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Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data are continually arriving and are analyzed adaptively. We are concerned with the related, but distinct, offline version, in which retrospective analysis of an entire sequence is performed. For a set of multivariate observations of arbitrary dimension, we consider nonparametric estimation of both the number of change points and the positions at which they occur. We do not make any assumptions regarding the nature of the change in distribution or any distribution assumptions beyond the existence of the αth absolute moment, for some α ∈ (0, 2). Estimation is based on hierarchical clustering and we propose both divisive and agglomerative algorithms. The divisive method is shown to provide consistent estimates of both the number and the location of change points under standard regularity assumptions. We compare the proposed approach with competing methods in a simulation study. Methods from cluster analysis are applied to assess performance and to allow simple comparisons of location estimates, even when the estimated number differs. We conclude with applications in genetics, finance, and spatio-temporal analysis. Supplementary materials for this article are available online.

Advances in remote sensing and machine learning enable increasingly accurate, inexpensive, and timely estimation of poverty and malnutrition indicators to guide development and humanitarian agencies’ programming. However, state of the art models often rely on proprietary data and/or deep or transfer learning methods whose underlying mechanics may be challenging to interpret. We demonstrate how interpretable random forest models can produce estimates of a set of (potentially correlated) malnutrition and poverty prevalence measures using free, open access, regularly updated, georeferenced data. We demonstrate two use cases: contemporaneous prediction, which might be used for poverty mapping, geographic targeting, or monitoring and evaluation tasks, and a sequential nowcasting task that can inform early warning systems. Applied to data from 11 low and lower-middle income countries, we find predictive accuracy broadly comparable for both tasks to prior studies that use proprietary data and/or deep or transfer learning methods.

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building on a global–local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence between the local scale parameters. The resulting processes inherit the desirable shrinkage behaviour of popular global–local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modelling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a Pólya–gamma scale mixture representation of the process proposed. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than do competing methods, and we apply the model for irregular curve fitting of minute-by-minute Twitter central processor unit usage data. In addition, we develop an adaptive time varying parameter regression model to assess the efficacy of the Fama–French five-factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that, with the exception of the market risk, no other risk factors are significant except for brief periods.

This article introduces a novel statistical framework for independent component analysis (ICA) of multivariate data. We propose methodology for estimating mutually independent components, and a versatile resampling-based procedure for inference, including misspecification testing. Independent components are estimated by combining a nonparametric probability integral transformation with a generalized nonparametric whitening method based on distance covariance that simultaneously minimizes all forms of dependence among the components. We prove the consistency of our estimator under minimal regularity conditions and detail conditions for consistency under model misspecification, all while placing assumptions on the observations directly, not on the latent components. U statistics of certain Euclidean distances between sample elements are combined to construct a test statistic for mutually independent components. The proposed measures and tests are based on both necessary and sufficient conditions for mutual independence. We demonstrate the improvements of the proposed method over several competing methods in simulation studies, and we apply the proposed ICA approach to two real examples and contrast it with principal component analysis.

We propose Conditional Imputation GAN, an extended missing data imputation method based on Generative Adversarial Networks (GANs). The motivating use case is learning-to-rank, the cornerstone of modern search, recommendation system, and information retrieval applications. Empirical ranking datasets do not always follow standard Gaussian distributions or Missing Completely At Random (MCAR) mechanism, which are standard assumptions of classic missing data imputation methods. Our methodology provides a simple solution that offers compatible imputation guarantees while relaxing assumptions for missing mechanisms and sidesteps approximating intractable distributions to improve imputation quality. We prove that the optimal GAN imputation is achieved for Extended Missing At Random and Extended Always Missing At Random mechanisms, beyond the naive MCAR. Our method demonstrates the highest imputation quality on the open-source Microsoft Research Ranking Dataset and a synthetic ranking dataset compared to state-of-the-art benchmarks and across various feature distributions. Using a proprietary Amazon Search ranking dataset, we also demonstrate comparable ranking quality metrics for ranking models trained on GAN-imputed data compared to ground-truth data.

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data-functional, time dependent, and multivariate components-we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-invariant functional basis for the functional observations, which is smooth and interpretable, and can be made common across multivariate observations for additional information sharing. The Bayesian framework permits joint estimation of the model parameters, provides exact inference (up to MCMC error) on specific parameters, and allows generalized dependence structures. Sampling from the posterior distribution is accomplished with an efficient Gibbs sampling algorithm. We illustrate the proposed framework with two applications: (1) multi-economy yield curve data from the recent global recession, and (2) local field potential brain signals in rats, for which we develop a multivariate functional time series approach for multivariate time-frequency analysis. Supplementary materials, including R code and the multi-economy yield curve data, are available online.

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with nonnegligible measurement error. The latent process is dynamically modeled as a functional autoregression (FAR) with Gaussian process innovations. We propose a fully nonparametric dynamic functional factor model for the dynamic innovation process, with broader applicability and improved computational efficiency over standard Gaussian process models. We prove finite-sample forecasting and interpolation optimality properties of the proposed model, which remain valid with the Gaussian assumption relaxed. An efficient Gibbs sampling algorithm is developed for estimation, inference, and forecasting, with extensions for FAR(p) models with model averaging over the lag p. Extensive simulations demonstrate substantial improvements in forecasting performance and recovery of the autoregressive surface over competing methods, especially under sparse designs. We apply the proposed methods to forecast nominal and real yield curves using daily U.S. data. Real yields are observed more sparsely than nominal yields, yet the proposed methods are highly competitive in both settings. Supplementary materials, including R code and the yield curve data, are available online.

Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis (PCA) is used for dimension reduction prior to ICA (PCA+ICA), which could remove important information. The problem is that interesting independent components (ICs) could be mixed in several principal components that are discarded and then these ICs cannot be recovered. We formulate a linear non-Gaussian component model with Gaussian noise components. To estimate the model parameters, we propose likelihood component analysis (LCA), in which dimension reduction and latent variable estimation are achieved simultaneously. Our method orders components by their marginal likelihood rather than ordering components by variance as in PCA. We present a parametric LCA using the logistic density and a semiparametric LCA using tilted Gaussians with cubic B-splines. Our algorithm is scalable to datasets common in applications (e.g., hundreds of thousands of observations across hundreds of variables with dozens of latent components). In simulations, latent components are recovered that are discarded by PCA+ICA methods. We apply our method to multivariate data and demonstrate that LCA is a useful data visualization and dimension reduction tool that reveals features not apparent from PCA or PCA+ICA. We also apply our method to a functional magnetic resonance imaging experiment from the Human Connectome Project and identify artifacts missed by PCA+ICA. We present theoretical results on identifiability of the linear non-Gaussian component model and consistency of LCA. Supplementary materials for this article are available online.

A deep convolutional neural network has been developed to denoise atomic-resolution transmission electron microscope image datasets of nanoparticles acquired using direct electron counting detectors, for applications where the image signal is severely limited by shot noise. The network was applied to a model system of CeO2-supported Pt nanoparticles. We leverage multislice image simulations to generate a large and flexible dataset for training the network. The proposed network outperforms state-of-the-art denoising methods on both simulated and experimental test data. Factors contributing to the performance are identified, including (a) the geometry of the images used during training and (b) the size of the network's receptive field. Through a gradient-based analysis, we investigate the mechanisms learned by the network to denoise experimental images. This shows that the network exploits both extended and local information in the noisy measurements, for example, by adapting its filtering approach when it encounters atomic-level defects at the nanoparticle surface. Extensive analysis has been done to characterize the network's ability to correctly predict the exact atomic structure at the nanoparticle surface. Finally, we develop an approach based on the log-likelihood ratio test that provides a quantitative measure of the agreement between the noisy observation and the atomic-level structure in the network-denoised image.

Ambulance demand estimation at fine time and location scales is critical for fleet management and dynamic deployment. We are motivated by the problem of estimating the spatial distribution of ambulance demand in Toronto, Canada, as it changes over discrete 2 hr intervals. This large-scale dataset is sparse at the desired temporal resolutions and exhibits location-specific serial dependence, daily, and weekly seasonality. We address these challenges by introducing a novel characterization of time-varying Gaussian mixture models. We fix the mixture component distributions across all time periods to overcome data sparsity and accurately describe Toronto's spatial structure, while representing the complex spatio-temporal dynamics through time-varying mixture weights. We constrain the mixture weights to capture weekly seasonality, and apply a conditionally autoregressive prior on the mixture weights of each component to represent location-specific short-term serial dependence and daily seasonality. While estimation may be performed using a fixed number of mixture components, we also extend to estimate the number of components using birth-and-death Markov chain Monte Carlo. The proposed model is shown to give higher statistical predictive accuracy and to reduce the error in predicting emergency medical service operational performance by as much as two-thirds compared to a typical industry practice.