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We describe a (nonparametric) prediction algorithm for spatial data, based on a canonical factorization of the spectral density function. We provide theoretical results showing that the predictor has desirable asymptotic properties. Finite sample performance is assessed in a Monte Carlo study that also compares our algorithm to a rival nonparametric method based on the infinite AR representation of the dynamics of the data. Finally, we apply our methodology to predict house prices in Los Angeles.

We consider a potential outcomes model in which interference may be present between any two units but the extent of interference diminishes with spatial distance. The causal estimand is the global average treatment effect, which compares counterfactual outcomes when all units are treated to outcomes when none are. We study a class of designs in which space is partitioned into clusters that are randomized into treatment and control. For each design, we estimate the treatment effect using a Horovitz-Thompson estimator that compares the average outcomes of units with all neighbors treated to units with no neighbors treated, where the neighborhood radius is of the same order as the cluster size dictated by the design. We derive the estimator's rate of convergence as a function of the design and degree of interference and use this to obtain estimator-design pairs in this class that achieve near-optimal rates of convergence under relatively minimal assumptions on interference. We prove that the estimators are asymptotically normal and provide a variance estimator. Finally, we discuss practical implementation of the designs by partitioning space using clustering algorithms.

In this paper, I propose a general algorithm for multiple change point analysis via multivariate distribution-free nonparametric testing based on the concept of ranks that are defined by measure transportation. Multivariate ranks and the usual one-dimensional ranks both share an important property: they are both distribution-free. This finding allows for the creation of nonparametric tests that are distribution-free under the null hypothesis. This method has applications in a variety of fields, and in this paper I implement this algorithm to a microarray dataset for individuals with bladder tumors, an ECoG snapshot for a patient with epilepsy, and in the context of trajectories of CASI scores by education level and dementia status. Each change point denotes a shift in the rate of change of Cognitive Abilities score over years, indicating the existence of preclinical dementia. Here I will estimate the number of change points and each of their locations within a multivariate series of time-ordered observations. This paper will examine the multiple change point question in a broad setting in which the observed distributions and number of change points are unspecified, rather than assume the time series observations follow a parametric model or there is one change point, as many works in this area assume. The objective here is to create an algorithm for change point detection while making as few assumptions about the dataset as possible. Presented are the theoretical properties of this new algorithm and the conditions under which the approximate number of change points and their locations can be estimated. This algorithm has also been successfully implemented in the R package recp, which is available on GitHub. A section of this paper is dedicated to the execution of this procedure, as well as the use of the recp package.

With the increasing complexity of the production process, the diversity of data types contributes to the urgency of developing the network monitoring technology. This paper mainly focuses on an online algorithm to detect the serially correlated directed network robustly and sensitively. Firstly, a transition probability matrix is considered here to overcome the double correlation of primary data. Furthermore, since the sum of each row of the transition probability matrix is one, it also standardizes data that facilitates subsequent modeling. Then we extend the spring-length-based method to the multivariate case and propose an adaptive cumulative sum (CUSUM) control chart on the strength of a weighted statistic to monitor directed networks. The novel approach only assumes that the process observation is associated with nearby points without any parametric time series models, which should be coincided with the fact. Simulation results and a real example of metro transportation demonstrate the superiority of our design.

In clinical research, the effect of a treatment or intervention is widely assessed through clinical importance, instead of statistical significance. In this paper, we propose a principled statistical inference framework to learning the minimal clinically important difference (MCID), a vital concept in assessing clinical importance. We formulate the scientific question into a novel statistical learning problem, develop an efficient algorithm for parameter estimation, and establish the asymptotic theory for the proposed estimator. We conduct comprehensive simulation studies to examine the finite sample performance of the proposed method. We also re-analyze the ChAMP (Chondral Lesions And Meniscus Procedures) trial, where the primary outcome is the patient-reported pain score and the ultimate goal is to determine whether there exists a significant difference in post-operative knee pain between patients undergoing debridement versus observation of chondral lesions during the surgery. Some previous analysis of this trial exhibited that the effect of debriding the chondral lesions does not reach a statistical significance. Our analysis reinforces this conclusion that the effect of debriding the chondral lesions is not only statistically non-significant, but also clinically un-important.

The first step towards investigating the effectiveness of a treatment is to split the population into the control and the treatment groups, then compare the average responses of the two groups to the treatment. In order to ensure that the difference in the two groups is only caused by the treatment, it is crucial for the control and the treatment groups to have similar statistics. The validity and reliability of trials are determined by the similarity of two groups' statistics. Covariate balancing methods increase the similarity between the distributions of the two groups' covariates. However, often in practice, there are not enough samples to accurately estimate the groups' covariate distributions. In this paper, we empirically show that covariate balancing with the standardized means difference covariate balancing measure is susceptible to adversarial treatment assignments in limited population sizes. Adversarial treatment assignments are those admitted by the covariate balance measure, but result in large ATE estimation errors. To support this argument, we provide an optimization-based algorithm, namely Adversarial Treatment ASsignment in TREatment Effect Trials (ATASTREET), to find the adversarial treatment assignments for the IHDP-1000 dataset.

The inference of Neural Networks is usually restricted by the resources (e.g., computing power, memory, bandwidth) on edge devices. In addition to improving the hardware design and deploying efficient models, it is possible to aggregate the computing power of many devices to enable the machine learning models. In this paper, we proposed a novel method of exploiting model parallelism to separate a neural network for distributed inferences. To achieve a better balance between communication latency, computation latency, and performance, we adopt neural architecture search (NAS) to search for the best transmission policy and reduce the amount of communication. The best model we found decreases by 86.6% of the amount of data transmission compared to the baseline and does not impact performance much. Under proper specifications of devices and configurations of models, our experiments show that the inference of large neural networks on edge clusters can be distributed and accelerated, which provides a new solution for the deployment of intelligent applications in the internet of things (IoT).

Deep neural network architectures have traditionally been designed and explored with human expertise in a long-lasting trial-and-error process. This process requires huge amount of time, expertise, and resources. To address this tedious problem, we propose a novel algorithm to optimally find hyperparameters of a deep network architecture automatically. We specifically focus on designing neural architectures for medical image segmentation task. Our proposed method is based on a policy gradient reinforcement learning for which the reward function is assigned a segmentation evaluation utility (i.e., dice index). We show the efficacy of the proposed method with its low computational cost in comparison with the state-of-the-art medical image segmentation networks. We also present a new architecture design, a densely connected encoder-decoder CNN, as a strong baseline architecture to apply the proposed hyperparameter search algorithm. We apply the proposed algorithm to each layer of the baseline architectures. As an application, we train the proposed system on cine cardiac MR images from Automated Cardiac Diagnosis Challenge (ACDC) MICCAI 2017. Starting from a baseline segmentation architecture, the resulting network architecture obtains the state-of-the-art results in accuracy without performing any trial-and-error based architecture design approaches or close supervision of the hyperparameters changes.

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.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.