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.

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.

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.

Unsupervised out-of-distribution (U-OOD) detection is to identify OOD data samples with a detector trained solely on unlabeled in-distribution (ID) data. The likelihood function estimated by a deep generative model (DGM) could be a natural detector, but its performance is limited in some popular "hard" benchmarks, such as FashionMNIST (ID) vs. MNIST (OOD). Recent studies have developed various detectors based on DGMs to move beyond likelihood. However, despite their success on "hard" benchmarks, most of them struggle to consistently surpass or match the performance of likelihood on some "non-hard" cases, such as SVHN (ID) vs. CIFAR10 (OOD) where likelihood could be a nearly perfect detector. Therefore, we appeal for more attention to incremental effectiveness on likelihood, i.e., whether a method could always surpass or at least match the performance of likelihood in U-OOD detection. We first investigate the likelihood of variational DGMs and find its detection performance could be improved in two directions: i) alleviating latent distribution mismatch, and ii) calibrating the dataset entropy-mutual integration. Then, we apply two techniques for each direction, specifically post-hoc prior and dataset entropy-mutual calibration. The final method, named Resultant, combines these two directions for better incremental effectiveness compared to either technique alone. Experimental results demonstrate that the Resultant could be a new state-of-the-art U-OOD detector while maintaining incremental effectiveness on likelihood in a wide range of tasks.

The rapid evolution of mobile networks from 5G to 6G has necessitated the development of autonomous network management systems, such as Zero-Touch Networks (ZTNs). However, the increased complexity and automation of these networks have also escalated cybersecurity risks. Existing Intrusion Detection Systems (IDSs) leveraging traditional Machine Learning (ML) techniques have shown effectiveness in mitigating these risks, but they often require extensive manual effort and expert knowledge. To address these challenges, this paper proposes an Automated Machine Learning (AutoML)-based autonomous IDS framework towards achieving autonomous cybersecurity for next-generation networks. To achieve autonomous intrusion detection, the proposed AutoML framework automates all critical procedures of the data analytics pipeline, including data pre-processing, feature engineering, model selection, hyperparameter tuning, and model ensemble. Specifically, it utilizes a Tabular Variational Auto-Encoder (TVAE) method for automated data balancing, tree-based ML models for automated feature selection and base model learning, Bayesian Optimization (BO) for hyperparameter optimization, and a novel Optimized Confidence-based Stacking Ensemble (OCSE) method for automated model ensemble. The proposed AutoML-based IDS was evaluated on two public benchmark network security datasets, CICIDS2017 and 5G-NIDD, and demonstrated improved performance compared to state-of-the-art cybersecurity methods. This research marks a significant step towards fully autonomous cybersecurity in next-generation networks, potentially revolutionizing network security applications.

Bayesian observer and actor models have provided normative explanations for many behavioral phenomena in perception, sensorimotor control, and other areas of cognitive science and neuroscience. They attribute behavioral variability and biases to different interpretable entities such as perceptual and motor uncertainty, prior beliefs, and behavioral costs. However, when extending these models to more complex tasks with continuous actions, solving the Bayesian decision-making problem is often analytically intractable. Moreover, inverting such models to perform inference over their parameters given behavioral data is computationally even more difficult. Therefore, researchers typically constrain their models to easily tractable components, such as Gaussian distributions or quadratic cost functions, or resort to numerical methods. To overcome these limitations, we amortize the Bayesian actor using a neural network trained on a wide range of different parameter settings in an unsupervised fashion. Using the pre-trained neural network enables performing gradient-based Bayesian inference of the Bayesian actor model's parameters. We show on synthetic data that the inferred posterior distributions are in close alignment with those obtained using analytical solutions where they exist. Where no analytical solution is available, we recover posterior distributions close to the ground truth. We then show that identifiability problems between priors and costs can arise in more complex cost functions. Finally, we apply our method to empirical data and show that it explains systematic individual differences of behavioral patterns.

Cycling has gained global popularity for its health benefits and positive urban impacts. To effectively promote cycling, early studies have extensively investigated the relationship between cycling behaviors and environmental factors, especially cyclists' preferences when making route decisions. However, these studies often struggle to comprehensively describe detailed cycling procedures at a large scale due to data limitations, and they tend to overlook the complex nature of cyclists' preferences. To address these issues, we propose a novel framework aimed to quantify and interpret cyclists' complicated street visual preferences from cycling records by leveraging maximum entropy deep inverse reinforcement learning (MEDIRL) and explainable artificial intelligence (XAI). Implemented in Bantian Sub-district, Shenzhen, we adapt MEDIRL model for efficient estimation of cycling reward function by integrating dockless-bike-sharing (DBS) trajectory and street view images (SVIs), which serves as a representation of cyclists' preferences for street visual environments during routing. In addition, we demonstrate the feasibility and reliability of MEDIRL in discovering cyclists' street visual preferences. Further analysis reveals the nonlinear and interactive effects of street visual elements on cyclists' preferences, offering a holistic perspective on streetscape design. Our proposed framework advances the understanding of individual cycling behaviors and provides actionable insights for urban planners to design bicycle-friendly streetscapes that prioritize cyclists' preferences.

Efficient management of infrastructure systems is crucial for economic stability, sustainability, and public safety. However, infrastructure management is challenging due to the vast scale of systems, stochastic deterioration of components, partial observability, and resource constraints. While data-driven approaches like reinforcement learning (RL) offer a promising avenue for optimizing management policies, their application to infrastructure has been limited by the lack of suitable simulation environments. We introduce InfraLib, a comprehensive framework for modeling and analyzing infrastructure management problems. InfraLib employs a hierarchical, stochastic approach to realistically model infrastructure systems and their deterioration. It supports practical functionality such as modeling component unavailability, cyclical budgets, and catastrophic failures. To facilitate research, InfraLib provides tools for expert data collection, simulation-driven analysis, and visualization. We demonstrate InfraLib's capabilities through case studies on a real-world road network and a synthetic benchmark with 100,000 components.

This work studies offline Reinforcement Learning (RL) in a class of non-Markovian environments called Regular Decision Processes (RDPs). In RDPs, the unknown dependency of future observations and rewards from the past interactions can be captured by some hidden finite-state automaton. For this reason, many RDP algorithms first reconstruct this unknown dependency using automata learning techniques. In this paper, we show that it is possible to overcome two strong limitations of previous offline RL algorithms for RDPs, notably RegORL. This can be accomplished via the introduction of two original techniques: the development of a new pseudometric based on formal languages, which removes a problematic dependency on $L_\infty^\mathsf{p}$-distinguishability parameters, and the adoption of Count-Min-Sketch (CMS), instead of naive counting. The former reduces the number of samples required in environments that are characterized by a low complexity in language-theoretic terms. The latter alleviates the memory requirements for long planning horizons. We derive the PAC sample complexity bounds associated to each of these techniques, and we validate the approach experimentally.

Causal Temporal Representation Learning (Ctrl) methods aim to identify the temporal causal dynamics of complex nonstationary temporal sequences. Despite the success of existing Ctrl methods, they require either directly observing the domain variables or assuming a Markov prior on them. Such requirements limit the application of these methods in real-world scenarios when we do not have such prior knowledge of the domain variables. To address this problem, this work adopts a sparse transition assumption, aligned with intuitive human understanding, and presents identifiability results from a theoretical perspective. In particular, we explore under what conditions on the significance of the variability of the transitions we can build a model to identify the distribution shifts. Based on the theoretical result, we introduce a novel framework, Causal Temporal Representation Learning with Nonstationary Sparse Transition (CtrlNS), designed to leverage the constraints on transition sparsity and conditional independence to reliably identify both distribution shifts and latent factors. Our experimental evaluations on synthetic and real-world datasets demonstrate significant improvements over existing baselines, highlighting the effectiveness of our approach.