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Recently, several researchers have claimed that conclusions obtained from a Bayes factor (or the posterior odds) may contradict those obtained from Bayesian posterior estimation. In this short paper, we wish to point out that no such "incompatibility" exists if one is willing to consistently define one's priors and posteriors. The key for compatibility is that the (implied) prior model odds used for testing are the same as those used for estimation. Our recommendation is simple: If one reports a Bayes factor comparing two models, then one should also report posterior estimates which appropriately acknowledge the uncertainty with regards to which of the two models is correct.

Traffic speed is central to characterizing the fluidity of the road network. Many transportation applications rely on it, such as real-time navigation, dynamic route planning, and congestion management. Rapid advances in sensing and communication techniques make traffic speed detection easier than ever. However, due to sparse deployment of static sensors or low penetration of mobile sensors, speeds detected are incomplete and far from network-wide use. In addition, sensors are prone to error or missing data due to various kinds of reasons, speeds from these sensors can become highly noisy. These drawbacks call for effective techniques to recover credible estimates from the incomplete data. In this work, we first identify the problem as a spatiotemporal kriging problem and propose a unified graph embedded tensor (SGET) learning framework featuring both low-rankness and multi-dimensional correlations for network-wide traffic speed kriging under limited observations. To be specific, three types of speed correlation including temporal continuity, temporal periodicity, and spatial proximity are carefully chosen. We then design an efficient solution algorithm via several effective numeric techniques to scale up the proposed model to network-wide kriging. By performing experiments on two public million-level traffic speed datasets, we finally draw the conclusion and find our proposed SGET achieves the state-of-the-art kriging performance even under low observation rates, while at the same time saving more than half computing time compared with baseline methods. Some insights into spatiotemporal traffic data kriging at the network level are provided as well.

Two-stage randomized experiments are becoming an increasingly popular experimental design for causal inference when the outcome of one unit may be affected by the treatment assignments of other units in the same cluster. In this paper, we provide a methodological framework for general tools of statistical inference and power analysis for two-stage randomized experiments. Under the randomization-based framework, we consider the estimation of a new direct effect of interest as well as the average direct and spillover effects studied in the literature. We provide unbiased estimators of these causal quantities and their conservative variance estimators in a general setting. Using these results, we then develop hypothesis testing procedures and derive sample size formulas. We theoretically compare the two-stage randomized design with the completely randomized and cluster randomized designs, which represent two limiting designs. Finally, we conduct simulation studies to evaluate the empirical performance of our sample size formulas. For empirical illustration, the proposed methodology is applied to the randomized evaluation of the Indian national health insurance program. An open-source software package is available for implementing the proposed methodology.

In this document, some elements of the theory and algorithmics corresponding to the existence and computability of approximate joint eigenpairs for finite collections of matrices with applications to model order reduction, are presented. More specifically, given a finite collection $X_1,\ldots,X_d$ of Hermitian matrices in $\mathbb{C}^{n\times n}$, a positive integer $r\ll n$, and a collection of complex numbers $\hat{x}_{j,k}\in \mathbb{C}$ for $1\leq j\leq d$, $1\leq k\leq r$. First, we study the computability of a set of $r$ vectors $w_1,\ldots,w_r\in \mathbb{C}^{n}$, such that $w_k=\arg\min_{w\in \mathbb{C}^n}\sum_{j=1}^d\|X_jw-\hat{x}_{j,k} w\|^2$ for each $1\leq k \leq r$, then we present a model order reduction procedure based on the truncated joint approximate eigenbases computed with the aforementioned techniques. Some prototypical algorithms together with some numerical examples are presented as well.

Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model parameters. Likelihood based penalization methods are more computationally friendly, but resource intensive refitting techniques are needed for inference. In this paper, we proposed an efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are required through the use of plug-in empirical Bayes estimates of hyperparameters. Efficient maximum a posteriori probability (MAP) estimation is completed through the use of a partitioned and extended expectation conditional maximization (ECM) algorithm. The result is a PaRtitiOned empirical Bayes Ecm (PROBE) algorithm applied to sparse high-dimensional linear regression. We propose methods to estimate credible and prediction intervals for predictions of future values. We compare the empirical properties of predictions and our predictive inference to comparable approaches with numerous simulation studies and an analysis of cancer cell lines drug response study. The proposed approach is implemented in the R package probe.

High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix structure and temporal dynamics in such data, Wang et al. (2017) proposed a matrix factor model that is shown to provide effective analysis. In this paper, we establish a general framework for incorporating domain or prior knowledge in the matrix factor model through linear constraints. The proposed framework is shown to be useful in achieving parsimonious parameterization, facilitating interpretation of the latent matrix factor, and identifying specific factors of interest. Fully utilizing the prior-knowledge-induced constraints results in more efficient and accurate modeling, inference, dimension reduction as well as a clear and better interpretation of the results. In this paper, constrained, multi-term, and partially constrained factor models for matrix-variate time series are developed, with efficient estimation procedures and their asymptotic properties. We show that the convergence rates of the constrained factor loading matrices are much faster than those of the conventional matrix factor analysis under many situations. Simulation studies are carried out to demonstrate the finite-sample performance of the proposed method and its associated asymptotic properties. We illustrate the proposed model with three applications, where the constrained matrix-factor models outperform their unconstrained counterparts in the power of variance explanation under the out-of-sample 10-fold cross-validation setting.

This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of observations ($T$). We propose an estimation method called $\alpha$-PCA that preserves the matrix structure and aggregates mean and contemporary covariance through a hyper-parameter $\alpha$. We develop an inferential theory, establishing consistency, the rate of convergence, and the limiting distributions, under general conditions that allow for correlations across time, rows, or columns of the noise. We show both theoretical and empirical methods of choosing the best $\alpha$, depending on the use-case criteria. Simulation results demonstrate the adequacy of the asymptotic results in approximating the finite sample properties. The $\alpha$-PCA compares favorably with the existing ones. Finally, we illustrate its applications with a real numeric data set and two real image data sets. In all applications, the proposed estimation procedure outperforms previous methods in the power of variance explanation using out-of-sample 10-fold cross-validation.

Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More specifically, we propose the first use of such bounds to improve Gaussian process (GP) posterior sampling and Bayesian optimization (BO). That is, we transform a GP model satisfying the given bounds, and then sample and weight functions from its posterior. To further exploit these bounds in BO settings, we present bounded entropy search (BES) to select the point gaining the most information about the underlying function, estimated by the GP samples, while satisfying the output constraints. We characterize the sample variance bounds and show that the decision made by BES is explainable. Our proposed approach is conceptually straightforward and can be used as a plug in extension to existing methods for GP posterior sampling and Bayesian optimization.

With advancements in computer vision taking place day by day, recently a lot of light is being shed on activity recognition. With the range for real-world applications utilizing this field of study increasing across a multitude of industries such as security and healthcare, it becomes crucial for businesses to distinguish which machine learning methods perform better than others in the area. This paper strives to aid in this predicament i.e. building upon previous related work, it employs both classical and ensemble approaches on rich pose estimation (OpenPose) and HAR datasets. Making use of appropriate metrics to evaluate the performance for each model, the results show that overall, random forest yields the highest accuracy in classifying ADLs. Relatively all the models have excellent performance across both datasets, except for logistic regression and AdaBoost perform poorly in the HAR one. With the limitations of this paper also discussed in the end, the scope for further research is vast, which can use this paper as a base in aims of producing better results.

Performance tuning, software/hardware co-design, and job scheduling are among the many tasks that rely on models to predict application performance. We propose and evaluate low rank tensor decomposition for modeling application performance. We use tensors to represent regular grids that discretize the input and configuration domain of an application. Application execution times mapped within grid-cells are averaged and represented by tensor elements. We show that low-rank canonical-polyadic (CP) tensor decomposition is effective in approximating these tensors. We then employ tensor completion to optimize a CP decomposition given a sparse set of observed runtimes. We consider alternative piecewise/grid-based (P/G) and supervised learning models for six applications and demonstrate that P/G models are significantly more accurate relative to model size. Among P/G models, CP decomposition of regular grids (CPR) offers higher accuracy and memory-efficiency, faster optimization, and superior extensibility via user-selected loss functions and domain partitioning. CPR models achieve a 2.18x geometric mean decrease in mean prediction error relative to the most accurate alternative models of size $\le$10 kilobytes.