Grant: Discovery Grants Program - Individual

While statistical inference and learning have achieved remarkable success in many domains, their effectiveness hinges on the assumption of precisely and completely measured variables. In practice, however, noisy data with measurement error and missing values are pervasive, posing substantial challenges to accurate analysis and inference. The far-reaching vision of my research program aims to address the challenges posed by noisy data, bridging the gaps in statistics, biostatistics, and data science. The long-term objective is to introduce innovative methodologies that push the boundaries of these fields, while providing valuable insights and practical solutions for real-world applications. One of the primary short-term objectives is to investigate causal inference with missingness, censoring, and measurement error. I will assess the performance of naive methods that ignore missing data and measurement error and develop correction methods to mitigate their biases. Furthermore, I will explore the effects of measurement error on causal inference and investigate strategies to handle unmeasured confounders and missing observations. In addition to causal inference, this research proposal encompasses classification with missingness, measurement error, and high-dimensional covariates. I aim to extend existing binary classification research to multi-class and multi-label classification scenarios with noisy labels. My goal is to investigate the biases arising from ignoring missing labels or mis-labels and develop correction methods to enhance classification accuracy. Another crucial aspect I plan to address is variable selection in high-dimensional data with measurement error. By refining existing methods, I intend to identify relevant variables and improve the performance of classification models. Furthermore, it is important to assess the learnability of data subject to measurement error. Understanding the limitations and possibilities of learning from mismeasured data is crucial for practical applications. I will develop a foundational framework that defines and examines strong and weak learnability in the presence of measurement error. I plan to identify necessary and/or sufficient conditions for these types of learnability in classification and regression problems. Beyond these specific areas, my proposal embraces research concerning survival data analysis, handling noisy data, and leveraging machine learning techniques for genuine applications. The proposed research will focus on the detection and correction of label noise, and inference methods for data with multiple annotations in the platform with big data. The ultimate goal is to develop robust and interpretable models that enhance accuracy, reliability, and decision-making across various domains.