This paper studies how to integrate historical control data with experimental data to enhance A/B testing, while addressing the distributional shift between historical and experimental datasets. We propose a pessimistic data integration method that combines two causal effect estimators constructed based on experimental and historical datasets. Our main idea is to conceptualize the weight function for this combination as a policy so that existing pessimistic policy learning algorithms are applicable to learn the optimal weight that minimizes the resulting weighted estimator's mean squared error. Additionally, we conduct comprehensive theoretical and empirical analyses to compare our method against various baseline estimators across five scenarios. Both our theoretical and numerical findings demonstrate that the proposed estimator achieves near-optimal performance across all scenarios.

We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated learning, crowdsourcing, and sensor networks, yet existing robust estimators typically assume uniform or worst-case corruption, ignoring structural heterogeneity. For mean estimation for multivariate bounded distributions and univariate gaussian distributions, we give tight minimax rates for all heterogeneous corruption patterns. For multivariate gaussian mean estimation and linear regression, we establish the minimax rate for squared error up to a factor of d, where d is the dimension. Roughly, our findings suggest that samples beyond a certain corruption threshold may be discarded by the optimal estimators - this threshold is determined by the empirical distribution of the corruption rates given.

We study gradient descent (GD) with a constant stepsize for ℓ2-regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensure monotonic reduction of the optimization objective, achieving exponential convergence in eO(κ) steps with κ being the condition number. Surprisingly, we show that this can be accelerated to eO( κ)by simply using a large stepsize--for which the objective evolves nonmonotonically. The acceleration brought by large stepsizes extends to minimizing the population risk for separable distributions, improving on the best-known upper bounds on the number of steps to reach a nearoptimum. Finally, we characterize the largest stepsize for the local convergence of GD, which also determines the global convergence in special scenarios. Our results extend the analysis of Wu et al. (2024) from convex settings with minimizers at infinity to strongly convex cases with finite minimizers.

Transfer learning is a powerful paradigm for leveraging knowledge from source domains to enhance learning in a target domain. However, traditional transfer learning approaches often focus on scalar or multivariate data within Euclidean spaces, limiting their applicability to complex data structures such as probability distributions. To address this limitation, we introduce a novel transfer learning framework for regression models whose outputs are probability distributions residing in the Wasserstein space. When the informative subset of transferable source domains is known, we propose an estimator with provable asymptotic convergence rates, quantifying the impact of domain similarity on transfer efficiency. For cases where the informative subset is unknown, we develop a data-driven transfer learning procedure designed to mitigate negative transfer. The proposed methods are supported by rigorous theoretical analysis and are validated through extensive simulations and real-world applications. The code is available at https://github.com/h7nian/WaTL.

The technique of data augmentation (DA) is often used in machine learning for regularization purposes to better generalize under i.i.d.

In this paper, we explore the asymptotically optimal tuning parameter choice in ridge regression for estimating nuisance functions of a statistical functional that has recently gained prominence in conditional independence testing and causal inference. Given a sample of size n, we study estimators of the Expected Conditional Covariance (ECC) between variables Y and Agiven a high-dimensional covariate X Rp. Under linear regression models for Y and A on X and the proportional asymptotic regime p/n c (0,), we evaluate three existing ECC estimators and two sample splitting strategies for estimating the required nuisance functions. Since no consistent estimator of the nuisance functions exists in the proportional asymptotic regime without imposing further structure on the problem, we first derive debiased versions of the ECC estimators that utilize the ridge regression nuisance function estimators. We show that our bias correction strategy yields n-consistent estimators of the ECC across different sample splitting strategies and estimator choices. We then derive the asymptotic variances of these debiased estimators to illustrate the nuanced interplay between the sample splitting strategy, estimator choice, and tuning parameters of the nuisance function estimators for optimally estimating the ECC. Our analysis reveals that prediction-optimal tuning parameters (i.e., those that optimally estimate the nuisance functions) may not lead to the lowest asymptotic variance of the ECC estimator - thereby demonstrating the need to be careful in selecting tuning parameters based on the final goal of inference. Finally, we verify our theoretical results through extensive numerical experiments.

Most existing transfer learning algorithms for high-dimensional models employ a two-step regularization framework, whose success heavily hinges on the assumption that the pre-trained model closely resembles the target. To relax this assumption, we propose a co-regularization process to directly exploit beneficial knowledge from the source domain for high-dimensional generalized linear models. The proposed method learns the target parameter by constraining the source parameters to be close to the target one, thereby preventing fine-tuning failures caused by significantly deviated pre-trained parameters. Our theoretical analysis demonstrates that the proposed method accommodates a broader range of sources than existing two-step frameworks, thus being more robust to less similar sources. Its effectiveness is validated through extensive empirical studies.

Invariant object recognition-the ability to identify objects despite changes in appearance-is a hallmark of visual processing in the brain, yet its understanding remains a central challenge in systems neuroscience. Artificial neural networks trained to predict neural responses to visual stimuli ("digital twins") could provide a powerful framework for studying such complex computations in silico. However, while current models accurately capture single-neuron responses within individual visual areas, their ability to reproduce how populations of neurons represent object identity, and how these representations transform across the cortical hierarchy, remains largely unexplored. Here we examine key functional signatures observed experimentally and find that current models account for hierarchical changes in basic single-neuron properties, such as receptive field size, but fail to capture more complex population-level phenomena, particularly invariant object representations. To address this gap, we introduce a biologically inspired hierarchical readout scheme that mirrors cortical anatomy, modeling each visual area as a projection from a distinct depth within a shared core network. This approach significantly improves the prediction of population-level representational transformations, outperforming standard models that use only the final layer, as well as alternatives with modified architecture, regularization, and loss function. Our results suggest that incorporating anatomical information provides a strong inductive bias in digital twin models, enabling them to better capture general principles of brain function.

Transformer architectures can solve unseen tasks based on input-output pairs in a given prompt due to in-context learning (ICL). Existing theoretical studies on ICL have mainly focused on linear regression tasks, often with i.i.d.

Characterizing interactions between brain areas is a fundamental goal of systems neuroscience. While such analyses are possible when areas are recorded simultaneously, it is rare to observe all combinations of areas of interest within a single animal or recording session. How can we leverage multi-animal datasets to better understand multi-area interactions? Building on recent progress in large-scale, multi-animal models, we introduce NeuroPaint, a masked autoencoding approach for inferring the dynamics of unrecorded brain areas. By training across animals with overlapping subsets of recorded areas, NeuroPaint learns to reconstruct activity in missing areas based on shared structure across individuals. We train and evaluate our approach on synthetic data and two multi-animal, multi-area Neuropixels datasets. Our results demonstrate that models trained across animals with partial observations can successfully in-paint the dynamics of unrecorded areas, enabling 39th Conference on Neural Information Processing Systems (NeurIPS 2025).