Optimal Treatment Regimes for Proximal Causal Learning

A common concern when a policymaker draws causal inferences from and makes decisions based on observational data is that the measured covariates are insufficiently rich to account for all sources of confounding, i.e., the standard no confoundedness assumption fails to hold. The recently proposed proximal causal inference framework shows that proxy variables that abound in real-life scenarios can be leveraged to identify causal effects and therefore facilitate decision-making. Building upon this line of work, we propose a novel optimal individualized treatment regime based on so-called outcome and treatment confounding bridges. We then show that the value function of this new optimal treatment regime is superior to that of existing ones in the literature. Theoretical guarantees, including identification, superiority, excess value bound, and consistency of the estimated regime, are established. Furthermore, we demonstrate the proposed optimal regime via numerical experiments and a real data application.Comment: NeurIPS 202

Relativistic Stochastic Dynamics I: Langevin Equation from Observer's Perspective

Two different versions of relativistic Langevin equation in generic curved spacetime background are constructed, both are manifestly general covariant. It is argued that, from the observer's point of view, the version which takes the proper time of the Brownian particle as evolution parameter contains some conceptual issues, while the one which makes use of the proper time of the observer is more physically sound. The two versions of the relativistic Langevin equation are connected by a reparametrization scheme. In spite of the issues contained in the first version of the relativistic Langevin equation, it still permits to extract the physical probability distributions of the Brownian particles, as is shown by Monte Carlo simulation in the example case of Brownian motion in $(1+1)$-dimensional Minkowski spacetime.Comment: 23 page

Optimizing Guided Traversal for Fast Learned Sparse Retrieval

Recent studies show that BM25-driven dynamic index skipping can greatly accelerate MaxScore-based document retrieval based on the learned sparse representation derived by DeepImpact. This paper investigates the effectiveness of such a traversal guidance strategy during top k retrieval when using other models such as SPLADE and uniCOIL, and finds that unconstrained BM25-driven skipping could have a visible relevance degradation when the BM25 model is not well aligned with a learned weight model or when retrieval depth k is small. This paper generalizes the previous work and optimizes the BM25 guided index traversal with a two-level pruning control scheme and model alignment for fast retrieval using a sparse representation. Although there can be a cost of increased latency, the proposed scheme is much faster than the original MaxScore method without BM25 guidance while retaining the relevance effectiveness. This paper analyzes the competitiveness of this two-level pruning scheme, and evaluates its tradeoff in ranking relevance and time efficiency when searching several test datasets.Comment: This paper is published in WWW'2

A Unified Model for the Two-stage Offline-then-Online Resource Allocation

With the popularity of the Internet, traditional offline resource allocation has evolved into a new form, called online resource allocation. It features the online arrivals of agents in the system and the real-time decision-making requirement upon the arrival of each online agent. Both offline and online resource allocation have wide applications in various real-world matching markets ranging from ridesharing to crowdsourcing. There are some emerging applications such as rebalancing in bike sharing and trip-vehicle dispatching in ridesharing, which involve a two-stage resource allocation process. The process consists of an offline phase and another sequential online phase, and both phases compete for the same set of resources. In this paper, we propose a unified model which incorporates both offline and online resource allocation into a single framework. Our model assumes non-uniform and known arrival distributions for online agents in the second online phase, which can be learned from historical data. We propose a parameterized linear programming (LP)-based algorithm, which is shown to be at most a constant factor of $1/4$ from the optimal. Experimental results on the real dataset show that our LP-based approaches outperform the LP-agnostic heuristics in terms of robustness and effectiveness.Comment: Accepted by IJCAI 2020 (http://static.ijcai.org/2020-accepted_papers.html) and SOLE copyright holder is IJCAI (International Joint Conferences on Artificial Intelligence), all rights reserve