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Debiased machine learning is a meta algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals (i.e. scalar summaries) of machine learning algorithms. For example, an analyst may desire the confidence interval for a treatment effect estimated with a neural network. We provide a nonasymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm that satisfies a few simple, interpretable conditions. Formally, we prove consistency, Gaussian approximation, and semiparametric efficiency by finite sample arguments. The rate of convergence is $n^{-1/2}$ for global functionals, and it degrades gracefully for local functionals. Our results culminate in a simple set of conditions that an analyst can use to translate modern learning theory rates into traditional statistical inference. The conditions reveal a general double robustness property for ill posed inverse problems.

When combining data from multiple sources, inconsistent data complicates the production of a coherent result. In this paper, we introduce a new type of constraints called edit rules under a partial key (EPKs). These constraints can model inconsistencies both within and between sources, but in a loosely-coupled matter. We show that we can adapt the well-known set cover methodology to the setting of EPKs and this yields an efficient algorithm to find minimal cost repairs of sources. This algorithm is implemented in a repair engine called Parker. Empirical results show that Parker is several orders of magnitude faster than state-of-the-art repair tools. At the same time, the quality of the repairs in terms of $F_1$-score ranges from comparable to better compared to these tools.

Probabilistic databases (PDBs) model uncertainty in data in a quantitative way. In the established formal framework, probabilistic (relational) databases are finite probability spaces over relational database instances. This finiteness can clash with intuitive query behavior (Ceylan et al., KR 2016), and with application scenarios that are better modeled by continuous probability distributions (Dalvi et al., CACM 2009). We formally introduced infinite PDBs in (Grohe and Lindner, PODS 2019) with a primary focus on countably infinite spaces. However, an extension beyond countable probability spaces raises nontrivial foundational issues concerned with the measurability of events and queries and ultimately with the question whether queries have a well-defined semantics. We argue that finite point processes are an appropriate model from probability theory for dealing with general probabilistic databases. This allows us to construct suitable (uncountable) probability spaces of database instances in a systematic way. Our main technical results are measurability statements for relational algebra queries as well as aggregate queries and Datalog queries.

We consider the problems of exploration and point-goal navigation in previously unseen environments, where the spatial complexity of indoor scenes and partial observability constitute these tasks challenging. We argue that learning occupancy priors over indoor maps provides significant advantages towards addressing these problems. To this end, we present a novel planning framework that first learns to generate occupancy maps beyond the field-of-view of the agent, and second leverages the model uncertainty over the generated areas to formulate path selection policies for each task of interest. For point-goal navigation the policy chooses paths with an upper confidence bound policy for efficient and traversable paths, while for exploration the policy maximizes model uncertainty over candidate paths. We perform experiments in the visually realistic environments of Matterport3D using the Habitat simulator and demonstrate: 1) Improved results on exploration and map quality metrics over competitive methods, and 2) The effectiveness of our planning module when paired with the state-of-the-art DD-PPO method for the point-goal navigation task.

Deploying reconfigurable intelligent surface (RIS) to enhance wireless transmission is a promising approach. In this paper, we investigate large-scale multi-RIS-assisted multi-cell systems, where multiple RISs are deployed in each cell. Different from the full-buffer scenario, the mutual interference in our system is not known a priori, and for this reason we apply the load coupling model to analyze this system. The objective is to minimize the total resource consumption subject to user demand requirement by optimizing the reflection coefficients in the cells. The cells are highly coupled and the overall problem is non-convex. To tackle this, we first investigate the single-cell case with given interference, and propose a low-complexity algorithm based on the Majorization-Minimization method to obtain a locally optimal solution. Then, we embed this algorithm into an algorithmic framework for the overall multi-cell problem, and prove its feasibility and convergence to a solution that is at least locally optimal. Simulation results demonstrate the benefit of RIS in time-frequency resource utilization in the multi-cell system.

We adapt recent tools developed for the analysis of Stochastic Gradient Descent (SGD) in non-convex optimization to obtain convergence and sample complexity guarantees for the vanilla policy gradient (PG). Our only assumptions are that the expected return is smooth w.r.t. the policy parameters, that its $H$-step truncated gradient is close to the exact gradient, and a certain ABC assumption. This assumption requires the second moment of the estimated gradient to be bounded by $A \geq 0$ times the suboptimality gap, $B \geq 0$ times the norm of the full batch gradient and an additive constant $C \geq 0$, or any combination of aforementioned. We show that the ABC assumption is more general than the commonly used assumptions on the policy space to prove convergence to a stationary point. We provide a single convergence theorem that recovers the $\widetilde{\mathcal{O}}(\epsilon^{-4})$ sample complexity of PG. Our results also affords greater flexibility in the choice of hyper parameters such as the step size and places no restriction on the batch size $m$, including the single trajectory case (i.e., $m=1$). We then instantiate our theorem in different settings, where we both recover existing results and obtained improved sample complexity, e.g., for convergence to the global optimum for Fisher-non-degenerated parameterized policies.

In this paper we address the problem of constructing $G^2$ planar Pythagorean--hodograph (PH) spline curves, that interpolate points, tangent directions and curvatures, and have prescribed arc-length. The interpolation scheme is completely local. Each spline segment is defined as a PH biarc curve of degree $7$, which results in having a closed form solution of the $G^2$ interpolation equations depending on four free parameters. By fixing two of them to zero, it is proven that the length constraint can be satisfied for any data and any chosen ratio between the two boundary tangents. Length interpolation equation reduces to one algebraic equation with four solutions in general. To select the best one, the value of the bending energy is observed. Several numerical examples are provided to illustrate the obtained theoretical results and to numerically confirm that the approximation order is $5$.

Many descent methods for multiobjective optimization problems have been developed in recent years. In 2000, the steepest descent method was proposed for differentiable multiobjective optimization problems. Afterward, the proximal gradient method, which can solve composite problems, was also considered. However, the accelerated versions are not sufficiently studied. In this paper, we propose a multiobjective accelerated proximal gradient algorithm, in which we solve subproblems with terms that only appear in the multiobjective case. We also show the proposed method's global convergence rate ($O(1/k^2)$) under reasonable assumptions, using a merit function to measure the complexity. Moreover, we present an efficient way to solve the subproblem via its dual, and we confirm the validity of the proposed method through preliminary numerical experiments.

In this work, we investigate the different sensing schemes for the detection of four targets as observed through a vector Poisson and Gaussian channels when the sensing time resource is limited and the source signals can be observed through a variety of sum combinations during that fixed time. For this purpose, we can maximize the mutual information or the detection probability with respect to the time allocated to different sum combinations, for a given total fixed time. It is observed that for both Poisson and Gaussian channels; mutual information and Bayes risk with $0-1$ cost are not necessarily consistent with each other. Concavity of mutual information between input and output, for certain sensing schemes, in Poisson channel and Gaussian channel is shown to be concave w.r.t given times as linear time constraint is imposed. No optimal sensing scheme for any of the two channels is investigated in this work.

This paper considers the integrated problem of quay crane assignment, quay crane scheduling, yard location assignment, and vehicle dispatching operations at a container terminal. The main objective is to minimize vessel turnover times and maximize the terminal throughput, which are key economic drivers in terminal operations. Due to their computational complexities, these problems are not optimized jointly in existing work. This paper revisits this limitation and proposes Mixed Integer Programming (MIP) and Constraint Programming (CP) models for the integrated problem, under some realistic assumptions. Experimental results show that the MIP formulation can only solve small instances, while the CP model finds optimal solutions in reasonable times for realistic instances derived from actual container terminal operations.