We consider an auction mechanism design problem where a seller sells multiple homogeneous items to a set of buyers who are connected to form a network. Each buyer only knows the buyers he directly connects with and has a diminishing marginal utility valuation for the items. The seller initially also only connects to some of the buyers. The goal is to design an auction to incentivize the buyers who are aware of the auction to further invite their neighbors to join the auction. This is challenging because the buyers are competing for the items and they would not invite each other by default. Solutions have been proposed recently for the settings where each buyer requires at most one unit and demonstrated the difficulties for the design even in the simple settings. We move this forward to propose the very first diffusion auction for the multi-unit demand settings. We also show that it improves both the social welfare and the revenue to incentivize the seller to apply it.
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We introduce a family of pairwise stochastic gradient estimators for gradients of expectations, which are related to the log-derivative trick, but involve pairwise interactions between samples. The simplest example of our new estimator, dubbed the fundamental trick estimator, is shown to arise from either a) introducing and approximating an integral representation based on the fundamental theorem of calculus, or b) applying the reparameterisation trick to an implicit parameterisation under infinitesimal perturbation of the parameters. From the former perspective we generalise to a reproducing kernel Hilbert space representation, giving rise to a locality parameter in the pairwise interactions mentioned above, yielding our representer trick estimator. The resulting estimators are unbiased and shown to offer an independent component of useful information in comparison with the log-derivative estimator. We provide a further novel theoretical analysis which further characterises the variance reduction afforded by the new techniques. Promising analytical and numerical examples confirm the theory and intuitions behind the new estimators.
Current practices in metric evaluation focus on one single dataset, e.g., Newstest dataset in each year's WMT Metrics Shared Task. However, in this paper, we qualitatively and quantitatively show that the performances of metrics are sensitive to data. The ranking of metrics varies when the evaluation is conducted on different datasets. Then this paper further investigates two potential hypotheses, i.e., insignificant data points and the deviation of Independent and Identically Distributed (i.i.d) assumption, which may take responsibility for the issue of data variance. In conclusion, our findings suggest that when evaluating automatic translation metrics, researchers should take data variance into account and be cautious to claim the result on a single dataset, because it may leads to inconsistent results with most of other datasets.
For relational structures A, B of the same signature, the Promise Constraint Satisfaction Problem PCSP(A,B) asks whether a given input structure maps homomorphically to A or does not even map to B. We are promised that the input satisfies exactly one of these two cases. If there exists a structure C with homomorphisms $A\to C\to B$, then PCSP(A,B) reduces naturally to CSP(C). To the best of our knowledge all known tractable PCSPs reduce to tractable CSPs in this way. However Barto showed that some PCSPs over finite structures A, B require solving CSPs over infinite C. We show that even when such a reduction to finite C is possible, this structure may become arbitrarily large. For every integer $n>1$ and every prime p we give A, B of size n with a single relation of arity $n^p$ such that PCSP(A, B) reduces via a chain of homomorphisms $ A\to C\to B$ to a tractable CSP over some C of size p but not over any smaller structure. In a second family of examples, for every prime $p\geq 7$ we construct A, B of size $p-1$ with a single ternary relation such that PCSP(A, B) reduces via $A\to C\to B$ to a tractable CSP over some C of size p but not over any smaller structure. In contrast we show that if A, B are graphs and PCSP(A,B) reduces to tractable CSP(C) for some finite digraph C, then already A or B has a tractable CSP. This extends results and answers a question of Deng et al.
Recent developments in Artificial Intelligence (AI) have fueled the emergence of human-AI collaboration, a setting where AI is a coequal partner. Especially in clinical decision-making, it has the potential to improve treatment quality by assisting overworked medical professionals. Even though research has started to investigate the utilization of AI for clinical decision-making, its potential benefits do not imply its adoption by medical professionals. While several studies have started to analyze adoption criteria from a technical perspective, research providing a human-centered perspective with a focus on AI's potential for becoming a coequal team member in the decision-making process remains limited. Therefore, in this work, we identify factors for the adoption of human-AI collaboration by conducting a series of semi-structured interviews with experts in the healthcare domain. We identify six relevant adoption factors and highlight existing tensions between them and effective human-AI collaboration.
We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spiliopoulos (2018)} to solve a number of partial differential equations (PDEs) that arise in the context of optimal stochastic control and mean field games. First, we consider PDEs where the function is constrained to be positive and integrate to unity, as is the case with Fokker-Planck equations. Our approach involves reparameterizing the solution as the exponential of a neural network appropriately normalized to ensure both requirements are satisfied. This then gives rise to nonlinear a partial integro-differential equation (PIDE) where the integral appearing in the equation is handled by a novel application of importance sampling. Secondly, we tackle a number of Hamilton-Jacobi-Bellman (HJB) equations that appear in stochastic optimal control problems. The key contribution is that these equations are approached in their unsimplified primal form which includes an optimization problem as part of the equation. We extend the DGM algorithm to solve for the value function and the optimal control \simultaneously by characterizing both as deep neural networks. Training the networks is performed by taking alternating stochastic gradient descent steps for the two functions, a technique inspired by the policy improvement algorithms (PIA).
This paper studies the application of reconfigurable intelligent surface (RIS) to cooperative non-orthogonal multiple access (C-NOMA) networks with simultaneous wireless information and power transfer (SWIPT). We aim for maximizing the rate of the strong user with guaranteed weak user's quality of service (QoS) by jointly optimizing power splitting factors, beamforming coefficients, and RIS reflection coefficients in two transmission phases. The formulated problem is difficult to solve due to its complex and non-convex constraints. To tackle this challenging problem, we first use alternating optimization (AO) framework to transform it into three subproblems, and then use the penalty-based arithmetic-geometric mean approximation (PBAGM) algorithm and the successive convex approximation (SCA)-based method to solve them. Numerical results verify the superiority of the proposed algorithm over the baseline schemes.
In the interdependent values (IDV) model introduced by Milgrom and Weber [1982], agents have private signals that capture their information about different social alternatives, and the valuation of every agent is a function of all agent signals. While interdependence has been mainly studied for auctions, it is extremely relevant for a large variety of social choice settings, including the canonical setting of public projects. The IDV model is very challenging relative to standard independent private values, and welfare guarantees have been achieved through two alternative conditions known as {\em single-crossing} and {\em submodularity over signals (SOS)}. In either case, the existing theory falls short of solving the public projects setting. Our contribution is twofold: (i) We give a workable characterization of truthfulness for IDV public projects for the largest class of valuations for which such a characterization exists, and term this class \emph{decomposable valuations}; (ii) We provide possibility and impossibility results for welfare approximation in public projects with SOS valuations. Our main impossibility result is that, in contrast to auctions, no universally truthful mechanism performs better for public projects with SOS valuations than choosing a project at random. Our main positive result applies to {\em excludable} public projects with SOS, for which we establish a constant factor approximation similar to auctions. Our results suggest that exclusion may be a key tool for achieving welfare guarantees in the IDV model.
A High-dimensional and sparse (HiDS) matrix is frequently encountered in a big data-related application like an e-commerce system or a social network services system. To perform highly accurate representation learning on it is of great significance owing to the great desire of extracting latent knowledge and patterns from it. Latent factor analysis (LFA), which represents an HiDS matrix by learning the low-rank embeddings based on its observed entries only, is one of the most effective and efficient approaches to this issue. However, most existing LFA-based models perform such embeddings on a HiDS matrix directly without exploiting its hidden graph structures, thereby resulting in accuracy loss. To address this issue, this paper proposes a graph-incorporated latent factor analysis (GLFA) model. It adopts two-fold ideas: 1) a graph is constructed for identifying the hidden high-order interaction (HOI) among nodes described by an HiDS matrix, and 2) a recurrent LFA structure is carefully designed with the incorporation of HOI, thereby improving the representa-tion learning ability of a resultant model. Experimental results on three real-world datasets demonstrate that GLFA outperforms six state-of-the-art models in predicting the missing data of an HiDS matrix, which evidently supports its strong representation learning ability to HiDS data.
In this paper we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), several of which are based on Abadie (2003)'s kappa theorem. Our framework presumes a binary endogenous explanatory variable ("treatment") and a binary instrumental variable, which may only be valid after conditioning on additional covariates. We argue that one of the Abadie estimators, which we show is weight normalized, is likely to dominate the others in many contexts. A notable exception is in settings with one-sided noncompliance, where certain unnormalized estimators have the advantage of being based on a denominator that is bounded away from zero. We use a simulation study and three empirical applications to illustrate our findings. In applications to causal effects of college education using the college proximity instrument (Card, 1995) and causal effects of childbearing using the sibling sex composition instrument (Angrist and Evans, 1998), the unnormalized estimates are clearly unreasonable, with "incorrect" signs, magnitudes, or both. Overall, our results suggest that (i) the relative performance of different kappa weighting estimators varies with features of the data-generating process; and that (ii) the normalized version of Tan (2006)'s estimator may be an attractive alternative in many contexts. Applied researchers with access to a binary instrumental variable should also consider covariate balancing or doubly robust estimators of the LATE.
Models for dependent data are distinguished by their targets of inference. Marginal models are useful when interest lies in quantifying associations averaged across a population of clusters. When the functional form of a covariate-outcome association is unknown, flexible regression methods are needed to allow for potentially non-linear relationships. We propose a novel marginal additive model (MAM) for modelling cluster-correlated data with non-linear population-averaged associations. The proposed MAM is a unified framework for estimation and uncertainty quantification of a marginal mean model, combined with inference for between-cluster variability and cluster-specific prediction. We propose a fitting algorithm that enables efficient computation of standard errors and corrects for estimation of penalty terms. We demonstrate the proposed methods in simulations and in application to (i) a longitudinal study of beaver foraging behaviour, and (ii) a spatial analysis of Loaloa infection in West Africa. R code for implementing the proposed methodology is available at //github.com/awstringer1/mam.
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