchangeable with their counterpart variables without changing the underlying distribution of the data. We test our method on synthetic as well as real-world time series datasets. Overall our method outperforms the widely used vector autoregressive Granger causality and PCMCI in detecting nonlinear causal dependency in multivariate time series.
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