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The Causal Roadmap outlines a systematic approach to asking and answering questions of cause-and-effect: define quantity of interest, evaluate needed assumptions, conduct statistical estimation, and carefully interpret results. It is paramount that the algorithm for statistical estimation and inference be carefully pre-specified to optimize its expected performance for the specific real-data application. Simulations that realistically reflect the application, including key characteristics such as strong confounding and dependent or missing outcomes, can help us gain a better understanding of an estimator's applied performance. We illustrate this with two examples, using the Causal Roadmap and realistic simulations to inform estimator selection and full specification of the Statistical Analysis Plan. First, in an observational longitudinal study, outcome-blind simulations are used to inform nuisance parameter estimation and variance estimation for longitudinal targeted maximum likelihood estimation (TMLE). Second, in a cluster-randomized controlled trial with missing outcomes, treatment-blind simulations are used to ensure control for Type-I error in Two-Stage TMLE. In both examples, realistic simulations empower us to pre-specify an estimator that is expected to have strong finite sample performance and also yield quality-controlled computing code for the actual analysis. Together, this process helps to improve the rigor and reproducibility of our research.

Like the notion of computation via (strong) monads serves to classify various flavours of impurity, including exceptions, non-determinism, probability, local and global store, the notion of guardedness classifies well-behavedness of cycles in various settings. In its most general form, the guardedness discipline applies to general symmetric monoidal categories and further specializes to Cartesian and co-Cartesian categories, where it governs guarded recursion and guarded iteration respectively. Here, even more specifically, we deal with the semantics of call-by-value guarded iteration. It was shown by Levy, Power and Thielecke that call-by-value languages can be generally interpreted in Freyd categories, but in order to represent effectful function spaces, such a category must canonically arise from a strong monad. We generalize this fact by showing that representing guarded effectful function spaces calls for certain parametrized monads (in the sense of Uustalu). This provides a description of guardedness as an intrinsic categorical property of programs, complementing the existing description of guardedness as a predicate on a category.

Integer linear programming (ILP) models a wide range of practical combinatorial optimization problems and significantly impacts industry and management sectors. This work proposes new characterizations of ILP with the concept of boundary solutions. Motivated by the new characterizations, we develop a new local search algorithm Local-ILP, which is efficient for solving general ILP validated on a large heterogeneous problem dataset. We propose a new local search framework that switches between three modes, namely Search, Improve, and Restore modes. Two new operators are proposed, namely the tight move and the lift move operators, which are associated with appropriate scoring functions. Different modes apply different operators to realize different search strategies and the algorithm switches between three modes according to the current search state. Putting these together, we develop a local search ILP solver called Local-ILP. Experiments conducted on the MIPLIB dataset show the effectiveness of our algorithm in solving large-scale hard ILP problems. In the aspect of finding a good feasible solution quickly, Local-ILP is competitive and complementary to the state-of-the-art commercial solver Gurobi and significantly outperforms the state-of-the-art non-commercial solver SCIP. Moreover, our algorithm establishes new records for 6 MIPLIB open instances. The theoretical analysis of our algorithm is also presented, which shows our algorithm could avoid visiting unnecessary regions.

This paper intends to apply the sample-average-approximation (SAA) scheme to solve a system of stochastic equations (SSE), which has many applications in a variety of fields. The SAA is an effective paradigm to address risks and uncertainty in stochastic models from the perspective of Monte Carlo principle. Nonetheless, a numerical conflict arises from the sample size of SAA when one has to make a tradeoff between the accuracy of solutions and the computational cost. To alleviate this issue, we incorporate a gradually reinforced SAA scheme into a differentiable homotopy method and develop a gradually reinforced sample-average-approximation (GRSAA) differentiable homotopy method in this paper. By introducing a series of continuously differentiable functions of the homotopy parameter $t$ ranging between zero and one, we establish a differentiable homotopy system, which is able to gradually increase the sample size of SAA as $t$ descends from one to zero. The set of solutions to the homotopy system contains an everywhere smooth path, which starts from an arbitrary point and ends at a solution to the SAA with any desired accuracy. The GRSAA differentiable homotopy method serves as a bridge to link the gradually reinforced SAA scheme and a differentiable homotopy method and retains the nice property of global convergence the homotopy method possesses while greatly reducing the computational cost for attaining a desired solution to the original SSE. Several numerical experiments further confirm the effectiveness and efficiency of the proposed method.

In this paper, the energy-efficient unmanned aerial vehicle (UAV) swarm assisted mobile edge computing (MEC) with dynamic clustering and scheduling is studied. In the considered system model, UAVs are divided into multiple swarms, with each swarm consisting of a leader UAV and several follower UAVs to provide computing services to end-users. Unlike existing work, we allow UAVs to dynamically cluster into different swarms, i.e., each follower UAV can change its leader based on the time-varying spatial positions, updated application placement, etc. in a dynamic manner. Meanwhile, UAVs are required to dynamically schedule their energy replenishment, application placement, trajectory planning and task delegation. With the aim of maximizing the long-term energy efficiency of the UAV swarm assisted MEC system, a joint optimization problem of dynamic clustering and scheduling is formulated. Taking into account the underlying cooperation and competition among intelligent UAVs, we further reformulate this optimization problem as a combination of a series of strongly coupled multi-agent stochastic games, and then propose a novel reinforcement learning-based UAV swarm dynamic coordination (RLDC) algorithm for obtaining the equilibrium. Simulations are conducted to evaluate the performance of the RLDC algorithm and demonstrate its superiority over counterparts.

We derive and study time-uniform confidence spheres -- confidence sphere sequences (CSSs) -- which contain the mean of random vectors with high probability simultaneously across all sample sizes. Inspired by the original work of Catoni and Giulini, we unify and extend their analysis to cover both the sequential setting and to handle a variety of distributional assumptions. Our results include an empirical-Bernstein CSS for bounded random vectors (resulting in a novel empirical-Bernstein confidence interval with asymptotic width scaling proportionally to the true unknown variance), CSSs for sub-$\psi$ random vectors (which includes sub-gamma, sub-Poisson, and sub-exponential), and CSSs for heavy-tailed random vectors (two moments only). Finally, we provide two CSSs that are robust to contamination by Huber noise. The first is a robust version of our empirical-Bernstein CSS, and the second extends recent work in the univariate setting to heavy-tailed multivariate distributions.

The problem of substructure characteristic modes is reformulated using a scattering matrix-based formulation, generalizing subregion characteristic mode decomposition to arbitrary computational tools. It is shown that the scattering formulation is identical to the classical formulation based on the background Green's function for lossless systems. The scattering formulation, however, opens a variety of new subregion scenarios unavailable within previous formulations, including cases with lumped or wave ports or subregions in circuits. Thanks to its scattering nature, the formulation is solver-agnostic with the possibility to utilize an arbitrary full-wave method.

We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.

Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.