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Health disparity research often evaluates health outcomes across demographic subgroups. Multilevel regression and poststratification (MRP) is a popular approach for small subgroup estimation due to its ability to stabilize estimates by fitting multilevel models and to adjust for selection bias by poststratifying on auxiliary variables, which are population characteristics predictive of the analytic outcome. However, the granularity and quality of the estimates produced by MRP are limited by the availability of the auxiliary variables' joint distribution; data analysts often only have access to the marginal distributions. To overcome this limitation, we embed the estimation of population cell counts needed for poststratification into the MRP workflow: embedded MRP (EMRP). Under EMRP, we generate synthetic populations of the auxiliary variables before implementing MRP. All sources of estimation uncertainty are propagated with a fully Bayesian framework. Through simulation studies, we compare different methods and demonstrate EMRP's improvements over alternatives on the bias-variance tradeoff to yield valid subpopulation inferences of interest. As an illustration, we apply EMRP to the Longitudinal Survey of Wellbeing and estimate food insecurity prevalence among vulnerable groups in New York City. We find that all EMRP estimators can correct for the bias in classical MRP while maintaining lower standard errors and narrower confidence intervals than directly imputing with the WFPBB and design-based estimates. Performances from the EMRP estimators do not differ substantially from each other, though we would generally recommend the WFPBB-MRP for its consistently high coverage rates.

Classical methods for quantile regression fail in cases where the quantile of interest is extreme and only few or no training data points exceed it. Asymptotic results from extreme value theory can be used to extrapolate beyond the range of the data, and several approaches exist that use linear regression, kernel methods or generalized additive models. Most of these methods break down if the predictor space has more than a few dimensions or if the regression function of extreme quantiles is complex. We propose a method for extreme quantile regression that combines the flexibility of random forests with the theory of extrapolation. Our extremal random forest (ERF) estimates the parameters of a generalized Pareto distribution, conditional on the predictor vector, by maximizing a local likelihood with weights extracted from a quantile random forest. We penalize the shape parameter in this likelihood to regularize its variability in the predictor space. Under general domain of attraction conditions, we show consistency of the estimated parameters in both the unpenalized and penalized case. Simulation studies show that our ERF outperforms both classical quantile regression methods and existing regression approaches from extreme value theory. We apply our methodology to extreme quantile prediction for U.S. wage data.

This paper is concerned with the optimal allocation of detection resources (sensors) to mitigate multi-stage attacks, in the presence of the defender's uncertainty in the attacker's intention. We model the attack planning problem using a Markov decision process and characterize the uncertainty in the attacker's intention using a finite set of reward functions -- each reward represents a type of the attacker. Based on this modeling framework, we employ the paradigm of the worst-case absolute regret minimization from robust game theory and develop mixed-integer linear program (MILP) formulations for solving the worst-case regret minimizing sensor allocation strategies for two classes of attack-defend interactions: one where the defender and attacker engage in a zero-sum game, and another where they engage in a non-zero-sum game. We demonstrate the effectiveness of our framework using a stochastic gridworld example.

Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by learning the inherent structure of action-wise similar MDP to appropriately balance the performance degradation versus sample/computational complexity. In particular, we partition the action spaces into multiple groups based on the similarity in transition distribution and reward function, and build a linear decomposition model to capture the difference between the intra-group transition kernel and the intra-group rewards. Both our theoretical analysis and experiments reveal a \emph{surprising and counter-intuitive result}: while a more refined grouping strategy can reduce the approximation error caused by treating actions in the same group as identical, it also leads to increased estimation error when the size of samples or the computation resources is limited. This finding highlights the grouping strategy as a new degree of freedom that can be optimized to minimize the overall performance loss. To address this issue, we formulate a general optimization problem for determining the optimal grouping strategy, which strikes a balance between performance loss and sample/computational complexity. We further propose a computationally efficient method for selecting a nearly-optimal grouping strategy, which maintains its computational complexity independent of the size of the action space.

Simultaneous localisation and mapping (SLAM) play a vital role in autonomous robotics. Robotic platforms are often resource-constrained, and this limitation motivates resource-efficient SLAM implementations. While sparse visual SLAM algorithms offer good accuracy for modest hardware requirements, even these more scalable sparse approaches face limitations when applied to large-scale and long-term scenarios. A contributing factor is that the point clouds resulting from SLAM are inefficient to use and contain significant redundancy. This paper proposes the use of subset selection algorithms to reduce the map produced by sparse visual SLAM algorithms. Information-theoretic techniques have been applied to simpler related problems before, but they do not scale if applied to the full visual SLAM problem. This paper proposes a number of novel information\hyp{}theoretic utility functions for map point selection and optimises these functions using greedy algorithms. The reduced maps are evaluated using practical data alongside an existing visual SLAM implementation (ORB-SLAM 2). Approximate selection techniques proposed in this paper achieve trajectory accuracy comparable to an offline baseline while being suitable for online use. These techniques enable the practical reduction of maps for visual SLAM with competitive trajectory accuracy. Results also demonstrate that SLAM front-end performance can significantly impact the performance of map point selection. This shows the importance of testing map point selection with a front-end implementation. To exploit this, this paper proposes an approach that includes a model of the front-end in the utility function when additional information is available. This approach outperforms alternatives on applicable datasets and highlights future research directions.

The storage, management, and application of massive spatio-temporal data are widely applied in various practical scenarios, including public safety. However, due to the unique spatio-temporal distribution characteristics of re-al-world data, most existing methods have limitations in terms of the spatio-temporal proximity of data and load balancing in distributed storage. There-fore, this paper proposes an efficient partitioning method of large-scale public safety spatio-temporal data based on information loss constraints (IFL-LSTP). The IFL-LSTP model specifically targets large-scale spatio-temporal point da-ta by combining the spatio-temporal partitioning module (STPM) with the graph partitioning module (GPM). This approach can significantly reduce the scale of data while maintaining the model's accuracy, in order to improve the partitioning efficiency. It can also ensure the load balancing of distributed storage while maintaining spatio-temporal proximity of the data partitioning results. This method provides a new solution for distributed storage of mas-sive spatio-temporal data. The experimental results on multiple real-world da-tasets demonstrate the effectiveness and superiority of IFL-LSTP.

A logical zonotope, which is a new set representation for binary vectors, is introduced in this paper. A logical zonotope is constructed by XOR-ing a binary vector with a combination of other binary vectors called generators. Such a zonotope can represent up to 2^n binary vectors using only n generators. It is shown that logical operations over sets of binary vectors can be performed on the zonotopes' generators and, thus, significantly reduce the computational complexity of various logical operations (e.g., XOR, NAND, AND, OR, and semi-tensor products). Similar to traditional zonotopes' role in the formal verification of dynamical systems over real vector spaces, logical zonotopes can be used to analyze discrete dynamical systems defined over binary vector spaces efficiently. We illustrate the approach and its ability to reduce the computational complexity in two use cases: (1) encryption key discovery of a linear feedback shift register and (2) safety verification of a road traffic intersection protocol.

We consider leader election in clique networks, where $n$ nodes are connected by point-to-point communication links. For the synchronous clique under simultaneous wake-up, i.e., where all nodes start executing the algorithm in round $1$, we show a tradeoff between the number of messages and the amount of time. More specifically, we show that any deterministic algorithm with a message complexity of $n f(n)$ requires $\Omega\left(\frac{\log n}{\log f(n)+1}\right)$ rounds, for $f(n) = \Omega(\log n)$. Our result holds even if the node IDs are chosen from a relatively small set of size $\Theta(n\log n)$, as we are able to avoid using Ramsey's theorem. We also give an upper bound that improves over the previously-best tradeoff. Our second contribution for the synchronous clique under simultaneous wake-up is to show that $\Omega(n\log n)$ is in fact a lower bound on the message complexity that holds for any deterministic algorithm with a termination time $T(n)$. We complement this result by giving a simple deterministic algorithm that achieves leader election in sublinear time while sending only $o(n\log n)$ messages, if the ID space is of at most linear size. We also show that Las Vegas algorithms (that never fail) require $\Theta(n)$ messages. For the synchronous clique under adversarial wake-up, we show that $\Omega(n^{3/2})$ is a tight lower bound for randomized $2$-round algorithms. Finally, we turn our attention to the asynchronous clique: Assuming adversarial wake-up, we give a randomized algorithm that achieves a message complexity of $O(n^{1 + 1/k})$ and an asynchronous time complexity of $k+8$. For simultaneous wake-up, we translate the deterministic tradeoff algorithm of Afek and Gafni to the asynchronous model, thus partially answering an open problem they pose.

Relation prediction for knowledge graphs aims at predicting missing relationships between entities. Despite the importance of inductive relation prediction, most previous works are limited to a transductive setting and cannot process previously unseen entities. The recent proposed subgraph-based relation reasoning models provided alternatives to predict links from the subgraph structure surrounding a candidate triplet inductively. However, we observe that these methods often neglect the directed nature of the extracted subgraph and weaken the role of relation information in the subgraph modeling. As a result, they fail to effectively handle the asymmetric/anti-symmetric triplets and produce insufficient embeddings for the target triplets. To this end, we introduce a \textbf{C}\textbf{o}mmunicative \textbf{M}essage \textbf{P}assing neural network for \textbf{I}nductive re\textbf{L}ation r\textbf{E}asoning, \textbf{CoMPILE}, that reasons over local directed subgraph structures and has a vigorous inductive bias to process entity-independent semantic relations. In contrast to existing models, CoMPILE strengthens the message interactions between edges and entitles through a communicative kernel and enables a sufficient flow of relation information. Moreover, we demonstrate that CoMPILE can naturally handle asymmetric/anti-symmetric relations without the need for explosively increasing the number of model parameters by extracting the directed enclosing subgraphs. Extensive experiments show substantial performance gains in comparison to state-of-the-art methods on commonly used benchmark datasets with variant inductive settings.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.