Time series is a special type of sequence data, a set of observations collected at even intervals of time and ordered chronologically. Existing deep learning techniques use generic sequence models (e.g., recurrent neural network, Transformer model, or temporal convolutional network) for time series analysis, which ignore some of its unique properties. For example, the downsampling of time series data often preserves most of the information in the data, while this is not true for general sequence data such as text sequence and DNA sequence. Motivated by the above, in this paper, we propose a novel neural network architecture and apply it for the time series forecasting problem, wherein we conduct sample convolution and interaction at multiple resolutions for temporal modeling. The proposed architecture, namelySCINet, facilitates extracting features with enhanced predictability. Experimental results show that SCINet achieves significant prediction accuracy improvement over existing solutions across various real-world time series forecasting datasets. In particular, it can achieve high fore-casting accuracy for those temporal-spatial datasets without using sophisticated spatial modeling techniques. Our codes and data are presented in the supplemental material.
We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage consumption and computational complexity. Furthermore, the method can be regarded as a regularization technique, which improves the generalizability of learned target functions. We demonstrate significant improvements in comparison to the computation of data-driven predictions involving the full training data set. The method is applied to classification and regression problems from different application areas such as image recognition, system identification, and oceanographic time series analysis.
Learning the continuous equations of motion from discrete observations is a common task in all areas of physics. However, not any discretization of a Gaussian continuous-time stochastic process can be adopted in parametric inference. We show that discretizations yielding consistent estimators have the property of `invariance under coarse-graining', and correspond to fixed points of a renormalization group map on the space of autoregressive moving average (ARMA) models (for linear processes). This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order stochastic differential equations, even if the corresponding integration schemes may be acceptably good for numerical simulations.
The Wiener-Hopf equations are a Toeplitz system of linear equations that have several applications in time series. These include the update and prediction step of the stationary Kalman filter equations and the prediction of bivariate time series. The Wiener-Hopf technique is the classical tool for solving the equations, and is based on a comparison of coefficients in a Fourier series expansion. The purpose of this note is to revisit the (discrete) Wiener-Hopf equations and obtain an alternative expression for the solution that is more in the spirit of time series analysis. Specifically, we propose a solution to the Wiener-Hopf equations that combines linear prediction with deconvolution. The solution of the Wiener-Hopf equations requires one to obtain the spectral factorization of the underlying spectral density function. For general spectral density functions this is infeasible. Therefore, it is usually assumed that the spectral density is rational, which allows one to obtain a computationally tractable solution. This leads to an approximation error when the underlying spectral density is not a rational function. We use the proposed solution together with Baxter's inequality to derive an error bound for the rational spectral density approximation.
We propose a data-centric pipeline able to generate exogenous observation data for the New Fashion Product Performance Forecasting (NFPPF) problem, i.e., predicting the performance of a brand-new clothing probe with no available past observations. Our pipeline manufactures the missing past starting from a single, available image of the clothing probe. It starts by expanding textual tags associated with the image, querying related fashionable or unfashionable images uploaded on the web at a specific time in the past. A binary classifier is robustly trained on these web images by confident learning, to learn what was fashionable in the past and how much the probe image conforms to this notion of fashionability. This compliance produces the POtential Performance (POP) time series, indicating how performing the probe could have been if it were available earlier. POP proves to be highly predictive for the probe's future performance, ameliorating the sales forecasts of all state-of-the-art models on the recent VISUELLE fast-fashion dataset. We also show that POP reflects the ground-truth popularity of new styles (ensembles of clothing items) on the Fashion Forward benchmark, demonstrating that our webly-learned signal is a truthful expression of popularity, accessible by everyone and generalizable to any time of analysis. Forecasting code, data and the POP time series are available at: https://github.com/HumaticsLAB/POP-Mining-POtential-Performance
Recently, Electrical Distribution Systems are extensively penetrated with the Distributed Energy Resources (DERs) to cater the energy demands with general perception that it enhances the system resiliency. However, it may be adverse for the grid operation due to various factors like its intermittent availability, dynamics in weather condition, introduction of nonlinearity, complexity etc. This needs a detailed understanding of system resiliency that our method proposes here. We introduce a methodology using complex network theory to identify the resiliency of distribution system when incorporated with Solar PV generation under various undesirable configurations. Complex correlated networks for different conditions were obtained and various network parameters were computed for identifying the resiliency of those networks. The proposed methodology identifies the hosting capacity of solar panels in the system while maintaining the resiliency under different unwanted conditions hence helps to obtain an optimal allocation topology for solar panels in the system. The proposed method also identifies the critical nodes that are highly sensitive to the changes and could drive the system into non-resiliency. This framework was demonstrated on IEEE-123 Test Feeder system with time-series data generated using GridLAB-D and variety of analysis were performed using complex network and machine learning models.
Access to labeled time series data is often limited in the real world, which constrains the performance of deep learning models in the field of time series analysis. Data augmentation is an effective way to solve the problem of small sample size and imbalance in time series datasets. The two key factors of data augmentation are the distance metric and the choice of interpolation method. SMOTE does not perform well on time series data because it uses a Euclidean distance metric and interpolates directly on the object. Therefore, we propose a DTW-based synthetic minority oversampling technique using siamese encoder for interpolation named DTWSSE. In order to reasonably measure the distance of the time series, DTW, which has been verified to be an effective method forts, is employed as the distance metric. To adapt the DTW metric, we use an autoencoder trained in an unsupervised self-training manner for interpolation. The encoder is a Siamese Neural Network for mapping the time series data from the DTW hidden space to the Euclidean deep feature space, and the decoder is used to map the deep feature space back to the DTW hidden space. We validate the proposed methods on a number of different balanced or unbalanced time series datasets. Experimental results show that the proposed method can lead to better performance of the downstream deep learning model.
Stock market prediction has been an important topic for investors, researchers, and analysts. Because it is affected by too many factors, stock market prediction is a difficult task to handle. In this study, we propose a novel method that is based on deep reinforcement learning methodologies for the direction prediction of stocks using sentiments of community and knowledge graph. For this purpose, we firstly construct a social knowledge graph of users by analyzing relations between connections. After that, time series analysis of related stock and sentiment analysis is blended with deep reinforcement methodology. Turkish version of Bidirectional Encoder Representations from Transformers (BerTurk) is employed to analyze the sentiments of the users while deep Q-learning methodology is used for the deep reinforcement learning side of the proposed model to construct the deep Q network. In order to demonstrate the effectiveness of the proposed model, Garanti Bank (GARAN), Akbank (AKBNK), T\"urkiye \.I\c{s} Bankas{\i} (ISCTR) stocks in Istanbul Stock Exchange are used as a case study. Experiment results show that the proposed novel model achieves remarkable results for stock market prediction task.
Non-linear (large) time warping is a challenging source of nuisance in time-series analysis. In this paper, we propose a novel diffeomorphic temporal transformer network for both pairwise and joint time-series alignment. Our ResNet-TW (Deep Residual Network for Time Warping) tackles the alignment problem by compositing a flow of incremental diffeomorphic mappings. Governed by the flow equation, our Residual Network (ResNet) builds smooth, fluid and regular flows of velocity fields and consequently generates smooth and invertible transformations (i.e. diffeomorphic warping functions). Inspired by the elegant Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, the final transformation is built by the flow of time-dependent vector fields which are none other than the building blocks of our Residual Network. The latter is naturally viewed as an Eulerian discretization schema of the flow equation (an ODE). Once trained, our ResNet-TW aligns unseen data by a single inexpensive forward pass. As we show in experiments on both univariate (84 datasets from UCR archive) and multivariate time-series (MSR Action-3D, Florence-3D and MSR Daily Activity), ResNet-TW achieves competitive performance in joint alignment and classification.