Active Statistical Inference (2403.03208v2)

Abstract: Inspired by the concept of active learning, we propose active inference$\unicode{x2013}$a methodology for statistical inference with machine-learning-assisted data collection. Assuming a budget on the number of labels that can be collected, the methodology uses a machine learning model to identify which data points would be most beneficial to label, thus effectively utilizing the budget. It operates on a simple yet powerful intuition: prioritize the collection of labels for data points where the model exhibits uncertainty, and rely on the model's predictions where it is confident. Active inference constructs provably valid confidence intervals and hypothesis tests while leveraging any black-box machine learning model and handling any data distribution. The key point is that it achieves the same level of accuracy with far fewer samples than existing baselines relying on non-adaptively-collected data. This means that for the same number of collected samples, active inference enables smaller confidence intervals and more powerful p-values. We evaluate active inference on datasets from public opinion research, census analysis, and proteomics.

• The paper introduces active inference that integrates machine learning predictions to prioritize labeling high-uncertainty data points.
• The methodology adapts both batch and sequential settings to efficiently select data for inference under strict budget constraints.
• Empirical results show over 80% sample budget savings while yielding tighter confidence intervals and more powerful p-values compared to classical methods.

Active Inference: Enhancing Statistical Inference Through Machine-Learning-Assisted Data Collection

Introduction

The collection of high-quality labeled data is a significant challenge in data-driven research, constrained by budgets that limit the number of labels that can be feasibly collected. Inspired by active learning frameworks, we introduce a novel methodology termed \emph{active inference}, aimed at statistical inference with machine-learning-assisted data collection. This approach prioritizes labeling data points where predictive models exhibit uncertainty, leveraging machine learning predictions to effectively utilize the budget for label collection.

Methodology

Active inference is built upon a foundation of adaptively selecting data points for labeling, guided by the predictions from a machine learning model. The approach utilizes a sampling rule derived from the model's uncertainty, allowing for the strategic collection of labels under budget constraints. The methodology is conducive to any black-box machine learning model, offering versatility across a wide range of data distributions. Two key settings are considered: the batch setting, where labeling decisions are made all at once utilizing a pre-trained model; and the sequential setting, where the model and labeling decisions are updated iteratively as more labels are collected.

Numerical Results

Empirical evaluations show that active inference achieves significantly smaller confidence intervals and more powerful p-values with far fewer samples than classical methods that do not incorporate machine learning predictions into data collection. Notably, in datasets from public opinion research, census analysis, and proteomics, active inference demonstrated the capability to save over $80\%$ of the sample budget required by traditional inference methods.

Implications

The practical and theoretical implications of active inference are profound. The methodology not only presents a means to conduct rigorous statistical inference under stringent budget constraints but also illustrates the utility of machine learning in enhancing the efficiency of data collection strategies. From a practical standpoint, active inference enables more informed decision-making regarding which data points to label, thereby maximizing the utility derived from each label collected. Theoretically, the approach underscores the potential of integrating machine learning with traditional statistical inference methods, opening avenues for future research in this interdisciplinary field.

Future Directions

Looking ahead, the exploration of active inference in more complex and high-dimensional settings poses an interesting challenge. Further research could delve into the nuances of different data distributions and the impact of model uncertainty on the efficacy of active inference. Additionally, investigating the potential biases introduced by adaptive data collection and developing corrective measures will be crucial for broadening the applicability of this methodology.

Conclusion

Active inference represents a promising advance in the field of statistical inference, merging the predictive power of machine learning with strategic data collection. By prioritizing the collection of labels for data points where models exhibit the most uncertainty, active inference achieves higher statistical power, enabling more precise and reliable inferences with fewer resources. This methodology not only offers immediate benefits for applications constrained by labeling budgets but also sets the stage for further exploration at the intersection of machine learning and statistical inference.