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With continuous outcomes, the average causal effect is typically defined using a contrast of expected potential outcomes. However, in the presence of skewed outcome data, the expectation may no longer be meaningful. In practice the typical approach is to either "ignore or transform" - ignore the skewness altogether or transform the outcome to obtain a more symmetric distribution, although neither approach is entirely satisfactory. Alternatively the causal effect can be redefined as a contrast of median potential outcomes, yet discussion of confounding-adjustment methods to estimate this parameter is limited. In this study we described and compared confounding-adjustment methods to address this gap. The methods considered were multivariable quantile regression, an inverse probability weighted (IPW) estimator, weighted quantile regression and two little-known implementations of g-computation for this problem. Motivated by a cohort investigation in the Longitudinal Study of Australian Children, we conducted a simulation study that found the IPW estimator, weighted quantile regression and g-computation implementations minimised bias when the relevant models were correctly specified, with g-computation additionally minimising the variance. These methods provide appealing alternatives to the common "ignore or transform" approach and multivariable quantile regression, enhancing our capability to obtain meaningful causal effect estimates with skewed outcome data.

Causal inference on populations embedded in social networks poses technical challenges, since the typical no interference assumption may no longer hold. For instance, in the context of social research, the outcome of a study unit will likely be affected by an intervention or treatment received by close neighbors. While inverse probability-of-treatment weighted (IPW) estimators have been developed for this setting, they are often highly inefficient. In this work, we assume that the network is a union of disjoint components and propose doubly robust (DR) estimators combining models for treatment and outcome that are consistent and asymptotically normal if either model is correctly specified. We present empirical results that illustrate the DR property and the efficiency gain of DR over IPW estimators when both the outcome and treatment models are correctly specified. Simulations are conducted for networks with equal and unequal component sizes and outcome data with and without a multilevel structure. We apply these methods in an illustrative analysis using the Add Health network, examining the impact of maternal college education on adolescent school performance, both direct and indirect.

Network anomaly detection is a very relevant research area nowadays, especially due to its multiple applications in the field of network security. The boost of new models based on variational autoencoders and generative adversarial networks has motivated a reevaluation of traditional techniques for anomaly detection. It is, however, essential to be able to understand these new models from the perspective of the experience attained from years of evaluating network security data for anomaly detection. In this paper, we revisit anomaly detection techniques based on PCA from a probabilistic generative model point of view, and contribute a mathematical model that relates them. Specifically, we start with the probabilistic PCA model and explain its connection to the Multivariate Statistical Network Monitoring (MSNM) framework. MSNM was recently successfully proposed as a means of incorporating industrial process anomaly detection experience into the field of networking. We have evaluated the mathematical model using two different datasets. The first, a synthetic dataset created to better understand the analysis proposed, and the second, UGR'16, is a specifically designed real-traffic dataset for network security anomaly detection. We have drawn conclusions that we consider to be useful when applying generative models to network security detection.

Economists frequently estimate average treatment effects (ATEs) for transformations of the outcome that are well-defined at zero but behave like $\log(y)$ when $y$ is large (e.g., $\log(1+y)$, $\mathrm{arcsinh}(y)$). We show that these ATEs depend arbitrarily on the units of the outcome, and thus cannot be interpreted as percentage effects. Moreover, we prove that when the outcome can equal zero, there is no parameter of the form $E_P[g(Y(1),Y(0))]$ that is point-identified and unit-invariant. We discuss sensible alternative target parameters for settings with zero-valued outcomes that relax at least one of these requirements.

Offline reinforcement learning is important in domains such as medicine, economics, and e-commerce where online experimentation is costly, dangerous or unethical, and where the true model is unknown. However, most methods assume all covariates used in the behavior policy's action decisions are observed. This untestable assumption may be incorrect. We study robust policy evaluation and policy optimization in the presence of unobserved confounders. We assume the extent of possible unobserved confounding can be bounded by a sensitivity model, and that the unobserved confounders are sequentially exogenous. We propose and analyze an (orthogonalized) robust fitted-Q-iteration that uses closed-form solutions of the robust Bellman operator to derive a loss minimization problem for the robust Q function. Our algorithm enjoys the computational ease of fitted-Q-iteration and statistical improvements (reduced dependence on quantile estimation error) from orthogonalization. We provide sample complexity bounds, insights, and show effectiveness in simulations.

In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an endpoint and are colored differently. Equivalently, the goal can also be described as assigning colors to the vertices in a way that fits the edge-coloring as well as possible. As this problem is NP-hard, we build on previous work by studying its parameterized complexity. We give a $2^{\mathcal O(k)} \cdot n^{\mathcal O(1)}$-time algorithm where $k$ is the number of edges to be selected and $n$ the number of vertices. We also prove the existence of a problem kernel of size $\mathcal O(k^{5/2} )$, resolving an open problem posed in the literature. We consider parameters that are smaller than $k$, the number of edges to be selected, and $r$, the number of edges that can be deleted. Such smaller parameters are obtained by considering the difference between $k$ or $r$ and some lower bound on these values. We give both algorithms and lower bounds for Colored Clustering with such parameterizations. Finally, we settle the parameterized complexity of Colored Clustering with respect to structural graph parameters by showing that it is $W[1]$-hard with respect to both vertex cover number and tree-cut width, but fixed-parameter tractable with respect to slim tree-cut width.

The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various applications such as MRI, solution of PDEs, etc., are interested in the inverse problem, i.,e., computing Fourier coefficients from given nonequispaced data. In this paper we survey different kinds of approaches to tackle this problem. In contrast to iterative procedures, where multiple iteration steps are needed for computing a solution, we focus especially on so-called direct inversion methods. We review density compensation techniques and introduce a new scheme that leads to an exact reconstruction for trigonometric polynomials. In addition, we consider a matrix optimization approach using Frobenius norm minimization to obtain an inverse NFFT.

Hierarchical Clustering is a popular unsupervised machine learning method with decades of history and numerous applications. We initiate the study of differentially private approximation algorithms for hierarchical clustering under the rigorous framework introduced by (Dasgupta, 2016). We show strong lower bounds for the problem: that any $\epsilon$-DP algorithm must exhibit $O(|V|^2/ \epsilon)$-additive error for an input dataset $V$. Then, we exhibit a polynomial-time approximation algorithm with $O(|V|^{2.5}/ \epsilon)$-additive error, and an exponential-time algorithm that meets the lower bound. To overcome the lower bound, we focus on the stochastic block model, a popular model of graphs, and, with a separation assumption on the blocks, propose a private $1+o(1)$ approximation algorithm which also recovers the blocks exactly. Finally, we perform an empirical study of our algorithms and validate their performance.

Analyzing observational data from multiple sources can be useful for increasing statistical power to detect a treatment effect; however, practical constraints such as privacy considerations may restrict individual-level information sharing across data sets. This paper develops federated methods that only utilize summary-level information from heterogeneous data sets. Our federated methods provide doubly-robust point estimates of treatment effects as well as variance estimates. We derive the asymptotic distributions of our federated estimators, which are shown to be asymptotically equivalent to the corresponding estimators from the combined, individual-level data. We show that to achieve these properties, federated methods should be adjusted based on conditions such as whether models are correctly specified and stable across heterogeneous data sets.

The prevalence of networked sensors and actuators in many real-world systems such as smart buildings, factories, power plants, and data centers generate substantial amounts of multivariate time series data for these systems. The rich sensor data can be continuously monitored for intrusion events through anomaly detection. However, conventional threshold-based anomaly detection methods are inadequate due to the dynamic complexities of these systems, while supervised machine learning methods are unable to exploit the large amounts of data due to the lack of labeled data. On the other hand, current unsupervised machine learning approaches have not fully exploited the spatial-temporal correlation and other dependencies amongst the multiple variables (sensors/actuators) in the system for detecting anomalies. In this work, we propose an unsupervised multivariate anomaly detection method based on Generative Adversarial Networks (GANs). Instead of treating each data stream independently, our proposed MAD-GAN framework considers the entire variable set concurrently to capture the latent interactions amongst the variables. We also fully exploit both the generator and discriminator produced by the GAN, using a novel anomaly score called DR-score to detect anomalies by discrimination and reconstruction. We have tested our proposed MAD-GAN using two recent datasets collected from real-world CPS: the Secure Water Treatment (SWaT) and the Water Distribution (WADI) datasets. Our experimental results showed that the proposed MAD-GAN is effective in reporting anomalies caused by various cyber-intrusions compared in these complex real-world systems.