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Multiple antenna arrays play a key role in wireless networks for communications but also localization and sensing. The use of large antenna arrays pushes towards a propagation regime in which the wavefront is no longer plane but spherical. This allows to infer the position and orientation of an arbitrary source from the received signal without the need of using multiple anchor nodes. To understand the fundamental limits of large antenna arrays for localization, this paper fusions wave propagation theory with estimation theory, and computes the Cram{\'e}r-Rao Bound (CRB) for the estimation of the three Cartesian coordinates of the source on the basis of the electromagnetic vector field, observed over a rectangular surface area. To simplify the analysis, we assume that the source is a dipole, whose center is located on the line perpendicular to the surface center, with an orientation a priori known. Numerical and asymptotic results are given to quantify the CRBs, and to gain insights into the effect of various system parameters on the ultimate estimation accuracy. It turns out that surfaces of practical size may guarantee a centimeter-level accuracy in the mmWave bands.

In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the original equation as a system of first order differential equations we introduce the method and show that the resulting discrete formulation is well-posed, stable and retains super-optimal rate of convergence with respect to the discretization parameters, namely the time step and the polynomial approximation degree. A set of two- and three-dimensional numerical experiments confirm the theoretical bounds. Finally, the method is applied to real geophysical applications.

We consider a randomized controlled trial between two groups. The objective is to identify a population with characteristics such that the test therapy is more effective than the control therapy. Such a population is called a subgroup. This identification can be made by estimating the treatment effect and identifying interactions between treatments and covariates. To date, many methods have been proposed to identify subgroups for a single outcome. There are also multiple outcomes, but they are difficult to interpret and cannot be applied to outcomes other than continuous values. In this paper, we propose a multivariate regression method that introduces latent variables to estimate the treatment effect on multiple outcomes simultaneously. The proposed method introduces latent variables and adds Lasso sparsity constraints to the estimated loadings to facilitate the interpretation of the relationship between outcomes and covariates. The framework of the generalized linear model makes it applicable to various types of outcomes. Interpretation of subgroups is made by visualizing treatment effects and latent variables. This allows us to identify subgroups with characteristics that make the test therapy more effective for multiple outcomes. Simulation and real data examples demonstrate the effectiveness of the proposed method.

Unbiased and consistent variance estimators generally do not exist for design-based treatment effect estimators because experimenters never observe more than one potential outcome for any unit. The problem is exacerbated by interference and complex experimental designs. In this paper, we consider variance estimation for linear treatment effect estimators under interference and arbitrary experimental designs. Experimenters must accept conservative estimators in this setting, but they can strive to minimize the conservativeness. We show that this task can be interpreted as an optimization problem in which one aims to find the lowest estimable upper bound of the true variance given one's risk preference and knowledge of the potential outcomes. We characterize the set of admissible bounds in the class of quadratic forms, and we demonstrate that the optimization problem is a convex program for many natural objectives. This allows experimenters to construct less conservative variance estimators, making inferences about treatment effects more informative. The resulting estimators are guaranteed to be conservative regardless of whether the background knowledge used to construct the bound is correct, but the estimators are less conservative if the knowledge is reasonably accurate.

We consider reinforcement learning (RL) in Markov Decision Processes in which an agent repeatedly interacts with an environment that is modeled by a controlled Markov process. At each time step $t$, it earns a reward, and also incurs a cost-vector consisting of $M$ costs. We design learning algorithms that maximize the cumulative reward earned over a time horizon of $T$ time-steps, while simultaneously ensuring that the average values of the $M$ cost expenditures are bounded by agent-specified thresholds $c^{ub}_i,i=1,2,\ldots,M$. The considerations on the cumulative cost expenditures departs from the existing literature, in that the agent now additionally needs to balance the cost expenses in an online manner, while simultaneously performing the exploration-exploitation trade-off that is typically encountered in RL tasks. In order to measure the performance of a reinforcement learning algorithm that satisfies the average cost constraints, we define an $M+1$ dimensional regret vector that is composed of its reward regret, and $M$ cost regrets. The reward regret measures the sub-optimality in the cumulative reward, while the $i$-th component of the cost regret vector is the difference between its $i$-th cumulative cost expense and the expected cost expenditures $Tc^{ub}_i$. We prove that with a high probablity, the regret vector of UCRL-CMDP is upper-bounded as $O\left( S\sqrt{AT^{1.5}\log(T)}\right)$, where $S$ is the number of states, $A$ is the number of actions, and $T$ is the time horizon. We further show how to reduce the regret of a desired subset of the $M$ costs, at the expense of increasing the regrets of rewards and the remaining costs. To the best of our knowledge, ours is the only work that considers non-episodic RL under average cost constraints, and derive algorithms that can~\emph{tune the regret vector} according to the agent's requirements on its cost regrets.

Estimating causal effects from randomized experiments is central to clinical research. Reducing the statistical uncertainty in these analyses is an important objective for statisticians. Registries, prior trials, and health records constitute a growing compendium of historical data on patients under standard-of-care that may be exploitable to this end. However, most methods for historical borrowing achieve reductions in variance by sacrificing strict type-I error rate control. Here, we propose a use of historical data that exploits linear covariate adjustment to improve the efficiency of trial analyses without incurring bias. Specifically, we train a prognostic model on the historical data, then estimate the treatment effect using a linear regression while adjusting for the trial subjects' predicted outcomes (their prognostic scores). We prove that, under certain conditions, this prognostic covariate adjustment procedure attains the minimum variance possible among a large class of estimators. When those conditions are not met, prognostic covariate adjustment is still more efficient than raw covariate adjustment and the gain in efficiency is proportional to a measure of the predictive accuracy of the prognostic model above and beyond the linear relationship with the raw covariates. We demonstrate the approach using simulations and a reanalysis of an Alzheimer's Disease clinical trial and observe meaningful reductions in mean-squared error and the estimated variance. Lastly, we provide a simplified formula for asymptotic variance that enables power calculations that account for these gains. Sample size reductions between 10% and 30% are attainable when using prognostic models that explain a clinically realistic percentage of the outcome variance.

We explore the application of super-resolution techniques to satellite imagery, and the effects of these techniques on object detection algorithm performance. Specifically, we enhance satellite imagery beyond its native resolution, and test if we can identify various types of vehicles, planes, and boats with greater accuracy than native resolution. Using the Very Deep Super-Resolution (VDSR) framework and a custom Random Forest Super-Resolution (RFSR) framework we generate enhancement levels of 2x, 4x, and 8x over five distinct resolutions ranging from 30 cm to 4.8 meters. Using both native and super-resolved data, we then train several custom detection models using the SIMRDWN object detection framework. SIMRDWN combines a number of popular object detection algorithms (e.g. SSD, YOLO) into a unified framework that is designed to rapidly detect objects in large satellite images. This approach allows us to quantify the effects of super-resolution techniques on object detection performance across multiple classes and resolutions. We also quantify the performance of object detection as a function of native resolution and object pixel size. For our test set we note that performance degrades from mean average precision (mAP) = 0.53 at 30 cm resolution, down to mAP = 0.11 at 4.8 m resolution. Super-resolving native 30 cm imagery to 15 cm yields the greatest benefit; a 13-36% improvement in mAP. Super-resolution is less beneficial at coarser resolutions, though still provides a small improvement in performance.

Learning robot objective functions from human input has become increasingly important, but state-of-the-art techniques assume that the human's desired objective lies within the robot's hypothesis space. When this is not true, even methods that keep track of uncertainty over the objective fail because they reason about which hypothesis might be correct, and not whether any of the hypotheses are correct. We focus specifically on learning from physical human corrections during the robot's task execution, where not having a rich enough hypothesis space leads to the robot updating its objective in ways that the person did not actually intend. We observe that such corrections appear irrelevant to the robot, because they are not the best way of achieving any of the candidate objectives. Instead of naively trusting and learning from every human interaction, we propose robots learn conservatively by reasoning in real time about how relevant the human's correction is for the robot's hypothesis space. We test our inference method in an experiment with human interaction data, and demonstrate that this alleviates unintended learning in an in-person user study with a 7DoF robot manipulator.

Modern CNN-based object detectors rely on bounding box regression and non-maximum suppression to localize objects. While the probabilities for class labels naturally reflect classification confidence, localization confidence is absent. This makes properly localized bounding boxes degenerate during iterative regression or even suppressed during NMS. In the paper we propose IoU-Net learning to predict the IoU between each detected bounding box and the matched ground-truth. The network acquires this confidence of localization, which improves the NMS procedure by preserving accurately localized bounding boxes. Furthermore, an optimization-based bounding box refinement method is proposed, where the predicted IoU is formulated as the objective. Extensive experiments on the MS-COCO dataset show the effectiveness of IoU-Net, as well as its compatibility with and adaptivity to several state-of-the-art object detectors.

Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested processes and study the dependence structures they induce. Dependence ranges between homogeneity, corresponding to full exchangeability, and maximum heterogeneity, corresponding to (unconditional) independence across samples. The popular nested Dirichlet process is shown to degenerate to the fully exchangeable case when there are ties across samples at the observed or latent level. To overcome this drawback, inherent to nesting general discrete random measures, we introduce a novel class of latent nested processes. These are obtained by adding common and group-specific completely random measures and, then, normalising to yield dependent random probability measures. We provide results on the partition distributions induced by latent nested processes, and develop an Markov Chain Monte Carlo sampler for Bayesian inferences. A test for distributional homogeneity across groups is obtained as a by product. The results and their inferential implications are showcased on synthetic and real data.