Understanding the bias-variance tradeoff in user representation learning is essential for improving recommendation quality in modern content platforms. While well studied in static settings, this tradeoff becomes significantly more complex when content creators strategically adapt to platform incentives. To analyze how such competition reshapes the tradeoff for maximizing user welfare, we introduce the Content Creator Competition with Bias-Variance Tradeoff (C3BV ) framework, a tractable game-theoretic model that captures the platform's decision on regularization strength in user feature estimation. We derive and compare the platform's optimal policy under two key settings: a non-strategic baseline with fixed content and a strategic environment where creators compete in response to the platform's algorithmic design.

In this paper, we present the Proportional Payoff Allocation Game (PPA-Game), which characterizes situations where agents compete for divisible resources. In the PPA-game, agents select from available resources, and their payoffs are proportionately determined based on heterogeneous weights attributed to them. Such dynamics simulate content creators on online recommender systems like YouTube and TikTok, who compete for finite consumer attention, with content exposure reliant on inherent and distinct quality. We first conduct a game-theoretical analysis of the PPA-Game. While the PPA-Game does not always guarantee the existence of a pure Nash equilibrium (PNE), we identify prevalent scenarios ensuring its existence. Simulated experiments further prove that the cases where PNE does not exist rarely happen. Beyond analyzing static payoffs, we further discuss the agents' online learning about resource payoffs by integrating a multi-player multi-armed bandit framework. We propose an online algorithm facilitating each agent's maximization of cumulative payoffs over T rounds. Theoretically, we establish that the regret of any agent is bounded by O(log^1 + η T) for any η > 0. Empirical results further validate the effectiveness of our online learning approach.

Treatment effect estimation from observational data is a fundamental problem in causal inference, and its critical challenge is to address the confounding bias arising from the confounders. The effectiveness of the conventional methods proposed to solve this problem depends on the unconfoundedness assumption. In practice, however, the unconfoundedness assumption is frequently violated since we cannot guarantee that all the confounders are measured. To this end, recent studies suggest using auxiliary network architectures to mine information about unmeasured confounders in the data to relax this assumption. However, these methods cannot address the confounding bias from unmeasured confounders unrelated to the network information. Inspired by the insight that some neighboring features that influence one's treatment choice (e.g., which movie to watch) but do not affect the outcome (e.g., assessment of the movie) can be treated as instrumental variables (IVs), we propose a novel Network Instrumental Variable Regression (NetIV) framework exploits IV information from neighborhoods to perform a two-stage regression for treatment effect estimation. Extensive experiments demonstrate that our NetIV method outperforms the state-of-the-art methods for treatment effect estimation in the presence of unmeasured confounders.

In this paper, we focus on the problem of stable prediction across unknown test data, where the test distribution might be different from the training one and is always agnostic when model training. In such a case, previous machine learning methods might exploit subtly spurious correlations induced by non-causal variables in training data for prediction. Those spurious correlations are changeable across data, leading to instability of prediction across unknown test data. To address this problem, we propose a conditional independence test based algorithm to screen out part of non-causal features and reduce those spurious correlations for a more stable prediction by leveraging a seed variable. We show, both theoretically and with empirical experiments, that our algorithm can precisely screen out the isolated non-causal variables, which have no causal relationship with other variables, and remove the spurious correlations induced by them, increasing the stability of prediction across unknown test data. Extensive experiments on both synthetic and real-world datasets demonstrate that our algorithm outperforms state-of-the-art methods for stable prediction across unknown test data.

Machine learning algorithms with empirical risk minimization are vulnerable under distributional shifts due to the greedy adoption of all the correlations found in training data. There is an emerging literature on tackling this problem by minimizing the worst-case risk over an uncertainty set. However, existing methods mostly construct ambiguity sets by treating all variables equally regardless of the stability of their correlations with the target, resulting in the overwhelmingly-large uncertainty set and low confidence of the learner. In this paper, we propose a novel Stable Adversarial Learning (SAL) algorithm that leverages heterogeneous data sources to construct a more practical uncertainty set and conduct differentiated robustness optimization, where covariates are differentiated according to the stability of their correlations with the target. We theoretically show that our method is tractable for stochastic gradient-based optimization and provide the performance guarantees for our method. Empirical studies on both simulation and real datasets validate the effectiveness of our method in terms of uniformly good performance across unknown distributional shifts.

In observational studies, confounder separation and balancing are the fundamental problems of treatment effect estimation. Most of the previous methods focused on addressing the problem of confounder balancing by treating all observed pre-treatment variables as confounders, ignoring confounder separation. In general, not all the observed pre-treatment variables are confounders that refer to the common causes of the treatment and the outcome, some variables only contribute to the treatment (i.e., instrumental variables) and some only contribute to the outcome (i.e., adjustment variables). Balancing those non-confounders, including instrumental variables and adjustment variables, would generate additional bias for treatment effect estimation. By modeling the different causal relations among observed pre-treatment variables, treatment variables and outcome variables, we propose a synergistic learning framework to i) separate confounders by learning decomposed representations of both confounders and non-confounders, ii) balance confounder with sample re-weighting technique, and simultaneously iii) estimate the treatment effect in observational studies via counterfactual inference. Empirical results on synthetic and real-world datasets demonstrate that the proposed method can precisely decompose confounders and achieve a more precise estimation of treatment effect than baselines.

Personalized pricing is a business strategy to charge different prices to individual consumers based on their characteristics and behaviors. It has become common practice in many industries nowadays due to the availability of a growing amount of high granular consumer data. The discriminatory nature of personalized pricing has triggered heated debates among policymakers and academics on how to design regulation policies to balance market efficiency and equity. In this paper, we propose two sound policy instruments, i.e., capping the range of the personalized prices or their ratios. We investigate the optimal pricing strategy of a profit-maximizing monopoly under both regulatory constraints and the impact of imposing them on consumer surplus, producer surplus, and social welfare. We theoretically prove that both proposed constraints can help balance consumer surplus and producer surplus at the expense of total surplus for common demand distributions, such as uniform, logistic, and exponential distributions. Experiments on both simulation and real-world datasets demonstrate the correctness of these theoretical results1. Our findings and insights shed light on regulatory policy design for the increasingly monopolized business in the digital era.

Instrumental variables (IVs), sources of treatment randomization that are conditionally independent of the outcome, play an important role in causal inference with unobserved confounders. However, the existing IV-based counterfactual prediction methods need well-predefined IVs, while it’s an art rather than science to find valid IVs in many real-world scenes. Moreover, the predefined hand-made IVs could be weak or erroneous by violating the conditions of valid IVs. These thorny facts hinder the application of the IV-based counterfactual prediction methods. In this article, we propose a novel Automatic Instrumental Variable decomposition (AutoIV) algorithm to automatically generate representations serving the role of IVs from observed variables (IV candidates). Specifically, we let the learned IV representations satisfy the relevance condition with the treatment and exclusion condition with the outcome via mutual information maximization and minimization constraints, respectively. We also learn confounder representations by encouraging them to be relevant to both the treatment and the outcome. The IV and confounder representations compete for the information with their constraints in an adversarial game, which allows us to get valid IV representations for IV-based counterfactual prediction. Extensive experiments demonstrate that our method generates valid IV representations for accurate IV-based counterfactual prediction.

Causal Inference plays an important role in decision making in many fields, such as social marketing, healthcare, and public policy. One fundamental problem in causal inference is the treatment effect estimation in observational studies when variables are confounded. Controlling for confounding effects is generally handled by propensity score. But it treats all observed variables as confounders and ignores the adjustment variables, which have no influence on treatment but are predictive of the outcome. Recently, it has been demonstrated that the adjustment variables are effective in reducing the variance of the estimated treatment effect. However, how to automatically separate the confounders and adjustment variables in observational studies is still an open problem, especially in the scenarios of high dimensional variables, which are common in the big data era. In this paper, we first propose a Data-Driven Variable Decomposition (D$^2$VD) algorithm, which can 1) automatically separate confounders and adjustment variables with a data-driven approach, and 2) simultaneously estimate treatment effect in observational studies with high dimensional variables. Under standard assumptions, we theoretically prove that our D$^2$VD algorithm can unbiased estimate treatment effect and achieve lower variance than traditional propensity score based methods. Moreover, to address the challenges from high-dimensional variables and nonlinear, we extend our D$^2$VD to a non-linear version, namely Nonlinear-D$^2$VD (N-D$^2$VD) algorithm. To validate the effectiveness of our proposed algorithms, we conduct extensive experiments on both synthetic and real-world datasets. The experimental results demonstrate that our D$^2$VD and N-D$^2$VD algorithms can automatically separate the variables precisely, and estimate treatment effect more accurately and with tighter confidence intervals than the state-of-the-art methods. We also demonstrated that the top-ranked features by our algorithm have the best prediction performance on an online advertising dataset.

Recently, as the applications of artificial intelligence gradually seeping into some risk-sensitive areas such as justice, healthcare and autonomous driving, an upsurge of research interest on model stability and robustness has arisen in the field of machine learning. Rather than purely fitting the observed training data, stable learning tries to learn a model with uniformly good performance under non-stationary and agnostic testing data. The key challenge of stable learning in practice is that we do not have any knowledge about the true model and test data distribution as a priori. Under such condition, we cannot expect a faithful estimation of model parameters and its stability over wild changing environments. Previous methods resort to a reweighting scheme to remove the correlations between all the variables through a set of new sample weights. However, we argue that such aggressive decorrelation between all the variables may cause the over-reduced sample size, which leads to the variance inflation and possible underperformance. In this paper, we incorporate the unlabled data from multiple environments into the variable decorrelation framework and propose a Differentiated Variable Decorrelation (DVD) algorithm based on the clustering of variables. Specifically, the variables are clustered according to the stability of their correlations and the variable decorrelation module learns a set of sample weights to remove the correlations merely between the variables of different clusters. Empirical studies on both synthetic and real world datasets clearly demonstrate the efficacy of our DVD algorithm on improving the model parameter estimation and the prediction stability over changing distributions.

Nowadays fairness issues have raised great concerns in decision-making systems. Various fairness notions have been proposed to measure the degree to which an algorithm is unfair. In practice, there frequently exist a certain set of variables we term as fair variables, which are pre-decision covariates such as users' choices. The effects of fair variables are irrelevant in assessing the fairness of the decision support algorithm. We thus define conditional fairness as a more sound fairness metric by conditioning on the fairness variables. Given different prior knowledge of fair variables, we demonstrate that traditional fairness notations, such as demographic parity and equalized odds, are special cases of our conditional fairness notations. Moreover, we propose a Derivable Conditional Fairness Regularizer (DCFR), which can be integrated into any decision-making model, to track the trade-off between precision and fairness of algorithmic decision making. Specifically, an adversarial representation based conditional independence loss is proposed in our DCFR to measure the degree of unfairness. With extensive experiments on three real-world datasets, we demonstrate the advantages of our conditional fairness notation and DCFR.

Treatment effect plays an important role on decision making in many fields, such as social marketing, healthcare, and public policy. The key challenge on estimating treatment effect in the wild observational studies is to handle confounding bias induced by imbalance of the confounder distributions between treated and control units. Traditional methods remove confounding bias by re-weighting units with supposedly accurate propensity score estimation under the unconfoundedness assumption. Controlling high-dimensional variables may make the unconfoundedness assumption more plausible, but poses new challenge on accurate propensity score estimation. One strand of recent literature seeks to directly optimize weights to balance confounder distributions, bypassing propensity score estimation. But existing balancing methods fail to do selection and differentiation among the pool of a large number of potential confounders, leading to possible underperformance in many high-dimensional settings. In this article, we propose a data-driven Differentiated Confounder Balancing (DCB) algorithm to jointly select confounders, differentiate weights of confounders and balance confounder distributions for treatment effect estimation in the wild high-dimensional settings. Besides, under some settings with heavy confounding bias, in order to further reduce the bias and variance of estimated treatment effect, we propose a Regression Adjusted Differentiated Confounder Balancing (RA-DCB) algorithm based on our DCB algorithm by incorporating outcome regression adjustment. The synergistic learning algorithms we proposed are more capable of reducing the confounding bias in many observational studies. To validate the effectiveness of our DCB and RA-DCB algorithms, we conduct extensive experiments on both synthetic and real-world datasets. The experimental results clearly demonstrate that our algorithms outperform the state-of-the-art methods. By incorporating regression adjustment, our RA-DCB algorithm achieves more precise estimation on treatment effect than DCB algorithm, especially under the settings with heavy confounding bias. Moreover, we show that the top features ranked by our algorithm generate accurate prediction of online advertising effect.

In many important machine learning applications, the training distribution used to learn a probabilistic classifier differs from the distribution on which the classifier will be used to make predictions. Traditional methods correct the distribution shift by reweighting training data with the ratio of the density between test and training data. However, in many applications training takes place without prior knowledge of the testing distribution. Recently, methods have been proposed to address the shift by learning the underlying causal structure, but those methods rely on diversity arising from multiple training data sets, and they further have complexity limitations in high dimensions. In this paper, we propose a novel Deep Global Balancing Regression (DGBR) algorithm to jointly optimize a deep auto-encoder model for feature selection and a global balancing model for stable prediction across unknown environments. The global balancing model constructs balancing weights that facilitate estimation of partial effects of features (holding fixed all other features), a problem that is challenging in high dimensions, and thus helps to identify stable, causal relationships between features and outcomes. The deep auto-encoder model is designed to reduce the dimensionality of the feature space, thus making global balancing easier. We show, both theoretically and with empirical experiments, that our algorithm can make stable predictions across unknown environments. Our experiments on both synthetic and real datasets demonstrate that our algorithm outperforms the state-of-the-art methods for stable prediction across unknown environments.

Estimating treatment effect plays an important role on decision making in many fields, such as social marketing, healthcare, and public policy. The key challenge on estimating treatment effect in the wild observational studies is to handle confounding bias induced by imbalance of the confounder distributions between treated and control units. Traditional methods remove confounding bias by re-weighting units with supposedly accurate propensity score estimation under the unconfoundedness assumption. Controlling high-dimensional variables may make the unconfoundedness assumption more plausible, but poses new challenge on accurate propensity score estimation. One strand of recent literature seeks to directly optimize weights to balance confounder distributions, bypassing propensity score estimation. But existing balancing methods fail to do selection and differentiation among the pool of a large number of potential confounders, leading to possible underperformance in many high dimensional settings. In this paper, we propose a data-driven Differentiated Confounder Balancing (DCB) algorithm to jointly select confounders, differentiate weights of confounders and balance confounder distributions for treatment effect estimation in the wild high dimensional settings. The synergistic learning algorithm we proposed is more capable of reducing the confounding bias in many observational studies. To validate the effectiveness of our DCB algorithm, we conduct extensive experiments on both synthetic and real datasets. The experimental results clearly demonstrate that our DCB algorithm outperforms the state-of-the-art methods. We further show that the top features ranked by our algorithm generate accurate prediction of online advertising effect.

Latent variable models have proven to be a useful tool for discovering latent structures from observational data. However, the data in social networks often come as streams, i.e., both text content (e.g., emails, user postings) and network structure (e.g., user friendship) evolve over time. To capture the time-evolving latent structures in such social streams, we propose a fully nonparametric Dynamic Topical Community Model (nDTCM), where infinite latent community variables coupled with infinite latent topic variables in each epoch, and the temporal dependencies between variables across epochs are modeled via the rich-gets-richer scheme. We focus on characterizing three dynamic aspects in social streams: the number of communities or topics changes (e.g., new communities or topics are born and old ones die out); the popularity of communities or topics evolves; the semantics such as community topic distribution, community participant distribution and topic word distribution drift. Furthermore, we develop an effective online posterior inference algorithm for nDTCM, which is concordant with the online nature of social streams. Experiments using real-world data show the effectiveness of our model at discovering the dynamic topical communities in social streams.