Intensive Longitudinal Data (ILD) is increasingly available to social and behavioral scientists. With this increased availability come new opportunities for modeling and predicting complex biological, behavioral, and physiological phenomena. Despite these new opportunities psychological researchers have not taken full advantage of promising opportunities inherent to this data, the potential to forecast psychological processes at the individual level. To address this gap in the literature we present a novel modeling framework that addresses a number of topical challenges and open questions in the psychological literature on modeling dynamic processes. First, how can we model and forecast ILD when the length of individual time series and the number of variables collected are roughly equivalent, or when time series lengths are shorter than what is typically required for time series analyses? Second, how can we best take advantage of the cross-sectional (between-person) information inherent to most ILD scenarios while acknowledging individuals differ both quantitatively (e.g. in parameter magnitude) and qualitatively (e.g. in structural dynamics)? Despite the acknowledged between-person heterogeneity in many psychological processes is it possible to leverage group-level information to support improved forecasting at the individual level? In the remainder of the manuscript, we attempt to address these and other pressing questions relevant to the forecasting of multiple-subject ILD.
Many recent developments in the high-dimensional statistical time series literature have centered around time-dependent applications that can be adapted to regularized least squares. Of particular interest is the lasso, which both serves to regularize and provide feature selection. The lasso requires the specification of a penalty parameter that determines the degree of sparsity to impose. The most popular penalty parameter selection approaches that respect time dependence are very computationally intensive and are not appropriate for modeling certain classes of time series. We propose enhanci…
São Paulo School of Economics, Getulio Vargas Foundation（圣保罗经济学院，杰图利奥·瓦加斯基金会）；Pontifical Catholic University of Rio de Janeiro（里约热内卢天主教大学）；Getulio Vargas Foundation（杰图利奥·瓦加斯基金会）
In this paper we survey the most recent advances in supervised machine learning and high-dimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention to penalized regressions and ensemble of models. The nonlinear methods considered in the paper include shallow and deep neural networks, in their feed-forward and recurrent versions, and tree-based methods, such as random forests and boosted trees. We also consider ensemble and hybrid models by combining ingredients from different alternatives. Tests for supe…
This paper characterizes the impact of covariate serial dependence on the non-asymptotic estimation error bound of penalized regressions (PRs). Focusing on the direct relationship between the degree of cross-correlation between covariates and the estimation error bound of PRs, we show that orthogonal or weakly cross-correlated stationary AR processes can exhibit high spurious correlations caused by serial dependence. We provide analytical results on the distribution of the sample cross-correlation in the case of two orthogonal Gaussian AR(1) processes, and extend and validate them through an e…
Czestochowa University of Technology（琴斯托霍瓦理工大学）；Uber Technologies（优步科技公司）
This work presents a hybrid and hierarchical deep learning model for mid-term load forecasting. The model combines exponential smoothing (ETS), advanced Long Short-Term Memory (LSTM) and ensembling. ETS extracts dynamically the main components of each individual time series and enables the model to learn their representation. Multi-layer LSTM is equipped with dilated recurrent skip connections and a spatial shortcut path from lower layers to allow the model to better capture long-term seasonal relationships and ensure more efficient training. A common learning procedure for LSTM and ETS, with …
This paper studies macroeconomic forecasting and variable selection using a folded-concave penalized regression with a very large number of predictors. The penalized regression approach leads to sparse estimates of the regression coefficients, and is applicable even if the dimensionality of the model is much larger than the sample size. The first half of the paper discusses the theoretical aspects of a folded-concave penalized regression when the model exhibits time series dependence. Specifically, we show the oracle inequality and the oracle property for ultrahigh-dimensional time-dependent r…
We consider forecasting the latent rate profiles of a time series of inhomogeneous Poisson processes. The work is motivated by operations management of queueing systems, in particular, telephone call centers, where accurate forecasting of call arrival rates is a crucial primitive for efficient staffing of such centers. Our forecasting approach utilizes dimension reduction through a factor analysis of Poisson variables, followed by time series modeling of factor score series. Time series forecasts of factor scores are combined with factor loadings to yield forecasts of future Poisson rate profi…
We present ARU, an Adaptive Recurrent Unit for streaming adaptation of deep globally trained time-series forecasting models. The ARU combines the advantages of learning complex data transformations across multiple time series from deep global models, with per-series localization offered by closed-form linear models. Unlike existing methods of adaptation that are either memory-intensive or non-responsive after training, ARUs require only fixed sized state and adapt to streaming data via an easy RNN-like update operation. The core principle driving ARU is simple --- maintain sufficient statistic…
Epidemic modeling is an essential tool to understand the spread of the novel coronavirus and ultimately assist in disease prevention, policymaking, and resource allocation. In this article, we establish a state of the art interface between classic mathematical and statistical models and propose a novel space-time epidemic modeling framework to study the spatial-temporal pattern in the spread of infectious disease. We propose a quasi-likelihood approach via the penalized spline approximation and alternatively reweighted least-squares technique to estimate the model. Furthermore, we provide a sh…
Learning vector autoregressive models from multivariate time series is conventionally approached through least squares or maximum likelihood estimation. These methods typically assume a fully connected model which provides no direct insight to the model structure and may lead to highly noisy estimates of the parameters. Because of these limitations, there has been an increasing interest towards methods that produce sparse estimates through penalized regression. However, such methods are computationally intensive and may become prohibitively time-consuming when the number of variables in the mo…
Robust Short-Term OEE Forecasting in Industry 4.0 via Topological Data Analysis
Institute of Applied Mathematics, Middle East Technical University（应用数学研究所，中东部技术大学）；Network Technologies Department, TÜBİTAK ULAKBİM（网络技术部门，TÜBİTAK ULAKBİM）；Department of Statistics, Middle East Technical University（统计学系，中东部技术大学）
Big data generated from the Internet offer great potential for predictive analysis. Here we focus on using online users' Internet search data to forecast unemployment initial claims weeks into the future, which provides timely insights into the direction of the economy. To this end, we present a novel method PRISM (Penalized Regression with Inferred Seasonality Module), which uses publicly available online search data from Google. PRISM is a semi-parametric method, motivated by a general state-space formulation, and employs nonparametric seasonal decomposition and penalized regression. For for…
University of Washington（华盛顿大学）；Microsoft Research（微软研究院）
Hundreds of millions of surgical procedures take place annually across the world, which generate a prevalent type of electronic health record (EHR) data comprising time series physiological signals. Here, we present a transferable embedding method (i.e., a method to transform time series signals into input features for predictive machine learning models) named PHASE (PHysiologicAl Signal Embeddings) that enables us to more accurately forecast adverse surgical outcomes based on physiological signals. We evaluate PHASE on minute-by-minute EHR data of more than 50,000 surgeries from two operating…
A highly dynamic urban space in a metropolis such as New York City, the spatio-temporal variation in demand for transportation, particularly taxis, is impacted by various factors such as commuting, weather, road work and closures, disruption in transit services, etc. To understand the user demand for taxis through space and time, a generalized spatio-temporal autoregressive (STAR) model is proposed in this study. In order to deal with the high dimensionality of the model, LASSO-type penalized methods are proposed to tackle the parameter estimation. The forecasting performance of the proposed m…
In this paper, we mainly focus on the penalized maximum likelihood estimation (MLE) of the high-dimensional approximate factor model. Since the current estimation procedure can not guarantee the positive definiteness of the error covariance matrix, by reformulating the estimation of error covariance matrix and based on the lagrangian duality, we propose an accelerated proximal gradient (APG) algorithm to give a positive definite estimate of the error covariance matrix. Combined the APG algorithm with EM method, a new estimation procedure is proposed to estimate the high-dimensional approximate…
Forecasting intra-individual changes of affective states taking into account inter-individual differences using intensive longitudinal data from a university student drop out study in math
This paper presents a data-based simple model for fitting the available data of the Covid-19 pandemic evolution in France. The time series concerning the 13 regions of mainland France have been considered for fitting and validating the model. An extremely simple, two-dimensional model with only two parameters demonstrated to be able to reproduce the time series concerning the number of daily demises caused by Covid-19, the hospitalizations, intensive care and emergency accesses, the daily number of positive test and other indicators, for the different French regions. These results might contri…
Kernel density estimation is a well known method involving a smoothing parameter (the bandwidth) that needs to be tuned by the user. Although this method has been widely used the bandwidth selection remains a challenging issue in terms of balancing algorithmic performance and statistical relevance. The purpose of this paper is to compare a recently developped bandwidth selection method for kernel density estimation to those which are commonly used by now (at least those which are implemented in the R-package). This new method is called Penalized Comparison to Overfitting (PCO). It has been pro…
