Learning causal structures from interventional data is a fundamental problem with broad applications across various fields. While many previous works have focused on recovering the entire causal graph, in practice, there are scenarios where learning only part of the causal graph suffices. This is called $targeted$ causal discovery. In our work, we focus on two such well-motivated problems: subset search and causal matching. We aim to minimize the number of interventions in both cases. Towards this, we introduce the $Meek~separator$, which is a subset of vertices that, when intervened, decomposes the remaining unoriented edges into smaller connected components. We then present an efficient algorithm to find Meek separators that are of small sizes. Such a procedure is helpful in designing various divide-and-conquer-based approaches. In particular, we propose two randomized algorithms that achieve logarithmic approximation for subset search and causal matching, respectively. Our results provide the first known average-case provable guarantees for both problems. We believe that this opens up possibilities to design near-optimal methods for many other targeted causal structure learning problems arising from various applications.
相關內容
Model counting, or counting the satisfying assignments of a Boolean formula, is a fundamental problem with diverse applications. Given #P-hardness of the problem, developing algorithms for approximate counting is an important research area. Building on the practical success of SAT-solvers, the focus has recently shifted from theory to practical implementations of approximate counting algorithms. This has brought to focus new challenges, such as the design of auditable approximate counters that not only provide an approximation of the model count, but also a certificate that a verifier with limited computational power can use to check if the count is indeed within the promised bounds of approximation. Towards generating certificates, we start by examining the best-known deterministic approximate counting algorithm that uses polynomially many calls to a $\Sigma_2^P$ oracle. We show that this can be audited via a $\Sigma_2^P$ oracle with the query constructed over $n^2 \log^2 n$ variables, where the original formula has $n$ variables. Since $n$ is often large, we ask if the count of variables in the certificate can be reduced -- a crucial question for potential implementation. We show that this is indeed possible with a tradeoff in the counting algorithm's complexity. Specifically, we develop new deterministic approximate counting algorithms that invoke a $\Sigma_3^P$ oracle, but can be certified using a $\Sigma_2^P$ oracle using certificates on far fewer variables: our final algorithm uses only $n \log n$ variables. Our study demonstrates that one can simplify auditing significantly if we allow the counting algorithm to access a slightly more powerful oracle. This shows for the first time how audit complexity can be traded for complexity of approximate counting.
In millimeter-wave (mmWave) cellular systems, reconfigurable intelligent surfaces (RISs) are foreseeably deployed with a large number of reflecting elements to achieve high beamforming gains. The large-sized RIS will make radio links fall in the near-field localization regime with spatial non-stationarity issues. Moreover, the discrete phase restriction on the RIS reflection coefficient incurs exponential complexity for discrete beamforming. It remains an open problem to find the optimal RIS reflection coefficient design in polynomial time. To address these issues, we propose a scalable partitioned-far-field protocol that considers both the near-filed non-stationarity and discrete beamforming. The protocol approximates near-field signal propagation using a partitioned-far-field representation to inherit the sparsity from the sophisticated far-field and facilitate the near-field localization scheme. To improve the theoretical localization performance, we propose a fast passive beamforming (FPB) algorithm that optimally solves the discrete RIS beamforming problem, reducing the search complexity from exponential order to linear order. Furthermore, by exploiting the partitioned structure of RIS, we introduce a two-stage coarse-to-fine localization algorithm that leverages both the time delay and angle information. Numerical results demonstrate that centimeter-level localization precision is achieved under medium and high signal-to-noise ratios (SNR), revealing that RISs can provide support for low-cost and high-precision localization in future cellular systems.
Many functions characterising physical systems are additively separable. This is the case, for instance, of mechanical Hamiltonian functions in physics, population growth equations in biology, and consumer preference and utility functions in economics. We consider the scenario in which a surrogate of a function is to be tested for additive separability. The detection that the surrogate is additively separable can be leveraged to improve further learning. Hence, it is beneficial to have the ability to test for such separability in surrogates. The mathematical approach is to test if the mixed partial derivative of the surrogate is zero; or empirically, lower than a threshold. We present and comparatively and empirically evaluate the eight methods to compute the mixed partial derivative of a surrogate function.
Uplift modeling is crucial in various applications ranging from marketing and policy-making to personalized recommendations. The main objective is to learn optimal treatment allocations for a heterogeneous population. A primary line of existing work modifies the loss function of the decision tree algorithm to identify cohorts with heterogeneous treatment effects. Another line of work estimates the individual treatment effects separately for the treatment group and the control group using off-the-shelf supervised learning algorithms. The former approach that directly models the heterogeneous treatment effect is known to outperform the latter in practice. However, the existing tree-based methods are mostly limited to a single treatment and a single control use case, except for a handful of extensions to multiple discrete treatments. In this paper, we propose a generalization of tree-based approaches to tackle multiple discrete and continuous-valued treatments. We focus on a generalization of the well-known causal tree algorithm due to its desirable statistical properties, but our generalization technique can be applied to other tree-based approaches as well. The efficacy of our proposed method is demonstrated using experiments and real data examples.
Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show that models of this structure in the category of matrices and natural numbers recover the traditional classical combinatorial objects, while models in the category of completely positive maps yield a new definition of quantum designs. We show that this generalizes both a previous notion of quantum designs given by Zauner and the traditional description of block designs. Furthermore, we demonstrate that there exists a functor which relates every categorical block design to a quantum one.
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.
Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.
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.
Generalization to out-of-distribution (OOD) data is a capability natural to humans yet challenging for machines to reproduce. This is because most learning algorithms strongly rely on the i.i.d.~assumption on source/target data, which is often violated in practice due to domain shift. Domain generalization (DG) aims to achieve OOD generalization by using only source data for model learning. Since first introduced in 2011, research in DG has made great progresses. In particular, intensive research in this topic has led to a broad spectrum of methodologies, e.g., those based on domain alignment, meta-learning, data augmentation, or ensemble learning, just to name a few; and has covered various vision applications such as object recognition, segmentation, action recognition, and person re-identification. In this paper, for the first time a comprehensive literature review is provided to summarize the developments in DG for computer vision over the past decade. Specifically, we first cover the background by formally defining DG and relating it to other research fields like domain adaptation and transfer learning. Second, we conduct a thorough review into existing methods and present a categorization based on their methodologies and motivations. Finally, we conclude this survey with insights and discussions on future research directions.
Knowledge graph completion aims to predict missing relations between entities in a knowledge graph. While many different methods have been proposed, there is a lack of a unifying framework that would lead to state-of-the-art results. Here we develop PathCon, a knowledge graph completion method that harnesses four novel insights to outperform existing methods. PathCon predicts relations between a pair of entities by: (1) Considering the Relational Context of each entity by capturing the relation types adjacent to the entity and modeled through a novel edge-based message passing scheme; (2) Considering the Relational Paths capturing all paths between the two entities; And, (3) adaptively integrating the Relational Context and Relational Path through a learnable attention mechanism. Importantly, (4) in contrast to conventional node-based representations, PathCon represents context and path only using the relation types, which makes it applicable in an inductive setting. Experimental results on knowledge graph benchmarks as well as our newly proposed dataset show that PathCon outperforms state-of-the-art knowledge graph completion methods by a large margin. Finally, PathCon is able to provide interpretable explanations by identifying relations that provide the context and paths that are important for a given predicted relation.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191