Machine Learning (stat.ML)

Abstract: This work is concerned with the use of Gaussian surrogate models for Bayesian inverse problems associated with linear partial differential equations. A particular focus is on the regime where only a small amount of training data is available. In this regime the type of Gaussian prior used is of critical importance with respect to how well the surrogate model will perform in terms of Bayesian inversion. We extend the framework of Raissi et. al. (2017) to construct PDE-informed Gaussian priors that we then use to construct different approximate posteriors. A number of different numerical experiments illustrate the superiority of the PDE-informed Gaussian priors over more traditional priors.

Abstract: Interpretability is a crucial aspect of machine learning models that enables humans to understand and trust the decision-making process of these models. In many real-world applications, the interpretability of models is essential for legal, ethical, and practical reasons. For instance, in the banking domain, interpretability is critical for lenders and borrowers to understand the reasoning behind the acceptance or rejection of loan applications as per fair lending laws. However, achieving interpretability in machine learning models is challenging, especially for complex high-performance models. Hence Explainable Boosting Machines (EBMs) have been gaining popularity due to their interpretable and high-performance nature in various prediction tasks. However, these models can suffer from issues such as spurious interactions with redundant features and single-feature dominance across all interactions, which can affect the interpretability and reliability of the model's predictions. In this paper, we explore novel approaches to address these issues by utilizing alternate Cross-feature selection, ensemble features and model configuration alteration techniques. Our approach involves a multi-step feature selection procedure that selects a set of candidate features, ensemble features and then benchmark the same using the EBM model. We evaluate our method on three benchmark datasets and show that the alternate techniques outperform vanilla EBM methods, while providing better interpretability and feature selection stability, and improving the model's predictive performance. Moreover, we show that our approach can identify meaningful interactions and reduce the dominance of single features in the model's predictions, leading to more reliable and interpretable models. Index Terms- Interpretability, EBM's, ensemble, feature selection.

Abstract: Single-cell technologies have provided valuable insights into the distribution of molecular features, such as gene expression and epigenomic modifications. However, comparing these complex distributions in a controlled and powerful manner poses methodological challenges. Here we propose to benefit from the kernel-testing framework to compare the complex cell-wise distributions of molecular features in a non-linear manner based on their kernel embedding. Our framework not only allows for feature-wise analyses but also enables global comparisons of transcriptomes or epigenomes, considering their intricate dependencies. By using a classifier to discriminate cells based on the variability of their embedding, our method uncovers heterogeneities in cell populations that would otherwise go undetected. We show that kernel testing overcomes the limitations of differential analysis methods dedicated to single-cell. Kernel testing is applied to investigate the reversion process of differentiating cells, successfully identifying cells in transition between reversion and differentiation stages. Additionally, we analyze single-cell ChIP-Seq data and identify a subpopulation of untreated breast cancer cells that exhibit an epigenomic profile similar to persister cells.

Abstract: Colorectal cancer is a deadly disease that has become increasingly prevalent in recent years. Early detection is crucial for saving lives, but traditional diagnostic methods such as colonoscopy and biopsy have limitations. Colonoscopy cannot provide detailed information within the tissues affected by cancer, while biopsy involves tissue removal, which can be painful and invasive. In order to improve diagnostic efficiency and reduce patient suffering, we studied machine-learningbased approach for colorectal tissue classification that uses acoustic resolution photoacoustic microscopy (ARPAM). With this tool, we were able to classify benign and malignant tissue using multiple machine learning methods. Our results were analyzed both quantitatively and qualitatively to evaluate the effectiveness of our approach.