Sequential Elimination Contests with All-Pay Auctions

We study a sequential elimination contest where players are filtered prior to the round of competing for prizes. This is motivated by the practice that many crowdsourcing contests have very limited resources of reviewers and want to improve the overall quality of the submissions. We first consider a setting where the designer knows the ranking of the abilities (types) of all $n_1$ registered players, and admit the top $n_2$ players with $2\leq n_2 \leq n_1$ into the contest. The players admitted into the contest update their beliefs about their opponents based on the signal that their abilities are among the top $n_2$. We find that their posterior beliefs, even with IID priors, are correlated and depend on players' private abilities. We explicitly characterize the symmetric and unique Bayesian equilibrium strategy. We find that each admitted player's equilibrium effort is increasing in $n_2$ when $n_2 \in [\lfloor{(n_1+1)/2}\rfloor+1,n_1]$, but not monotone in general when $n_2 \in [2,\lfloor{(n_1+1)/2}\rfloor+1]$. Surprisingly, despite this non-monotonicity, all players exert their highest efforts when $n_2=n_1$. As a sequence, if the designer has sufficient capacity, he should admit all players to maximize their equilibrium efforts. This result holds generally -- it is true under any ranking-based reward structure, ability distribution, and cost function. We also discuss the situation where the designer can only admit $c<n_1$ players. Our numerical results show that, in terms of the expected highest or total efforts, the optimal $n_2$ is either $2$ or $c$. Finally, we extend our model to a two-stage setting, where players with top first-stage efforts can proceed to the second stage competing for prizes. We establish an intriguing negative result in this setting: there does not exist a symmetric and monotone Perfect Bayesian equilibrium

Knockoffs-SPR: Clean Sample Selection in Learning with Noisy Labels

A noisy training set usually leads to the degradation of the generalization and robustness of neural networks. In this paper, we propose a novel theoretically guaranteed clean sample selection framework for learning with noisy labels. Specifically, we first present a Scalable Penalized Regression (SPR) method, to model the linear relation between network features and one-hot labels. In SPR, the clean data are identified by the zero mean-shift parameters solved in the regression model. We theoretically show that SPR can recover clean data under some conditions. Under general scenarios, the conditions may be no longer satisfied; and some noisy data are falsely selected as clean data. To solve this problem, we propose a data-adaptive method for Scalable Penalized Regression with Knockoff filters (Knockoffs-SPR), which is provable to control the False-Selection-Rate (FSR) in the selected clean data. To improve the efficiency, we further present a split algorithm that divides the whole training set into small pieces that can be solved in parallel to make the framework scalable to large datasets. While Knockoffs-SPR can be regarded as a sample selection module for a standard supervised training pipeline, we further combine it with a semi-supervised algorithm to exploit the support of noisy data as unlabeled data. Experimental results on several benchmark datasets and real-world noisy datasets show the effectiveness of our framework and validate the theoretical results of Knockoffs-SPR. Our code and pre-trained models are available at https://github.com/Yikai-Wang/Knockoffs-SPR.Comment: update: refined theory and analysis, release cod

Solvothermal Synthesis of Zn 2

Crystalline Zn2SnO4 nanoparticles were successfully synthesized via a simple solvothermal route by using Zn(CH3COO)2·2H2O and SnCl4·5H2O as source materials, NaOH as mineralizing agent, and water and ethanol as mixed solvents. The used amount of NaOH was found to have an important influence on the formation of Zn2SnO4. When the molar ratio of OH− : Zn2+ : Sn4+ was set in the range from 4 : 2 : 1 to 8 : 2 : 1, Zn2SnO4 nanoparticles with different shape and size were obtained. However, when the molar ratio of OH− : Zn2+ : Sn4+ was set as 10 : 2 : 1, a mixture phase of ZnO and ZnSn(OH)6 instead of Zn2SnO4 was obtained. Photodegradation measurements indicated that the Zn2SnO4 nanoparticles own better photocatalytic property to depredate methyl orange than the Zn2SnO4 nanopolyhedrons. The superior photocatalytic properties of Zn2SnO4 nanoparticles may be contributed to their small crystal size and high surface area

Doubly Robust Proximal Causal Learning for Continuous Treatments

Proximal causal learning is a promising framework for identifying the causal effect under the existence of unmeasured confounders. Within this framework, the doubly robust (DR) estimator was derived and has shown its effectiveness in estimation, especially when the model assumption is violated. However, the current form of the DR estimator is restricted to binary treatments, while the treatment can be continuous in many real-world applications. The primary obstacle to continuous treatments resides in the delta function present in the original DR estimator, making it infeasible in causal effect estimation and introducing a heavy computational burden in nuisance function estimation. To address these challenges, we propose a kernel-based DR estimator that can well handle continuous treatments. Equipped with its smoothness, we show that its oracle form is a consistent approximation of the influence function. Further, we propose a new approach to efficiently solve the nuisance functions. We then provide a comprehensive convergence analysis in terms of the mean square error. We demonstrate the utility of our estimator on synthetic datasets and real-world applications.Comment: Preprint, under revie