Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, ability to handle missing data, and probabilistic forecasting. However, the options for count time series are limited: Gaussian DLMs require continuous data, while Poisson-based alternatives often lack sufficient modeling flexibility. We introduce a novel semiparametric methodology for count time series by warping a Gaussian DLM. The warping function has two components: a (nonparametric) transformation operator that provides distributional flexibility and a rounding operator that ensures the correct support for the discrete data-generating process. We develop conjugate inference for the warped DLM, which enables analytic and recursive updates for the state space filtering and smoothing distributions. We leverage these results to produce customized and efficient algorithms for inference and forecasting, including Monte Carlo simulation for offline analysis and an optimal particle filter for online inference. This framework unifies and extends a variety of discrete time series models and is valid for natural counts, rounded values, and multivariate observations. Simulation studies illustrate the excellent forecasting capabilities of the warped DLM. The proposed approach is applied to a multivariate time series of daily overdose counts and demonstrates both modeling and computational successes.
相關內容
In recent years, there has been a growing interest in understanding complex microstructures and their effect on macroscopic properties. In general, it is difficult to derive an effective constitutive law for such microstructures with reasonable accuracy and meaningful parameters. One numerical approach to bridge the scales is computational homogenization, in which a microscopic problem is solved at every macroscopic point, essentially replacing the effective constitutive model. Such approaches are, however, computationally expensive and typically infeasible in multi-query contexts such as optimization and material design. To render these analyses tractable, surrogate models that can accurately approximate and accelerate the microscopic problem over a large design space of shapes, material and loading parameters are required. In previous works, such models were constructed in a data-driven manner using methods such as Neural Networks (NN) or Gaussian Process Regression (GPR). However, these approaches currently suffer from issues, such as need for large amounts of training data, lack of physics, and considerable extrapolation errors. In this work, we develop a reduced order model based on Proper Orthogonal Decomposition (POD), Empirical Cubature Method (ECM) and a geometrical transformation method with the following key features: (i) large shape variations of the microstructure are captured, (ii) only relatively small amounts of training data are necessary, and (iii) highly non-linear history-dependent behaviors are treated. The proposed framework is tested and examined in two numerical examples, involving two scales and large geometrical variations. In both cases, high speed-ups and accuracies are achieved while observing good extrapolation behavior.
In this study, we focus on the development and implementation of a comprehensive ensemble of numerical time series forecasting models, collectively referred to as the Group of Numerical Time Series Prediction Model (G-NM). This inclusive set comprises traditional models such as Autoregressive Integrated Moving Average (ARIMA), Holt-Winters' method, and Support Vector Regression (SVR), in addition to modern neural network models including Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM). G-NM is explicitly constructed to augment our predictive capabilities related to patterns and trends inherent in complex natural phenomena. By utilizing time series data relevant to these events, G-NM facilitates the prediction of such phenomena over extended periods. The primary objective of this research is to both advance our understanding of such occurrences and to significantly enhance the accuracy of our forecasts. G-NM encapsulates both linear and non-linear dependencies, seasonalities, and trends present in time series data. Each of these models contributes distinct strengths, from ARIMA's resilience in handling linear trends and seasonality, SVR's proficiency in capturing non-linear patterns, to LSTM's adaptability in modeling various components of time series data. Through the exploitation of the G-NM potential, we strive to advance the state-of-the-art in large-scale time series forecasting models. We anticipate that this research will represent a significant stepping stone in our ongoing endeavor to comprehend and forecast the complex events that constitute the natural world.
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the effects of initial conditions and other disturbances have decayed. However, modeling transient dynamics near an underlying manifold, as needed for real-time control and forecasting applications, is complicated by the effects of fast dynamics and nonnormal sensitivity mechanisms. To begin to address these issues, we introduce a parametric class of nonlinear projections described by constrained autoencoder neural networks in which both the manifold and the projection fibers are learned from data. Our architecture uses invertible activation functions and biorthogonal weight matrices to ensure that the encoder is a left inverse of the decoder. We also introduce new dynamics-aware cost functions that promote learning of oblique projection fibers that account for fast dynamics and nonnormality. To demonstrate these methods and the specific challenges they address, we provide a detailed case study of a three-state model of vortex shedding in the wake of a bluff body immersed in a fluid, which has a two-dimensional slow manifold that can be computed analytically. In anticipation of future applications to high-dimensional systems, we also propose several techniques for constructing computationally efficient reduced-order models using our proposed nonlinear projection framework. This includes a novel sparsity-promoting penalty for the encoder that avoids detrimental weight matrix shrinkage via computation on the Grassmann manifold.
Confounding is a significant obstacle to unbiased estimation of causal effects from observational data. For settings with high-dimensional covariates -- such as text data, genomics, or the behavioral social sciences -- researchers have proposed methods to adjust for confounding by adapting machine learning methods to the goal of causal estimation. However, empirical evaluation of these adjustment methods has been challenging and limited. In this work, we build on a promising empirical evaluation strategy that simplifies evaluation design and uses real data: subsampling randomized controlled trials (RCTs) to create confounded observational datasets while using the average causal effects from the RCTs as ground-truth. We contribute a new sampling algorithm, which we call RCT rejection sampling, and provide theoretical guarantees that causal identification holds in the observational data to allow for valid comparisons to the ground-truth RCT. Using synthetic data, we show our algorithm indeed results in low bias when oracle estimators are evaluated on the confounded samples, which is not always the case for a previously proposed algorithm. In addition to this identification result, we highlight several finite data considerations for evaluation designers who plan to use RCT rejection sampling on their own datasets. As a proof of concept, we implement an example evaluation pipeline and walk through these finite data considerations with a novel, real-world RCT -- which we release publicly -- consisting of approximately 70k observations and text data as high-dimensional covariates. Together, these contributions build towards a broader agenda of improved empirical evaluation for causal estimation.
Two-component mixture models have proved to be a powerful tool for modeling heterogeneity in several cluster analysis contexts. However, most methods based on these models assume a constant behavior for the mixture weights, which can be restrictive and unsuitable for some applications. In this paper, we relax this assumption and allow the mixture weights to vary according to the index (e.g., time) to make the model more adaptive to a broader range of data sets. We propose an efficient MCMC algorithm to jointly estimate both component parameters and dynamic weights from their posterior samples. We evaluate the method's performance by running Monte Carlo simulation studies under different scenarios for the dynamic weights. In addition, we apply the algorithm to a time series that records the level reached by a river in southern Brazil. The Taquari River is a water body whose frequent flood inundations have caused various damage to riverside communities. Implementing a dynamic mixture model allows us to properly describe the flood regimes for the areas most affected by these phenomena.
Time series forecasting lies at the core of important real-world applications in many fields of science and engineering. The abundance of large time series datasets that consist of complex patterns and long-term dependencies has led to the development of various neural network architectures. Graph neural network approaches, which jointly learn a graph structure based on the correlation of raw values of multivariate time series while forecasting, have recently seen great success. However, such solutions are often costly to train and difficult to scale. In this paper, we propose TimeGNN, a method that learns dynamic temporal graph representations that can capture the evolution of inter-series patterns along with the correlations of multiple series. TimeGNN achieves inference times 4 to 80 times faster than other state-of-the-art graph-based methods while achieving comparable forecasting performance
Deep learning (DL) approaches are being increasingly used for time-series forecasting, with many efforts devoted to designing complex DL models. Recent studies have shown that the DL success is often attributed to effective data representations, fostering the fields of feature engineering and representation learning. However, automated approaches for feature learning are typically limited with respect to incorporating prior knowledge, identifying interactions among variables, and choosing evaluation metrics to ensure that the models are reliable. To improve on these limitations, this paper contributes a novel visual analytics framework, namely TimeTuner, designed to help analysts understand how model behaviors are associated with localized correlations, stationarity, and granularity of time-series representations. The system mainly consists of the following two-stage technique: We first leverage counterfactual explanations to connect the relationships among time-series representations, multivariate features and model predictions. Next, we design multiple coordinated views including a partition-based correlation matrix and juxtaposed bivariate stripes, and provide a set of interactions that allow users to step into the transformation selection process, navigate through the feature space, and reason the model performance. We instantiate TimeTuner with two transformation methods of smoothing and sampling, and demonstrate its applicability on real-world time-series forecasting of univariate sunspots and multivariate air pollutants. Feedback from domain experts indicates that our system can help characterize time-series representations and guide the feature engineering processes.
Latent linear dynamical systems with Bernoulli observations provide a powerful modeling framework for identifying the temporal dynamics underlying binary time series data, which arise in a variety of contexts such as binary decision-making and discrete stochastic processes (e.g., binned neural spike trains). Here we develop a spectral learning method for fast, efficient fitting of probit-Bernoulli latent linear dynamical system (LDS) models. Our approach extends traditional subspace identification methods to the Bernoulli setting via a transformation of the first and second sample moments. This results in a robust, fixed-cost estimator that avoids the hazards of local optima and the long computation time of iterative fitting procedures like the expectation-maximization (EM) algorithm. In regimes where data is limited or assumptions about the statistical structure of the data are not met, we demonstrate that the spectral estimate provides a good initialization for Laplace-EM fitting. Finally, we show that the estimator provides substantial benefits to real world settings by analyzing data from mice performing a sensory decision-making task.
Co-evolving time series appears in a multitude of applications such as environmental monitoring, financial analysis, and smart transportation. This paper aims to address the following challenges, including (C1) how to incorporate explicit relationship networks of the time series; (C2) how to model the implicit relationship of the temporal dynamics. We propose a novel model called Network of Tensor Time Series, which is comprised of two modules, including Tensor Graph Convolutional Network (TGCN) and Tensor Recurrent Neural Network (TRNN). TGCN tackles the first challenge by generalizing Graph Convolutional Network (GCN) for flat graphs to tensor graphs, which captures the synergy between multiple graphs associated with the tensors. TRNN leverages tensor decomposition to model the implicit relationships among co-evolving time series. The experimental results on five real-world datasets demonstrate the efficacy of the proposed method.
This paper addresses the difficulty of forecasting multiple financial time series (TS) conjointly using deep neural networks (DNN). We investigate whether DNN-based models could forecast these TS more efficiently by learning their representation directly. To this end, we make use of the dynamic factor graph (DFG) from that we enhance by proposing a novel variable-length attention-based mechanism to render it memory-augmented. Using this mechanism, we propose an unsupervised DNN architecture for multivariate TS forecasting that allows to learn and take advantage of the relationships between these TS. We test our model on two datasets covering 19 years of investment funds activities. Our experimental results show that our proposed approach outperforms significantly typical DNN-based and statistical models at forecasting their 21-day price trajectory.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191