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Since out-of-distribution generalization is a generally ill-posed problem, various proxy targets (e.g., calibration, adversarial robustness, algorithmic corruptions, invariance across shifts) were studied across different research programs resulting in different recommendations. While sharing the same aspirational goal, these approaches have never been tested under the same experimental conditions on real data. In this paper, we take a unified view of previous work, highlighting message discrepancies that we address empirically, and providing recommendations on how to measure the robustness of a model and how to improve it. To this end, we collect 172 publicly available dataset pairs for training and out-of-distribution evaluation of accuracy, calibration error, adversarial attacks, environment invariance, and synthetic corruptions. We fine-tune over 31k networks, from nine different architectures in the many- and few-shot setting. Our findings confirm that in- and out-of-distribution accuracies tend to increase jointly, but show that their relation is largely dataset-dependent, and in general more nuanced and more complex than posited by previous, smaller scale studies.

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.

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.

In this paper we integrate the isotonic regression with Stone's cross-validation-based method to estimate discrete infinitely supported distribution. We prove that the estimator is strongly consistent, derive its rate of convergence for any underlying distribution, and for one-dimensional case we derive Marshal-type inequality for cumulative distribution function of the estimator. Also, we construct the asymptotically correct conservative global confidence band for the estimator. It is shown that, first, the estimator performs good even for small sized data sets, second, the estimator outperforms in the case of non-monotone underlying distribution, and, third, it performs almost as good as Grenander estimator when the true distribution is isotonic. Therefore, the new estimator provides a trade-off between goodness-of-fit, monotonicity and quality of probabilistic forecast. We apply the estimator to the time-to-onset data of visceral leishmaniasis in Brazil collected from 2007 to 2014.

We present a parallelized optimization method based on fast Neural Radiance Fields (NeRF) for estimating 6-DoF target poses. Given a single observed RGB image of the target, we can predict the translation and rotation of the camera by minimizing the residual between pixels rendered from a fast NeRF model and pixels in the observed image. We integrate a momentum-based camera extrinsic optimization procedure into Instant Neural Graphics Primitives, a recent exceptionally fast NeRF implementation. By introducing parallel Monte Carlo sampling into the pose estimation task, our method overcomes local minima and improves efficiency in a more extensive search space. We also show the importance of adopting a more robust pixel-based loss function to reduce error. Experiments demonstrate that our method can achieve improved generalization and robustness on both synthetic and real-world benchmarks.

This work investigates the use of a Deep Neural Network (DNN) to perform an estimation of the Weapon Engagement Zone (WEZ) maximum launch range. The WEZ allows the pilot to identify an airspace in which the available missile has a more significant probability of successfully engaging a particular target, i.e., a hypothetical area surrounding an aircraft in which an adversary is vulnerable to a shot. We propose an approach to determine the WEZ of a given missile using 50,000 simulated launches in variate conditions. These simulations are used to train a DNN that can predict the WEZ when the aircraft finds itself on different firing conditions, with a coefficient of determination of 0.99. It provides another procedure concerning preceding research since it employs a non-discretized model, i.e., it considers all directions of the WEZ at once, which has not been done previously. Additionally, the proposed method uses an experimental design that allows for fewer simulation runs, providing faster model training.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.

Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.