We prove that in an approximate factor model for an $n$-dimensional vector of stationary time series the factor loadings estimated via Principal Components are asymptotically equivalent, as $n\to\infty$, to those estimated by Quasi Maximum Likelihood. Both estimators are, in turn, also asymptotically equivalent, as $n\to\infty$, to the unfeasible Ordinary Least Squares estimator we would have if the factors were observed. We also show that the usual sandwich form of the asymptotic covariance matrix of the Quasi Maximum Likelihood estimator is asymptotically equivalent to the simpler asymptotic covariance matrix of the unfeasible Ordinary Least Squares. This provides a simple way to estimate asymptotic confidence intervals for the Quasi Maximum Likelihood estimator without the need of estimating the Hessian and Fisher information matrices whose expressions are very complex. All our results hold in the general case in which the idiosyncratic components are cross-sectionally heteroskedastic as well as serially and cross-sectionally weakly correlated.
相關內容
Achieving real-time capability is an essential prerequisite for the industrial implementation of nonlinear model predictive control (NMPC). Data-driven model reduction offers a way to obtain low-order control models from complex digital twins. In particular, data-driven approaches require little expert knowledge of the particular process and its model, and provide reduced models of a well-defined generic structure. Herein, we apply our recently proposed data-driven reduction strategy based on Koopman theory [Schulze et al. (2022), Comput. Chem. Eng.] to generate a low-order control model of an air separation unit (ASU). The reduced Koopman model combines autoencoders and linear latent dynamics and is constructed using machine learning. Further, we present an NMPC implementation that uses derivative computation tailored to the fixed block structure of reduced Koopman models. Our reduction approach with tailored NMPC implementation enables real-time NMPC of an ASU at an average CPU time decrease by 98 %.
This work studies the signal-to-interference-plus-noise-ratio (SINR) meta distribution for the uplink transmission of a Poisson network with Rayleigh fading by using the dominant interferer-based approximation. The proposed approach relies on computing the mix of exact and mean-field analysis of interference. In particular, it requires the distance distribution of the nearest interferer and the conditional average of the rest of the interference. Using the widely studied fractional path-loss inversion power control and modeling the spatial locations of base stations (BSs) by a Poisson point process (PPP), we obtain the meta distribution based on the proposed method and compare it with the traditional beta approximation, as well as the exact results obtained via Monte-Carlo simulations. Our numerical results validate that the proposed method shows good matching and is time competitive.
Wireless communication systems to date primarily rely on the orthogonality of resources to facilitate the design and implementation, from user access to data transmission. Emerging applications and scenarios in the sixth generation (6G) wireless systems will require massive connectivity and transmission of a deluge of data, which calls for more flexibility in the design concept that goes beyond orthogonality. Furthermore, recent advances in signal processing and learning have attracted considerable attention, as they provide promising approaches to various complex and previously intractable problems of signal processing in many fields. This article provides an overview of research efforts to date in the field of signal processing and learning for next-generation multiple access, with an emphasis on massive random access and non-orthogonal multiple access. The promising interplay with new technologies and the challenges in learning-based NGMA are discussed.
In epidemiological studies, zero-inflated and hurdle models are commonly used to handle excess zeros in reported infectious disease cases. However, they can not model the persistence (from presence to presence) and reemergence (from absence to presence) of a disease separately. Covariates can sometimes have different effects on the reemergence and persistence of a disease. Recently, a zero-inflated Markov switching negative binomial model was proposed to accommodate this issue. We present a Markov switching negative binomial hurdle model as a competitor of that approach, as hurdle models are often also used as alternatives to zero-inflated models for accommodating excess zeroes. We begin the comparison by inspecting the underlying assumptions made by both models. Hurdle models assume perfect detection of the disease cases while zero-inflated models implicitly assume the case counts can be under-reported, thus we investigate when a negative binomial distribution can approximate the true distribution of reported counts. A comparison of the fit of the two types of Markov switching models is undertaken on chikungunya cases across the neighborhoods of Rio de Janeiro. We find that, among the fitted models, the Markov switching negative binomial zero-inflated model produces the best predictions and both Markov switching models produce remarkably better predictions than more traditional negative binomial hurdle and zero-inflated models.
We propose employing a debiased-regularized, high-dimensional generalized method of moments (GMM) framework to perform inference on large-scale spatial panel networks. In particular, network structure with a flexible sparse deviation, which can be regarded either as latent or as misspecified from a predetermined adjacency matrix, is estimated using debiased machine learning approach. The theoretical analysis establishes the consistency and asymptotic normality of our proposed estimator, taking into account general temporal and spatial dependency inherent in the data-generating processes. The dimensionality allowance in presence of dependency is discussed. A primary contribution of our study is the development of uniform inference theory that enables hypothesis testing on the parameters of interest, including zero or non-zero elements in the network structure. Additionally, the asymptotic properties for the estimator are derived for both linear and nonlinear moments. Simulations demonstrate superior performance of our proposed approach. Lastly, we apply our methodology to investigate the spatial network effect of stock returns.
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for the approximation of the intractable transition dynamics of the Stochastic Differential Equation (SDE) model over finite time periods. The scheme is applied for a step-size that is either user-selected or determined by the data. Recent research has highlighted the critical ef-fect of the choice of numerical scheme on the behaviour of derived parameter estimates in the setting of hypo-elliptic SDEs. In brief, in our work, first, we develop two weak second order sampling schemes (to cover both hypo-elliptic and elliptic SDEs) and produce a small time expansion for the density of the schemes to form a proxy for the true intractable SDE transition density. Then, we establish a collection of analytic results for likelihood-based parameter estimates obtained via the formed proxies, thus providing a theoretical framework that showcases advantages from the use of the developed methodology for SDE calibration. We present numerical results from carrying out classical or Bayesian inference, for both elliptic and hypo-elliptic SDEs.
To determine if a convolutional neural network (CNN) deep learning model can accurately segment acute ischemic changes on non-contrast CT compared to neuroradiologists. Non-contrast CT (NCCT) examinations from 232 acute ischemic stroke patients who were enrolled in the DEFUSE 3 trial were included in this study. Three experienced neuroradiologists independently segmented hypodensity that reflected the ischemic core on each scan. The neuroradiologist with the most experience (expert A) served as the ground truth for deep learning model training. Two additional neuroradiologists (experts B and C) segmentations were used for data testing. The 232 studies were randomly split into training and test sets. The training set was further randomly divided into 5 folds with training and validation sets. A 3-dimensional CNN architecture was trained and optimized to predict the segmentations of expert A from NCCT. The performance of the model was assessed using a set of volume, overlap, and distance metrics using non-inferiority thresholds of 20%, 3ml, and 3mm. The optimized model trained on expert A was compared to test experts B and C. We used a one-sided Wilcoxon signed-rank test to test for the non-inferiority of the model-expert compared to the inter-expert agreement. The final model performance for the ischemic core segmentation task reached a performance of 0.46+-0.09 Surface Dice at Tolerance 5mm and 0.47+-0.13 Dice when trained on expert A. Compared to the two test neuroradiologists the model-expert agreement was non-inferior to the inter-expert agreement, p < 0.05. The CNN accurately delineates the hypodense ischemic core on NCCT in acute ischemic stroke patients with an accuracy comparable to neuroradiologists.
The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191