The chi-square statistic is a useful tool for understanding the relationship between two categorical variables. For the sake of example, let's say you work for a tech company that has rolled out a new product and you want to assess the relationship between this product and customer churn. In the age of data, tech or otherwise, many companies undergo to risk of taking evidence that is either anecdotal or perhaps a high level visualization to indicate certainty of a given relationship. The chi-square statistic gives us a way to quantify and assess the strength of a given pair of categorical variables. Let's explore chi-square from this lens of customer churn.

Research published recently by CSE investigators can make training machine learning (ML) models fairer and faster. With a tool called AlloX, Prof. Mosharaf Chowdhury and a team from Stony Brook University developed a new way to fairly schedule high volumes of ML jobs in data centers that make use of multiple different types of computing hardware, like CPUs, GPUs, and specialized accelerators. As these so-called heterogeneous clusters grow to be the norm, fair scheduling systems like AlloX will become essential to their efficient operation. This project is a new step for Chowdhury's lab, which has recently published a number of tools aimed at speeding up the process of training and testing ML models. Their past projects Tiresias and Salus sped up GPU resource sharing at multiple scales: both within a single GPU (Salus) and across many GPUs in a cluster (Tiresias).

While the gold standard for measuring airflow is to use a spirometer with an occlusive seal, this is not practical for ambulatory monitoring of patients. Advances in sensor technology have made measurement of motion of the thorax and abdomen feasible with small inexpensive devices, but estimation of airflow from these time series is challenging. We propose to use the nonlinear-type time-frequency analysis tool, synchrosqueezing transform, to properly represent the thoracic and abdominal movement signals as the features, which are used to recover the airflow by the locally stationary Gaussian process. We show that, using a dataset that contains respiratory signals under normal sleep conditions, an accurate prediction can be achieved by fitting the proposed model in the feature space both in the intra-and inter-subject setups. We also apply our method to a more challenging case, where subjects under general anesthesia underwent transitions from pressure support to unassisted ventilation to further demonstrate the utility of the proposed method. Keyword: high-frequency physiological data; Gaussian process regression; time-frequency analysis; synchrosqueezing transform.

This paper introduces link functions for transforming one probability distribution to another such that the Kullback-Leibler and R\'enyi divergences between the two distributions are symmetric. Two general classes of link models are proposed. The first model links two survival functions and is applicable to models such as the proportional odds and change point, which are used in survival analysis and reliability modeling. A prototype application involving the proportional odds model demonstrates advantages of symmetric divergence measures over asymmetric measures for assessing the efficacy of features and for model averaging purposes. The advantages include providing unique ranks for models and unique information weights for model averaging with one-half as much computation requirement of asymmetric divergences. The second model links two cumulative probability distribution functions. This model produces a generalized location model which are continuous counterparts of the binary probability models such as probit and logit models. Examples include the generalized probit and logit models which have appeared in the survival analysis literature, and a generalized Laplace model and a generalized Student-$t$ model, which are survival time models corresponding to the respective binary probability models. Lastly, extensions to symmetric divergence between survival functions and conditions for copula dependence information are presented.

We present a novel machine learning architecture that uses the exponential of a single input-dependent matrix as its only nonlinearity. The mathematical simplicity of this architecture allows a detailed analysis of its behaviour, providing robustness guarantees via Lipschitz bounds. Despite its simplicity, a single matrix exponential layer already provides universal approximation properties and can learn fundamental functions of the input, such as periodic functions or multivariate polynomials. This architecture outperforms other general-purpose architectures on benchmark problems, including CIFAR-10, using substantially fewer parameters.

The Alternating Direction Method of Multipliers (ADMM) and its distributed version have been widely used in machine learning. In the iterations of ADMM, model updates using local private data and model exchanges among agents impose critical privacy concerns. Despite some pioneering works to relieve such concerns, differentially private ADMM still confronts many research challenges. For example, the guarantee of differential privacy (DP) relies on the premise that the optimality of each local problem can be perfectly attained in each ADMM iteration, which may never happen in practice. The model trained by DP ADMM may have low prediction accuracy. In this paper, we address these concerns by proposing a novel (Improved) Plausible differentially Private ADMM algorithm, called PP-ADMM and IPP-ADMM. In PP-ADMM, each agent approximately solves a perturbed optimization problem that is formulated from its local private data in an iteration, and then perturbs the approximate solution with Gaussian noise to provide the DP guarantee. To further improve the model accuracy and convergence, an improved version IPP-ADMM adopts sparse vector technique (SVT) to determine if an agent should update its neighbors with the current perturbed solution. The agent calculates the difference of the current solution from that in the last iteration, and if the difference is larger than a threshold, it passes the solution to neighbors; or otherwise the solution will be discarded. Moreover, we propose to track the total privacy loss under the zero-concentrated DP (zCDP) and provide a generalization performance analysis. Experiments on real-world datasets demonstrate that under the same privacy guarantee, the proposed algorithms are superior to the state of the art in terms of model accuracy and convergence rate.

In this paper we present a novel algorithm to study the evolution of credit risk across complex multilayer networks. Pagerank-like algorithms allow for the propagation of an influence variable across single networks, and allow quantifying the risk single entities (nodes) are subject to given the connection they have to other nodes in the network. Multilayer networks, on the other hand, are networks where subset of nodes can be associated to a unique set (layer), and where edges connect elements either intra or inter networks. Our personalized PageRank algorithm for multilayer networks allows for quantifying how credit risk evolves across time and propagates through these networks. By using bipartite networks in each layer, we can quantify the risk of various components, not only the loans. We test our method in an agricultural lending dataset, and our results show how default risk is a challenging phenomenon that propagates and evolves through the network across time.

Whether the goal is to estimate the number of people that live in a congressional district, to estimate the number of individuals that have died in an armed conflict, or to disambiguate individual authors using bibliographic data, all these applications have a common theme - integrating information from multiple sources. Before such questions can be answered, databases must be cleaned and integrated in a systematic and accurate way, commonly known as record linkage, de-duplication, or entity resolution. In this article, we review motivational applications and seminal papers that have led to the growth of this area. Specifically, we review the foundational work that began in the 1940's and 50's that have led to modern probabilistic record linkage. We review clustering approaches to entity resolution, semi- and fully supervised methods, and canonicalization, which are being used throughout industry and academia in applications such as human rights, official statistics, medicine, citation networks, among others. Finally, we discuss current research topics of practical importance.

While the traditional viewpoint in machine learning and statistics assumes training and testing samples come from the same population, practice belies this fiction. One strategy---coming from robust statistics and optimization---is thus to build a model robust to distributional perturbations. In this paper, we take a different approach to describe procedures for robust predictive inference, where a model provides uncertainty estimates on its predictions rather than point predictions. We present a method that produces prediction sets (almost exactly) giving the right coverage level for any test distribution in an $f$-divergence ball around the training population. The method, based on conformal inference, achieves (nearly) valid coverage in finite samples, under only the condition that the training data be exchangeable. An essential component of our methodology is to estimate the amount of expected future data shift and build robustness to it; we develop estimators and prove their consistency for protection and validity of uncertainty estimates under shifts. By experimenting on several large-scale benchmark datasets, including Recht et al.'s CIFAR-v4 and ImageNet-V2 datasets, we provide complementary empirical results that highlight the importance of robust predictive validity.

In this paper, we study decentralized online stochastic non-convex optimization over a network of nodes. Integrating a technique called gradient tracking in decentralized stochastic gradient descent (DSGD), we show that the resulting algorithm, GT-DSGD, exhibits several important characteristics towards minimizing a sum of smooth non-convex functions. The main results of this paper can be divided into two categories: (1) For general smooth non-convex functions, we establish a non-asymptotic characterization of GT-DSGD and derive the conditions under which it achieves network-independent performance and matches centralized minibatch SGD. In comparison, the existing results suggest that the performance of GT-DSGD is always network-dependent and is therefore strictly worse than that of centralized minibatch SGD. (2) When the global function additionally satisfies the Polyak-Lojasiewics condition, we derive the exponential stability range for GT-DSGD under a constant step-size up to a steady-state error. Under stochastic approximation step-sizes, we establish, for the first time, the optimal global sublinear convergence rate on almost every sample path, in addition to the convergence rate in mean. Since strongly convex functions are a special case of this class of problems, our results are not only immediately applicable but also improve the currently known best convergence rates and their dependence on problem parameters.