Maximum Likelihood Estimation of continuous variable models can be very challenging in high dimensions, due to potentially complex probability distributions. The existence of multiple interdependencies among variables can make it very difficult to establish convergence guarantees. This leads to a wide use of brute-force methods, such as grid searching and Monte-Carlo sampling and, when applicable, complex and problem-specific algorithms. In this paper, we consider inference problems where the variables are related by multiaffine expressions. We propose a novel Alternating and Iteratively-Reweighted Least Squares (AIRLS) algorithm, and prove its convergence for problems with Generalized Normal Distributions. We also provide an efficient method to compute the variance of the estimates obtained using AIRLS. Finally, we show how the method can be applied to graphical statistical models. We perform numerical experiments on several inference problems, showing significantly better performance than state-of-the-art approaches in terms of scalability, robustness to noise, and convergence speed due to an empirically observed super-linear convergence rate.

The premise of semi-supervised learning (SSL) is that combining labeled and unlabeled data yields significantly more accurate models. Despite empirical successes, the theoretical understanding of SSL is still far from complete. In this work, we study SSL for high dimensional sparse Gaussian classification. To construct an accurate classifier a key task is feature selection, detecting the few variables that separate the two classes. % For this SSL setting, we analyze information theoretic lower bounds for accurate feature selection as well as computational lower bounds, assuming the low-degree likelihood hardness conjecture. % Our key contribution is the identification of a regime in the problem parameters (dimension, sparsity, number of labeled and unlabeled samples) where SSL is guaranteed to be advantageous for classification. Specifically, there is a regime where it is possible to construct in polynomial time an accurate SSL classifier. However, % any computationally efficient supervised or unsupervised learning schemes, that separately use only the labeled or unlabeled data would fail. Our work highlights the provable benefits of combining labeled and unlabeled data for {classification and} feature selection in high dimensions. We present simulations that complement our theoretical analysis.

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.

Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds sample size, penalized methods like lasso have been developed to address sparsity challenges. Bayesian methods, initially connected to quantile regression via the asymmetric Laplace likelihood, have also evolved, though issues with posterior variance have led to new approaches, including pseudo/score likelihoods. This paper presents a novel probabilistic machine learning approach for high-dimensional quantile prediction. It uses a pseudo-Bayesian framework with a scaled Student-t prior and Langevin Monte Carlo for efficient computation. The method demonstrates strong theoretical guarantees, through PAC-Bayes bounds, that establish non-asymptotic oracle inequalities, showing minimax-optimal prediction error and adaptability to unknown sparsity. Its effectiveness is validated through simulations and real-world data, where it performs competitively against established frequentist and Bayesian techniques.

In many biological systems, the developmental processes of individuals play a crucial role in shaping the traits, characteristics, and growth patterns of subsequent generations. Throughout various stages of growth and maturation, organisms undergo significant changes that impact their overall fitness and reproductive success. These developmental stages, ranging from early cellular differentiation to reproductive maturity, each contribute uniquely to the organism's ability to survive and transmit biological information to offspring. Conversely, hereditary processes also influence the developmental stages of subsequent generations, creating a feedback loop where the heritable traits and adaptations of individuals as well as their health statuses such as disease resistance, metabolic efficiency, or physiological robustness can impact the developmental trajectories of future generations. This feedback loop between developmental processes and heredity continually shapes evolutionary trajectories, driving adaptation and resilience in populations over time.