arXiv subjects

Nian Si

Publications and source records attributed to Nian Si.

35 records · Page 2Linked to original sources

arXiv2025

ScoreFusion: Fusing Score-based Generative Models via Kullback-Leibler Barycenters

We introduce ScoreFusion, a theoretically grounded method for fusing multiple pre-trained diffusion models that are assumed to generate from auxiliary populations. ScoreFusion is particularly useful for enhancing the generative modeling of a target population with limited observed data. Our starting point considers the family of KL barycenters of the auxiliary populations, which is proven to be an optimal parametric class in the KL sense, but difficult to learn. Nevertheless, by recasting the learning problem as score matching in denoising diffusion, we obtain a tractable way of computing the optimal KL barycenter weights. We prove a dimension-free sample complexity bound in total variation distance, provided that the auxiliary models are well-fitted for their own task and the auxiliary tasks combined capture the target well. The sample efficiency of ScoreFusion is demonstrated by learning handwritten digits. We also provide a simple adaptation of a Stable Diffusion denoising pipeline that enables sampling from the KL barycenter of two auxiliary checkpoints; on a portrait generation task, our method produces faces that enhance population heterogeneity relative to the auxiliary distributions.

stat.ML↗

arXiv2025

Knowledge-Guided Wasserstein Distributionally Robust Optimization

Transfer learning is a popular strategy to leverage external knowledge and improve statistical efficiency, particularly with a limited target sample. We propose a novel knowledge-guided Wasserstein Distributionally Robust Optimization (KG-WDRO) framework that adaptively incorporates multiple sources of external knowledge to overcome the conservativeness of vanilla WDRO, which often results in overly pessimistic shrinkage toward zero. Our method constructs smaller Wasserstein ambiguity sets by controlling the transportation along directions informed by the source knowledge. This strategy can alleviate perturbations on the predictive projection of the covariates and protect against information loss. Theoretically, we establish the equivalence between our WDRO formulation and the knowledge-guided shrinkage estimation based on collinear similarity, ensuring tractability and geometrizing the feasible set. This also reveals a novel and general interpretation for recent shrinkage-based transfer learning approaches from the perspective of distributional robustness. In addition, our framework can adjust for scaling differences in the regression models between the source and target and accommodates general types of regularization such as lasso and ridge. Extensive simulations demonstrate the superior performance and adaptivity of KG-WDRO in enhancing small-sample transfer learning.

cs.LG↗

arXiv2024

Multi-source Stable Variable Importance Measure via Adversarial Machine Learning

The quantification and inference of predictive importance for exposure covariates have recently gained significant attention in the context of interpretable machine learning. Contemporary scientific investigations often involve data originating from multiple sources with distributional heterogeneity. It is imperative to introduce a new notation of the variable importance measure that is stable across diverse environments. In this paper, we introduce MIMAL (Multi-source Importance Measure via Adversarial Learning), a novel statistical framework designed to quantify the importance of exposure variables by maximizing the worst-case predictive reward across source mixtures. The proposed framework is adaptable to a broad spectrum of machine learning methodologies for both confounding adjustment and exposure effect characterization. We establish the asymptotic normality of the data-dependent estimator of the multi-source variable importance measure under a general machine learning framework. Our framework requires the similar learning accuracy conditions compared to those required for single-source variable importance analysis. The finite-sample performance of MIMAL is demonstrated through extensive numerical studies encompassing diverse data generation scenarios and machine learning implementations. Furthermore, we illustrate the practical utility of our approach in a real-world case study of air pollution in Beijing, analyzing data collected from multiple locations.

stat.ME↗

arXiv2024

Sample Complexity of Variance-reduced Distributionally Robust Q-learning

Dynamic decision-making under distributional shifts is of fundamental interest in theory and applications of reinforcement learning: The distribution of the environment in which the data is collected can differ from that of the environment in which the model is deployed. This paper presents two novel model-free algorithms, namely the distributionally robust Q-learning and its variance-reduced counterpart, that can effectively learn a robust policy despite distributional shifts. These algorithms are designed to efficiently approximate the $q$-function of an infinite-horizon $γ$-discounted robust Markov decision process with Kullback-Leibler ambiguity set to an entry-wise $ε$-degree of precision. Further, the variance-reduced distributionally robust Q-learning combines the synchronous Q-learning with variance-reduction techniques to enhance its performance. Consequently, we establish that it attains a minimax sample complexity upper bound of $\tilde O(|\mathbf{S}||\mathbf{A}|(1-γ)^{-4}ε^{-2})$, where $\mathbf{S}$ and $\mathbf{A}$ denote the state and action spaces. This is the first complexity result that is independent of the ambiguity size $δ$, thereby providing new complexity theoretic insights. Additionally, a series of numerical experiments confirm the theoretical findings and the efficiency of the algorithms in handling distributional shifts.

cs.LG↗

arXiv2024

Drift Control of High-Dimensional RBM: A Computational Method Based on Neural Networks

Motivated by applications in queueing theory, we consider a stochastic control problem whose state space is the $d$-dimensional positive orthant. The controlled process $Z$ evolves as a reflected Brownian motion whose covariance matrix is exogenously specified, as are its directions of reflection from the orthant's boundary surfaces. A system manager chooses a drift vector $θ(t)$ at each time $t$ based on the history of $Z$, and the cost rate at time $t$ depends on both $Z(t)$ and $θ(t)$. In our initial problem formulation, the objective is to minimize expected discounted cost over an infinite planning horizon, after which we treat the corresponding ergodic control problem. Extending earlier work by Han et al. (Proceedings of the National Academy of Sciences, 2018, 8505-8510), we develop and illustrate a simulation-based computational method that relies heavily on deep neural network technology. For test problems studied thus far, our method is accurate to within a fraction of one percent, and is computationally feasible in dimensions up to at least $d=30$.

eess.SY↗

arXiv2024

A Finite Sample Complexity Bound for Distributionally Robust Q-learning

We consider a reinforcement learning setting in which the deployment environment is different from the training environment. Applying a robust Markov decision processes formulation, we extend the distributionally robust $Q$-learning framework studied in Liu et al. [2022]. Further, we improve the design and analysis of their multi-level Monte Carlo estimator. Assuming access to a simulator, we prove that the worst-case expected sample complexity of our algorithm to learn the optimal robust $Q$-function within an $ε$ error in the sup norm is upper bounded by $\tilde O(|S||A|(1-γ)^{-5}ε^{-2}p_{\wedge}^{-6}δ^{-4})$, where $γ$ is the discount rate, $p_{\wedge}$ is the non-zero minimal support probability of the transition kernels and $δ$ is the uncertainty size. This is the first sample complexity result for the model-free robust RL problem. Simulation studies further validate our theoretical results.

cs.LG↗

arXiv2024

Calibration-then-Calculation: A Variance Reduced Metric Framework in Deep Click-Through Rate Prediction Models

The adoption of deep learning across various fields has been extensive, yet there is a lack of focus on evaluating the performance of deep learning pipelines. Typically, with the increased use of large datasets and complex models, the training process is run only once and the result is compared to previous benchmarks. This practice can lead to imprecise comparisons due to the variance in neural network evaluation metrics, which stems from the inherent randomness in the training process. Traditional solutions, such as running the training process multiple times, are often infeasible due to computational constraints. In this paper, we introduce a novel metric framework, the Calibrated Loss Metric, designed to address this issue by reducing the variance present in its conventional counterpart. Consequently, this new metric enhances the accuracy in detecting effective modeling improvements. Our approach is substantiated by theoretical justifications and extensive experimental validations within the context of Deep Click-Through Rate Prediction Models.

cs.LG↗

arXiv2024

Singular Control of (Reflected) Brownian Motion: A Computational Method Suitable for Queueing Applications

Motivated by applications in queueing theory, we consider a class of singular stochastic control problems whose state space is the d-dimensional positive orthant. The original problem is approximated by a drift control problem, to which we apply a recently developed computational method that is feasible for dimensions up to d=30 or more. To show that nearly optimal solutions are obtainable using this method, we present computational results for a variety of examples, including queueing network examples that have appeared previously in the literature.

eess.SY↗

arXiv2024

Tackling Interference Induced by Data Training Loops in A/B Tests: A Weighted Training Approach

In modern recommendation systems, the standard pipeline involves training machine learning models on historical data to predict user behaviors and improve recommendations continuously. However, these data training loops can introduce interference in A/B tests, where data generated by control and treatment algorithms, potentially with different distributions, are combined. To address these challenges, we introduce a novel approach called weighted training. This approach entails training a model to predict the probability of each data point appearing in either the treatment or control data and subsequently applying weighted losses during model training. We demonstrate that this approach achieves the least variance among all estimators that do not cause shifts in the training distributions. Through simulation studies, we demonstrate the lower bias and variance of our approach compared to other methods.

stat.ME↗

arXiv2024

Seller-Side Experiments under Interference Induced by Feedback Loops in Two-Sided Platforms

Two-sided platforms are central to modern commerce and content sharing and often utilize A/B testing for developing new features. While user-side experiments are common, seller-side experiments become crucial for specific interventions and metrics. This paper investigates the effects of interference caused by feedback loops on seller-side experiments in two-sided platforms, with a particular focus on the counterfactual interleaving design, proposed in \citet{ha2020counterfactual,nandy2021b}. These feedback loops, often generated by pacing algorithms, cause outcomes from earlier sessions to influence subsequent ones. This paper contributes by creating a mathematical framework to analyze this interference, theoretically estimating its impact, and conducting empirical evaluations of the counterfactual interleaving design in real-world scenarios. Our research shows that feedback loops can result in misleading conclusions about the treatment effects.

stat.ME↗

arXiv2023

Distributionally Robust Batch Contextual Bandits

Policy learning using historical observational data is an important problem that has found widespread applications. Examples include selecting offers, prices, advertisements to send to customers, as well as selecting which medication to prescribe to a patient. However, existing literature rests on the crucial assumption that the future environment where the learned policy will be deployed is the same as the past environment that has generated the data -- an assumption that is often false or too coarse an approximation. In this paper, we lift this assumption and aim to learn a distributionally robust policy with incomplete observational data. We first present a policy evaluation procedure that allows us to assess how well the policy does under the worst-case environment shift. We then establish a central limit theorem type guarantee for this proposed policy evaluation scheme. Leveraging this evaluation scheme, we further propose a novel learning algorithm that is able to learn a policy that is robust to adversarial perturbations and unknown covariate shifts with a performance guarantee based on the theory of uniform convergence. Finally, we empirically test the effectiveness of our proposed algorithm in synthetic datasets and demonstrate that it provides the robustness that is missing using standard policy learning algorithms. We conclude the paper by providing a comprehensive application of our methods in the context of a real-world voting dataset.

cs.LG↗

arXiv2023

Calibration Matters: Tackling Maximization Bias in Large-scale Advertising Recommendation Systems

Calibration is defined as the ratio of the average predicted click rate to the true click rate. The optimization of calibration is essential to many online advertising recommendation systems because it directly affects the downstream bids in ads auctions and the amount of money charged to advertisers. Despite its importance, calibration optimization often suffers from a problem called "maximization bias". Maximization bias refers to the phenomenon that the maximum of predicted values overestimates the true maximum. The problem is introduced because the calibration is computed on the set selected by the prediction model itself. It persists even if unbiased predictions can be achieved on every datapoint and worsens when covariate shifts exist between the training and test sets. To mitigate this problem, we theorize the quantification of maximization bias and propose a variance-adjusting debiasing (VAD) meta-algorithm in this paper. The algorithm is efficient, robust, and practical as it is able to mitigate maximization bias problems under covariate shifts, neither incurring additional online serving costs nor compromising the ranking performance. We demonstrate the effectiveness of the proposed algorithm using a state-of-the-art recommendation neural network model on a large-scale real-world dataset.

cs.LG↗

arXiv2021

Testing Group Fairness via Optimal Transport Projections

We present a statistical testing framework to detect if a given machine learning classifier fails to satisfy a wide range of group fairness notions. The proposed test is a flexible, interpretable, and statistically rigorous tool for auditing whether exhibited biases are intrinsic to the algorithm or due to the randomness in the data. The statistical challenges, which may arise from multiple impact criteria that define group fairness and which are discontinuous on model parameters, are conveniently tackled by projecting the empirical measure onto the set of group-fair probability models using optimal transport. This statistic is efficiently computed using linear programming and its asymptotic distribution is explicitly obtained. The proposed framework can also be used to test for testing composite fairness hypotheses and fairness with multiple sensitive attributes. The optimal transport testing formulation improves interpretability by characterizing the minimal covariate perturbations that eliminate the bias observed in the audit.

stat.ML↗

arXiv2021

Confidence Regions in Wasserstein Distributionally Robust Estimation

Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance (in a Wasserstein sense) from the underlying empirical measure. While motivated by the need to identify optimal model parameters or decision choices that are robust to model misspecification, these distributionally robust estimators recover a wide range of regularized estimators, including square-root lasso and support vector machines, among others, as particular cases. This paper studies the asymptotic normality of these distributionally robust estimators as well as the properties of an optimal (in a suitable sense) confidence region induced by the Wasserstein distributionally robust optimization formulation. In addition, key properties of min-max distributionally robust optimization problems are also studied, for example, we show that distributionally robust estimators regularize the loss based on its derivative and we also derive general sufficient conditions which show the equivalence between the min-max distributionally robust optimization problem and the corresponding max-min formulation.

math.ST↗

arXiv2020

Robust Bayesian Classification Using an Optimistic Score Ratio

We build a Bayesian contextual classification model using an optimistic score ratio for robust binary classification when there is limited information on the class-conditional, or contextual, distribution. The optimistic score searches for the distribution that is most plausible to explain the observed outcomes in the testing sample among all distributions belonging to the contextual ambiguity set which is prescribed using a limited structural constraint on the mean vector and the covariance matrix of the underlying contextual distribution. We show that the Bayesian classifier using the optimistic score ratio is conceptually attractive, delivers solid statistical guarantees and is computationally tractable. We showcase the power of the proposed optimistic score ratio classifier on both synthetic and empirical data.

cs.LG↗

arXiv2020

Efficient Steady-state Simulation of High-dimensional Stochastic Networks

We propose and study an asymptotically optimal Monte Carlo estimator for steady-state expectations of a d-dimensional reflected Brownian motion. Our estimator is asymptotically optimal in the sense that it requires $\tilde{O}(d)$ (up to logarithmic factors in $d$) i.i.d. Gaussian random variables in order to output an estimate with a controlled error. Our construction is based on the analysis of a suitable multi-level Monte Carlo strategy which, we believe, can be applied widely. This is the first algorithm with linear complexity (under suitable regularity conditions) for steady-state estimation of RBM as the dimension increases.

math.PR↗

arXiv2019

Optimal Uncertainty Size in Distributionally Robust Inverse Covariance Estimation

In a recent paper, Nguyen, Kuhn, and Esfahani (2018) built a distributionally robust estimator for the precision matrix of the Gaussian distribution. The distributional uncertainty size is a key ingredient in the construction of this estimator. We develop a statistical theory which shows how to optimally choose the uncertainty size to minimize the associated Stein loss. Surprisingly, rather than the expected canonical square-root scaling rate, the optimal uncertainty size scales linearly with the sample size.

math.ST↗