This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used throughout the book and serve at a reminder of basic concepts in calculus, linear algebra and probability and also introduces some measure theoretic terminology, which can be used as a reading guide for the sections that use these tools. The introductory chapters also provide background material on matrix analysis and optimization. The latter chapter provides theoretical support to many algorithms that are used in the book, including stochastic gradient descent, proximal methods, etc. After discussing basic concepts for statistical prediction, the book includes an introduction to reproducing kernel theory and Hilbert space techniques, which are used in many places, before addressing the description of various algorithms for supervised statistical learning, including linear methods, support vector machines, decision trees, boosting, or neural networks. The subject then switches to generative methods, starting with a chapter that presents sampling methods and an introduction to the theory of Markov chains. The following chapter describe the theory of graphical models, an introduction to variational methods for models with latent variables, and to deep-learning based generative models. The next chapters focus on unsupervised learning methods, for clustering, factor analysis and manifold learning. The final chapter of the book is theory-oriented and discusses concentration inequalities and generalization bounds.

Few-shot image classifiers are designed to recognize and classify new data with minimal supervision and limited data but often show reliance on spurious correlations between classes and spurious attributes, known as spurious bias. Spurious correlations commonly hold in certain samples and few-shot classifiers can suffer from spurious bias induced from them. There is an absence of an automatic benchmarking system to assess the robustness of few-shot classifiers against spurious bias. In this paper, we propose a systematic and rigorous benchmark framework, termed FewSTAB, to fairly demonstrate and quantify varied degrees of robustness of few-shot classifiers to spurious bias. FewSTAB creates few-shot evaluation tasks with biased attributes so that using them for predictions can demonstrate poor performance. To construct these tasks, we propose attribute-based sample selection strategies based on a pre-trained vision-language model, eliminating the need for manual dataset curation. This allows FewSTAB to automatically benchmark spurious bias using any existing test data. FewSTAB offers evaluation results in a new dimension along with a new design guideline for building robust classifiers. Moreover, it can benchmark spurious bias in varied degrees and enable designs for varied degrees of robustness. Its effectiveness is demonstrated through experiments on ten few-shot learning methods across three datasets. We hope our framework can inspire new designs of robust few-shot classifiers. Our code is available at https://github.com/gtzheng/FewSTAB.

Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a comprehensive introduction to two key TML techniques, persistent homology and the Mapper algorithm, with an emphasis on practical applications. Persistent homology captures multi-scale topological features such as clusters, loops, and voids, while the Mapper algorithm creates an interpretable graph summarizing high-dimensional data. To enhance accessibility, we adopt a data-centric approach, enabling readers to gain hands-on experience applying these techniques to relevant tasks. We provide step-by-step explanations, implementations, hands-on examples, and case studies to demonstrate how these tools can be applied to real-world problems. The goal is to equip researchers and practitioners with the knowledge and resources to incorporate TML into their work, revealing insights often hidden from conventional machine learning methods. The tutorial code is available at https://github.com/cakcora/TopologyForML

Multi-output Gaussian process (MGP) is commonly used as a transfer learning method to leverage information among multiple outputs. A key advantage of MGP is providing uncertainty quantification for prediction, which is highly important for subsequent decision-making tasks. However, traditional MGP may not be sufficiently flexible to handle multivariate data with dynamic characteristics, particularly when dealing with complex temporal correlations. Additionally, since some outputs may lack correlation, transferring information among them may lead to negative transfer. To address these issues, this study proposes a non-stationary MGP model that can capture both the dynamic and sparse correlation among outputs. Specifically, the covariance functions of MGP are constructed using convolutions of time-varying kernel functions. Then a dynamic spike-and-slab prior is placed on correlation parameters to automatically decide which sources are informative to the target output in the training process. An expectation-maximization (EM) algorithm is proposed for efficient model fitting. Both numerical studies and a real case demonstrate its efficacy in capturing dynamic and sparse correlation structure and mitigating negative transfer for high-dimensional time-series data. Finally, a mountain-car reinforcement learning case highlights its potential application in decision making problems.

Chronic obstructive pulmonary disease (COPD) is a chronic inflammatory lung disease that causes obstructed airflow from the lungs. In the United States, more than 15.7 million Americans have been diagnosed with COPD, with 96% of individuals living with at least one other chronic health condition. It is the 4th leading cause of death in the country. Over 2.2 million patients are admitted to hospitals annually due to COPD exacerbations. Monitoring and predicting patient exacerbations on-time could save their life. This paper presents two different predictive models to predict COPD exacerbation using AI and natural language processing (NLP) approaches. These models use respiration summary notes, symptoms, and vital signs. To train and test these models, data records containing physiologic signals and vital signs time series were used. These records were captured from patient monitors and comprehensive clinical data obtained from hospital medical information systems for tens of thousands of Intensive Care Unit (ICU) patients. We achieved an area under the Receiver operating characteristic (ROC) curve of 0.82 in detection and prediction of COPD exacerbation.

Register Transfer Level (RTL) code optimization is crucial for enhancing the efficiency and performance of digital circuits during early synthesis stages. Currently, optimization relies heavily on manual efforts by skilled engineers, often requiring multiple iterations based on synthesis feedback. In contrast, existing compiler-based methods fall short in addressing complex designs. This paper introduces RTLRewriter, an innovative framework that leverages large models to optimize RTL code. A circuit partition pipeline is utilized for fast synthesis and efficient rewriting. A multi-modal program analysis is proposed to incorporate vital visual diagram information as optimization cues. A specialized search engine is designed to identify useful optimization guides, algorithms, and code snippets that enhance the model ability to generate optimized RTL. Additionally, we introduce a Cost-aware Monte Carlo Tree Search (C-MCTS) algorithm for efficient rewriting, managing diverse retrieved contents and steering the rewriting results. Furthermore, a fast verification pipeline is proposed to reduce verification cost. To cater to the needs of both industry and academia, we propose two benchmarking suites: the Large Rewriter Benchmark, targeting complex scenarios with extensive circuit partitioning, optimization trade-offs, and verification challenges, and the Small Rewriter Benchmark, designed for a wider range of scenarios and patterns. Our comparative analysis with established compilers such as Yosys and E-graph demonstrates significant improvements, highlighting the benefits of integrating large models into the early stages of circuit design. We provide our benchmarks at https://github.com/yaoxufeng/RTLRewriter-Bench.

Linear discriminant analysis (LDA), a traditional classification tool, suffers from limitations such as sensitivity to noise and computational challenges when dealing with non-invertible within-class scatter matrices. Traditional stepwise LDA frameworks, which iteratively select the most informative features, often exacerbate these issues by relying heavily on Wilks' $\Lambda$, potentially causing premature stopping of the selection process. This paper introduces a novel forward discriminant analysis framework that integrates Pillai's trace with Uncorrelated Linear Discriminant Analysis (ULDA) to address these challenges, and offers a unified and stand-alone classifier. Through simulations and real-world datasets, the new framework demonstrates effective control of Type I error rates and improved classification accuracy, particularly in cases involving perfect group separations. The results highlight the potential of this approach as a robust alternative to the traditional stepwise LDA framework.

Data scarcity poses a serious threat to modern machine learning and artificial intelligence, as their practical success typically relies on the availability of big datasets. One effective strategy to mitigate the issue of insufficient data is to first harness information from other data sources possessing certain similarities in the study design stage, and then employ the multi-task or meta learning framework in the analysis stage. In this paper, we focus on multi-task (or multi-source) linear models whose coefficients across tasks share an invariant low-rank component, a popular structural assumption considered in the recent multi-task or meta learning literature. Under this assumption, we propose a new algorithm, called Meta Subspace Pursuit (abbreviated as Meta-SP), that provably learns this invariant subspace shared by different tasks. Under this stylized setup for multi-task or meta learning, we establish both the algorithmic and statistical guarantees of the proposed method. Extensive numerical experiments are conducted, comparing Meta-SP against several competing methods, including popular, off-the-shelf model-agnostic meta learning algorithms such as ANIL. These experiments demonstrate that Meta-SP achieves superior performance over the competing methods in various aspects.

Mutagenicity is a concern due to its association with genetic mutations which can result in a variety of negative consequences, including the development of cancer. Earlier identification of mutagenic compounds in the drug development process is therefore crucial for preventing the progression of unsafe candidates and reducing development costs. While computational techniques, especially machine learning models have become increasingly prevalent for this endpoint, they rely on a single modality. In this work, we introduce a novel stacked ensemble based mutagenicity prediction model which incorporate multiple modalities such as simplified molecular input line entry system (SMILES) and molecular graph. These modalities capture diverse information about molecules such as substructural, physicochemical, geometrical and topological. To derive substructural, geometrical and physicochemical information, we use SMILES, while topological information is extracted through a graph attention network (GAT) via molecular graph. Our model uses a stacked ensemble of machine learning classifiers to make predictions using these multiple features. We employ the explainable artificial intelligence (XAI) technique SHAP (Shapley Additive Explanations) to determine the significance of each classifier and the most relevant features in the prediction. We demonstrate that our method surpasses SOTA methods on two standard datasets across various metrics. Notably, we achieve an area under the curve of 95.21\% on the Hansen benchmark dataset, affirming the efficacy of our method in predicting mutagenicity. We believe that this research will captivate the interest of both clinicians and computational biologists engaged in translational research.

Streaming data analysis is increasingly required in applications, e.g., IoT, cybersecurity, robotics, mechatronics or cyber-physical systems. Despite its relevance, it is still an emerging field with open challenges. SDO is a recent anomaly detection method designed to meet requirements of speed, interpretability and intuitive parameterization. In this work, we present SDOoop, which extends the capabilities of SDO's streaming version to retain temporal information of data structures. SDOoop spots contextual anomalies undetectable by traditional algorithms, while enabling the inspection of data geometries, clusters and temporal patterns. We used SDOoop to model real network communications in critical infrastructures and extract patterns that disclose their dynamics. Moreover, we evaluated SDOoop with data from intrusion detection and natural science domains and obtained performances equivalent or superior to state-of-the-art approaches. Our results show the high potential of new model-based methods to analyze and explain streaming data. Since SDOoop operates with constant per-sample space and time complexity, it is ideal for big data, being able to instantly process large volumes of information. SDOoop conforms to next-generation machine learning, which, in addition to accuracy and speed, is expected to provide highly interpretable and informative models.