Moulinath Banerjee

Subha Maity, Mikhail Yurochkin, Moulinath Banerjee et al.

Deploying machine learning models to new tasks is a major challenge despite the large size of the modern training datasets. However, it is conceivable that the training data can be reweighted to be more representative of the new (target) task. We consider the problem of reweighing the training samples to gain insights into the distribution of the target task. Specifically, we formulate a distribution shift model based on the exponential tilt assumption and learn train data importance weights minimizing the KL divergence between labeled train and unlabeled target datasets. The learned train data weights can then be used for downstream tasks such as target performance evaluation, fine-tuning, and model selection. We demonstrate the efficacy of our method on Waterbirds and Breeds benchmarks.

Daniele Bracale, Moulinath Banerjee, Cong Shi et al.

We study a sequential price competition among $N$ sellers, each influenced by the pricing decisions of their rivals. Specifically, the demand function for each seller $i$ follows the single index model $λ_i(\mathbf p) = μ_i(\langle \boldsymbol θ_{i,0}, \mathbf p \rangle)$, with known increasing link $μ_i$ and unknown parameter $\boldsymbol θ_{i,0}$, where the vector $\mathbf{p}$ denotes the vector of prices offered by all the sellers simultaneously at a given instant. Each seller observes only their own realized demand - unobservable to competitors - and the prices set by rivals. We propose a novel decentralized policy, PML-GLUCB, that combines penalized MLE with an upper-confidence pricing rule. Our approach (i) \emph{removes the need for coordinated front-loaded exploration phases across sellers} - which is integral to previous models - making our method aligned with realistic market conditions; (ii) generalizes existing approaches that focus solely on linear demand models; (iii) accommodates both binary and real-valued demand observations. Relative to a dynamic benchmark policy, each seller achieves $\widetilde{O}(\sqrt{T})$ regret, which matches the optimal rate known in the linear setting.

Subha Maity, Debarghya Mukherjee, Moulinath Banerjee et al.

Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process is often continuous in nature. We exploit this underlying continuity by developing predictor-corrector algorithms for time-varying stochastic optimizations. We provide error bounds for the iterates, both in presence of pure and noisy access to the queries from the relevant derivatives of the loss function. Furthermore, we show (theoretically and empirically in several examples) that our method outperforms non-predictor corrector methods that do not exploit the underlying continuous process.

Felipe Maia Polo, Yuekai Sun, Moulinath Banerjee

Conditional independence (CI) testing is a fundamental and challenging task in modern statistics and machine learning. Many modern methods for CI testing rely on powerful supervised learning methods to learn regression functions or Bayes predictors as an intermediate step; we refer to this class of tests as regression-based tests. Although these methods are guaranteed to control Type-I error when the supervised learning methods accurately estimate the regression functions or Bayes predictors of interest, their behavior is less understood when they fail due to misspecified inductive biases; in other words, when the employed models are not flexible enough or when the training algorithm does not induce the desired predictors. Then, we study the performance of regression-based CI tests under misspecified inductive biases. Namely, we propose new approximations or upper bounds for the testing errors of three regression-based tests that depend on misspecification errors. Moreover, we introduce the Rao-Blackwellized Predictor Test (RBPT), a regression-based CI test robust against misspecified inductive biases. Finally, we conduct experiments with artificial and real data, showcasing the usefulness of our theory and methods.

Jiwoo Han, Moulinath Banerjee, Yuekai Sun

When deploying a single predictor across multiple subpopulations, we propose a fundamentally different approach: interpreting group fairness as a bargaining problem among subpopulations. This game-theoretic perspective reveals that existing robust optimization methods such as minimizing worst-group loss or regret correspond to classical bargaining solutions and embody different fairness principles. We propose relative improvement, the ratio of actual risk reduction to potential reduction from a baseline predictor, which recovers the Kalai-Smorodinsky solution. Unlike absolute-scale methods that may not be comparable when groups have different potential predictability, relative improvement provides axiomatic justification including scale invariance and individual monotonicity. We establish finite-sample convergence guarantees under mild conditions.

Daniele Bracale, Moulinath Banerjee, Yuekai Sun et al.

We propose a shape-constrained approach to dynamic pricing for censored data in the linear valuation model eliminating the need for tuning parameters commonly required by existing methods. Previous works have addressed the challenge of unknown market noise distribution $F_0$ using strategies ranging from kernel methods to reinforcement learning algorithms, such as bandit techniques and upper confidence bounds (UCB), under the assumption that $F_0$ satisfies Lipschitz (or stronger) conditions. In contrast, our method relies on isotonic regression under the weaker assumption that $F_0$ is $α$-Hölder continuous for some $α\in (0,1]$, for which we derive a regret upper bound. Simulations and experiments with real-world data obtained by Welltower Inc (a major healthcare Real Estate Investment Trust) consistently demonstrate that our method attains lower empirical regret in comparison to several existing methods in the literature while offering the advantage of being tuning-parameter free.

Daniele Bracale, Moulinath Banerjee, Cong Shi et al.

We consider price competition among multiple sellers over a selling horizon of $T$ periods. In each period, sellers simultaneously offer their prices (which are made public) and subsequently observe their respective demand (not made public). The demand function of each seller depends on all sellers' prices through a private, unknown, and nonlinear relationship. We propose a dynamic pricing policy that uses semi-parametric least-squares estimation and show that when the sellers employ our policy, their prices converge at a rate of $O(T^{-1/7})$ to the Nash equilibrium prices that sellers would reach if they were fully informed. Each seller incurs a regret of $O(T^{5/7})$ relative to a dynamic benchmark policy. A theoretical contribution of our work is proving the existence of equilibrium under shape-constrained demand functions via the concept of $s$-concavity and establishing regret bounds of our proposed policy. Technically, we also establish new concentration results for the least squares estimator under shape constraints. Our findings offer significant insights into dynamic competition-aware pricing and contribute to the broader study of non-parametric learning in strategic decision-making.

Pramit Das, Moulinath Banerjee, Yuekai Sun

With the growing use of AI technology, many police departments use forecasting software to predict probable crime hotspots and allocate patrolling resources effectively for crime prevention. The clustered nature of crime data makes self-exciting Hawkes processes a popular modeling choice. However, one significant challenge in fitting such models is the inherent missingness in crime data due to non-reporting, which can bias the estimated parameters of the predictive model, leading to inaccurate downstream hotspot forecasts, often resulting in over or under-policing in various communities, especially the vulnerable ones. Our work introduces a Wasserstein Generative Adversarial Networks (WGAN) driven likelihood-free approach to account for unreported crimes in Spatiotemporal Hawkes models. We demonstrate through empirical analysis how this methodology improves the accuracy of parametric estimation in the presence of data missingness, leading to more reliable and efficient policing strategies.

Daniele Bracale, Subha Maity, Felipe Maia Polo et al.

Often in prediction tasks, the predictive model itself can influence the distribution of the target variable, a phenomenon termed performative prediction. Generally, this influence stems from strategic actions taken by stakeholders with a vested interest in predictive models. A key challenge that hinders the widespread adaptation of performative prediction in machine learning is that practitioners are generally unaware of the social impacts of their predictions. To address this gap, we propose a methodology for learning the distribution map that encapsulates the long-term impacts of predictive models on the population. Specifically, we model agents' responses as a cost-adjusted utility maximization problem and propose estimates for said cost. Our approach leverages optimal transport to align pre-model exposure (ex ante) and post-model exposure (ex post) distributions. We provide a rate of convergence for this proposed estimate and assess its quality through empirical demonstrations on a credit-scoring dataset.

Felipe Maia Polo, Xinhe Wang, Mikhail Yurochkin et al.

Large language models are increasingly used as judges (LLM-as-a-judge) to evaluate model outputs at scale, but their assessments often diverge systematically from human judgments. We present Bridge, a unified statistical framework that explicitly bridges human and LLM evaluations under both absolute scoring and pairwise comparison paradigms. Bridge posits a latent human preference score for each prompt-response pair and models LLM deviations as linear transformations of covariates that capture sources of discrepancies. This offers a simple and principled framework for refining LLM ratings and characterizing systematic discrepancies between humans and LLMs. We provide an efficient fitting algorithm with asymptotic guarantees for statistical inference. Using six LLM judges and two benchmarks (BigGen Bench and Chatbot Arena), Bridge achieves higher agreement with human ratings (accuracy, calibration, and KL divergence) and exposes systematic human-LLM gaps.

Felipe Maia Polo, Subha Maity, Mikhail Yurochkin et al.

Programmatic Weak Supervision (PWS) enables supervised model training without direct access to ground truth labels, utilizing weak labels from heuristics, crowdsourcing, or pre-trained models. However, the absence of ground truth complicates model evaluation, as traditional metrics such as accuracy, precision, and recall cannot be directly calculated. In this work, we present a novel method to address this challenge by framing model evaluation as a partial identification problem and estimating performance bounds using Fréchet bounds. Our approach derives reliable bounds on key metrics without requiring labeled data, overcoming core limitations in current weak supervision evaluation techniques. Through scalable convex optimization, we obtain accurate and computationally efficient bounds for metrics including accuracy, precision, recall, and F1-score, even in high-dimensional settings. This framework offers a robust approach to assessing model quality without ground truth labels, enhancing the practicality of weakly supervised learning for real-world applications.

Debarghya Mukherjee, Mikhail Yurochkin, Moulinath Banerjee et al.

Individual fairness is an intuitive definition of algorithmic fairness that addresses some of the drawbacks of group fairness. Despite its benefits, it depends on a task specific fair metric that encodes our intuition of what is fair and unfair for the ML task at hand, and the lack of a widely accepted fair metric for many ML tasks is the main barrier to broader adoption of individual fairness. In this paper, we present two simple ways to learn fair metrics from a variety of data types. We show empirically that fair training with the learned metrics leads to improved fairness on three machine learning tasks susceptible to gender and racial biases. We also provide theoretical guarantees on the statistical performance of both approaches.

Subha Maity, Yuekai Sun, Moulinath Banerjee

We study the minimax rates of the label shift problem in non-parametric classification. In addition to the unsupervised setting in which the learner only has access to unlabeled examples from the target domain, we also consider the setting in which a small number of labeled examples from the target domain is available to the learner. Our study reveals a difference in the difficulty of the label shift problem in the two settings, and we attribute this difference to the availability of data from the target domain to estimate the class conditional distributions in the latter setting. We also show that a class proportion estimation approach is minimax rate-optimal in the unsupervised setting.

Subha Maity, Yuekai Sun, Moulinath Banerjee

We consider the task of meta-analysis in high-dimensional settings in which the data sources are similar but non-identical. To borrow strength across such heterogeneous datasets, we introduce a global parameter that emphasizes interpretability and statistical efficiency in the presence of heterogeneity. We also propose a one-shot estimator of the global parameter that preserves the anonymity of the data sources and converges at a rate that depends on the size of the combined dataset. For high-dimensional linear model settings, we demonstrate the superiority of our identification restrictions in adapting to a previously seen data distribution as well as predicting for a new/unseen data distribution. Finally, we demonstrate the benefits of our approach on a large-scale drug treatment dataset involving several different cancer cell-lines.

Monika Bhattacharjee, Moulinath Banerjee, George Michailidis

We consider the problem of estimating the location of a single change point in a dynamic stochastic block model. We propose two methods of estimating the change point, together with the model parameters. The first employs a least squares criterion function and takes into consideration the full structure of the stochastic block model and is evaluated at each point in time. Hence, as an intermediate step, it requires estimating the community structure based on a clustering algorithm at every time point. The second method comprises of the following two steps: in the first one, a least squares function is used and evaluated at each time point, but ignores the community structures and just considers a random graph generating mechanism exhibiting a change point. Once the change point is identified, in the second step, all network data before and after it are used together with a clustering algorithm to obtain the corresponding community structures and subsequently estimate the generating stochastic block model parameters. A comparison between these two methods is illustrated. Further, for both methods under their respective identifiability and certain additional regularity conditions, we establish rates of convergence and derive the asymptotic distributions of the change point estimators. The results are illustrated on synthetic data.