Missing data represents a fundamental and pervasive challenge in modern data science, significantly impeding analytical capabilities and decision-making processes across an exceptionally broad spectrum of disciplines, including healthcare, bioinformatics, social science, e-commerce and industrial monitoring systems. Despite decades of research and the development of numerous imputation methodologies, existing literature remains fragmented across disciplinary boundaries, creating a critical need for a comprehensive, interdisciplinary synthesis that bridges statistical foundations with contemporary machine learning advances. This work systematically covers fundamental concepts – including missingness mechanisms, single vs. multiple imputation and varying imputation goals – and explores problem characteristics across different domains. The review extensively categorizes imputation methods, spanning classical techniques (e.g. regression and expectation-maximization algorithm) to modern approaches such as low-rank and high-rank matrix completion, deep learning models (autoencoders, generative adversarial networks, diffusion models and graph neural networks) and large language models. Special consideration is given to methods tailored for complex data types, including tensor data, time series, graph-structured data, categorical data and multimodal data, acknowledging their unique challenges and solution approaches. Beyond methodological considerations, they investigate the crucial integration of imputation with downstream machine learning tasks, including classification, clustering and anomaly detection, examining both sequential pipelines and joint optimization frameworks. The review also assesses theoretical guarantees for various methods, available benchmarking resources and comprehensive evaluation metrics. Finally, they identify critical challenges and future directions, emphasizing the complexities of model selection and hyperparameter optimization, the growing importance of privacy-preserving imputation through federated learning approaches and the ambitious pursuit of generalizable or universal imputation models that can adapt across domains and data types, thereby providing a roadmap for advancing this vital field of research.
Many important problems in science and engineering involve inferring a signal from noisy and/or incomplete observations, where the observation process is known. Historically, this problem has been tackled using hand-crafted regularization (e.g., sparsity, total-variation) to obtain meaningful estimates. Recent data-driven methods often offer better solutions by directly learning a solver from examples of ground-truth signals and associated observations. However, in many real-world applications, obtaining ground-truth references for training is expensive or impossible. Self-supervised learning methods offer a promising alternative by learning a solver from measurement data alone, bypassing the need for ground-truth references. This manuscript provides a comprehensive summary of different self-supervised methods for inverse problems, with a special emphasis on their theoretical underpinnings, and presents practical applications in imaging inverse problems.
Diffusion models have emerged as powerful deep generative techniques, producing high-quality and diverse samples in applications in various domains, including audio. While existing reviews provide overviews, there remains limited in-depth discussion of these specific design choices. The audio diffusion model literature also lacks principled guidance for the implementation of these design choices and their comparisons for different applications. This survey provides a comprehensive review of diffusion model design with an emphasis on design principles for quality improvement and conditioning for audio applications. The authors adopt the score modeling perspective as a unifying framework that accommodates various interpretations, including recent approaches like flow matching. They systematically examine the training and sampling procedures of diffusion models and audio applications through different conditioning mechanisms. To provide an integrated, unified codebase and to promote reproducible research and rapid prototyping, they introduce an open-source codebase (Link to the website of github) that implements their reviewed framework for various audio applications. They demonstrate its capabilities through three case studies: audio generation, speech enhancement and text-to-speech synthesis, with benchmark evaluations on standard data sets.
Generative adversarial networks (GANs) and diffusion models have dramatically advanced deepfake technology, and its threats to digital security, media integrity, and public trust have increased rapidly. This research explored zero-shot deepfake detection, an emerging method even when the models have never seen a particular deepfake variation. In this work, we studied self-supervised learning, transformer-based zero-shot classifier, generative model fingerprinting, and meta-learning techniques that better adapt to the ever-evolving deepfake threat. In addition, we suggested AI-driven prevention strategies that mitigated the underlying generation pipeline of the deepfakes before they occurred. They consisted of adversarial perturbations for creating deepfake generators, digital watermarking for content authenticity verification, real-time AI monitoring for content creation pipelines, and blockchain-based content verification frameworks. Despite these advancements, zero-shot detection and prevention faced critical challenges such as adversarial attacks, scalability constraints, ethical dilemmas, and the absence of standardized evaluation benchmarks. These limitations were addressed by discussing future research directions on explainable AI for deepfake detection, multimodal fusion based on image, audio, and text analysis, quantum AI for enhanced security, and federated learning for privacy-preserving deepfake detection. This further highlighted the need for an integrated defense framework for digital authenticity that utilized zero-shot learning in combination with preventive deepfake mechanisms. Finally, we highlighted the important role of interdisciplinary collaboration between AI researchers, cybersecurity experts, and policymakers to create resilient defenses against the rising tide of deepfake attacks.
Graph learning has rapidly evolved into a critical subfield of machine learning and artificial intelligence (AI). Its development began with early graph-theoretic methods, gaining significant momentum with the advent of graph neural networks (GNNs). Over the past decade, progress in scalable architectures, dynamic graph modeling, multimodal learning, generative AI, explainable AI (XAI), and responsible AI has broadened the applicability of graph learning to various challenging environments. Graph learning is significant due to its ability to model complex, non-Euclidean relationships that traditional machine learning struggles to capture, thus better supporting real-world applications ranging from drug discovery and fraud detection to recommender systems and scientific reasoning. However, challenges like scalability, generalization, heterogeneity, interpretability, and trustworthiness must be addressed to unlock its full potential. This survey provides a comprehensive introduction to graph learning, focusing on key dimensions including scalable, temporal, multimodal, generative, explainable, and responsible graph learning. We review state-of-the-art techniques for efficiently handling large-scale graphs, capturing dynamic temporal dependencies, integrating heterogeneous data modalities, generating novel graph samples, and enhancing interpretability to foster trust and transparency. We also explore ethical considerations, such as privacy and fairness, to ensure responsible deployment of graph learning models. Additionally, we identify and discuss emerging topics, highlighting recent integration of graph learning and other AI paradigms and offering insights into future directions. This survey serves as a valuable resource for researchers and practitioners seeking to navigate the rapidly evolving landscape of graph learning.
The spatial information of sound plays a crucial role in various situations, ranging from daily activities to advanced engineering technologies. To fully utilize its potential, numerous research studies on spatial audio signal processing have been carried out in the literature. Sound field estimation is one of the key foundational technologies that can be applied to a wide range of acoustic signal processing techniques, including sound field reproduction using loudspeakers and binaural playback through headphones. The purpose of this paper is to present an overview of sound field estimation methods. After providing the necessary mathematical background, two different approaches to sound field estimation will be explained. This paper focuses on clarifying the essential theories of each approach, while also referencing state-of-the-art developments. Finally, several acoustic signal processing technologies will be discussed as examples of the application of sound field estimation.
Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a powerful tool for learning to extract such representations, offering a way to incorporate structural bias, discover insight about the data, and interpret decisions. However, effective training is challenging, as neural networks are typically designed for continuous computation. This text explores three broad strategies for learning with discrete latent structure: continuous relaxation, surrogate gradients, and probabilistic estimation. Our presentation relies on consistent notations for a wide range of models. As such, we reveal many new connections between latent structure learning strategies, showing how most consist of the same small set of fundamental building blocks, but use them differently, leading to substantially different applicability and properties.
Causality has the potential to truly transform the way we solve a large number of real-world problems. Yet, so far, its potential largely remains to be unlocked as causality often requires crucial assumptions which cannot be tested in practice. To address this challenge, we propose a new way of thinking about causality -- we call this causal deep learning. Our causal deep learning framework spans three dimensions: (1) a structural dimension, which incorporates partial yet testable causal knowledge rather than assuming either complete or no causal knowledge among the variables of interest; (2) a parametric dimension, which encompasses parametric forms that capture the type of relationships among the variables of interest; and (3) a temporal dimension, which captures exposure times or how the variables of interest interact (possibly causally) over time. Causal deep learning enables us to make progress on a variety of real-world problems by leveraging partial causal knowledge (including independencies among variables) and quantitatively characterising causal relationships among variables of interest (possibly over time). Our framework clearly identifies which assumptions are testable and which ones are not, such that the resulting solutions can be judiciously adopted in practice. Using our formulation we can combine or chain together causal representations to solve specific problems without losing track of which assumptions are required to build these solutions, pushing real-world impact in healthcare, economics and business, environmental sciences and education, through causal deep learning.
This monograph presents a theoretical background and a broad introduction to the M in-Max Framework for M ajori- zation-Minimization (MM4MM), an algorithmic methodology for solving minimization problems by formulating them as min-max problems and then employing majorizationminimization. The monograph lays out the mathematical basis of the approach used to reformulate a minimization problem as a min-max problem. With the prerequisites covered, including multiple illustrations of the formulations for convex and non-convex functions, this work serves as a guide for developing MM4MM-based algorithms for solving non-convex optimization problems in various areas of signal processing. As special cases, we discuss using the majorization-minimization technique to solve min-max problems encountered in signal processing applications and min- max problems formulated using the Lagrangian. Lastly, we present detailed examples of using MM4MM in ten signal processing applications such as phase retrieval, source localization, independent vector analysis, beamforming and optimal sensor placement in wireless sensor networks. The devised MM4MM algorithms are free of hyper-parameters and enjoy the advantages inherited from the use of the majorization-minimization technique such as monotonicity.
Energy-Based Models (EBMs) are an important class of probabilistic models, also known as random fields and undirected graphical models. EBMs are un-normalized and thus radically different from other popular self-normalized probabilistic models such as hidden Markov models (HMMs), autoregressive models, generative adversarial nets (GANs) and variational auto-encoders (VAEs). Over the past years, EBMs have attracted increasing interest not only from the core machine learning community, but also from application domains such as speech, vision, natural language processing (NLP) and so on, due to significant theoretical and algorithmic progress. The sequential nature of speech and language also presents special challenges and needs a different treatment from processing fix-dimensional data (e.g., images). Therefore, the purpose of this monograph is to present a systematic introduction to energy-based models, including both algorithmic progress and applications in speech and language processing. First, the basics of EBMs are introduced, including classic models, recent models parameterized by neural networks, sampling methods, and various learning methods from the classic learning algorithms to the most advanced ones. Then, the application of EBMs in three different scenarios is presented, i.e., for modeling marginal, conditional and joint distributions, respectively. 1) EBMs for sequential data with applications in language modeling, where the main focus is on the marginal distribution of a sequence itself; 2) EBMs for modeling conditional distributions of target sequences given observation sequences, with applications in speech recognition, sequence labeling and text generation; 3) EBMs for modeling joint distributions of both sequences of observations and targets, and their applications in semi-supervised learning and calibrated natural language understanding.
Graph signal processing (GSP) has seen rapid developments in recent years. Since its introduction around ten years ago, we have seen numerous new ideas and practical applications related to the field. In this tutorial, we give an overview of some recent advances in generalizing GSP, with a focus on the extension to high-dimensional spaces, models, and structures. Alongside new frameworks proposed to tackle such problems, many new mathematical tools are being introduced. In the first part of the monograph, we will review traditional GSP, highlight the challenges it faces, and motivate efforts in overcoming such challenges, which will be the theme of the rest of the monograph.
Deep learning has achieved remarkable success in many machine learning tasks such as image classification, speech recognition, and game playing. However, these breakthroughs are often difficult to translate into real-world engineering systems because deep learning models require a massive number of training samples, which are costly to obtain in practice. To address labeled data scarcity, few-shot meta-learning optimizes learning algorithms that can efficiently adapt to new tasks quickly. While meta-learning is gaining significant interest in the machine learning literature, its working principles and theoretic fundamentals are not as well understood in the engineering community. This review monograph provides an introduction to meta-learning by covering principles, algorithms, theory, and engineering applications. After introducing meta-learning in comparison with conventional and joint learning, we describe the main meta-learning algorithms, as well as a general bilevel optimization framework for the definition of meta-learning techniques. Then, we summarize known results on the generalization capabilities of meta-learning from a statistical learning viewpoint. Applications to communication systems, including decoding and power allocation, are discussed next, followed by an introduction to aspects related to the integration of meta-learning with emerging computing technologies, namely neuromorphic and quantum computing. The monograph is concluded with an overview of open research challenges.
We consider the well-studied problem of decomposing a vector time series signal into components with different characteristics, such as smooth, periodic, nonnegative, or sparse. We describe a simple and general framework in which the components are defined by loss functions (which include constraints), and the signal decomposition is carried out by minimizing the sum of losses of the components (subject to the constraints). When each loss function is the negative log-likelihood of a density for the signal component, this framework coincides with maximum a posteriori probability (MAP) estimation; but it also includes many other interesting cases. Summarizing and clarifying prior results, we give two distributed optimization methods for computing the decomposition, which find the optimal decomposition when the component class loss functions are convex, and are good heuristics when they are not. Both methods require only the masked proximal operator of each of the component loss functions, a generalization of the well-known proximal operator that handles missing entries in its argument. Both methods are distributed, i.e., handle each component separately. We derive tractable methods for evaluating the masked proximal operators of some loss functions that, to our knowledge, have not appeared in the literature.
Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information, and additional domain knowledge. Simple classical models are useful but sensitive to inaccuracies and may lead to poor performance when real systems display complex or dynamic behavior. On the other hand, purely data-driven approaches that are model-agnostic are becoming increasingly popular as datasets become abundant and the power of modern deep learning pipelines increases. Deep neural networks (DNNs) use generic architectures that learn to operate from data and demonstrate excellent performance, especially for supervised problems. However, DNNs typically require massive amounts of data and immense computational resources, limiting their applicability for some scenarios. In this article, we present the leading approaches for studying and designing model-based deep learning systems. These are methods that combine principled mathematical models with data-driven systems to benefit from the advantages of both approaches. Such model-based deep learning methods exploit both partial domain knowledge, via mathematical structures designed for specific problems, and learning from limited data. Among the applications detailed in our examples for model-based deep learning are compressed sensing, digital communications, and tracking in state-space models. Our aim is to facilitate the design and study of future systems at the intersection of signal processing and machine learning that incorporate the advantages of both domains.
This monograph deals with principal component analysis (PCA), kernel component analysis (KPCA), and independent component analysis (ICA), highlighting their applications to streaming-data implementations. The basic concepts related to PCA, KPCA, and ICA are widely available in the literature; however, very few texts deal with their practical implementation in computationally limited resources. The presentation tries to emphasize the current solutions considering possible constraints in power consumption and desirable computational complexity. For instance, there are good examples in biomedical engineering applications where tools like PCA and ICA can sort out the human body's activities. For example, it is possible to remove noise and undesirable artifacts from a target signal such as EEG and ECG, among others. In turn, KPCA may be a valuable resource for non-linear image denoising. Nonetheless, many current solutions rely on batch processing implemented in general-purpose computing resources. In general terms, PCA consists of a sequence of uncorrelated data projections ordered according to their variances and employing mutually orthogonal directions. PCA is mighty in extracting hidden linear structures in high-dimension datasets. The standard PCA implementation computes the eigenvectors of the data-covariance matrix, retaining those directions to which the data exhibit the highest projection variances. This concept can be extended to the so-called Kernel PCA, wherein the data instances are implicitly mapped into a high-dimensional feature space via some non-linear transform, typically unknown. Conversely, ICA strengthens the PCA maximization variance approach by imposing the strict premise of mutual independence on the resulting projections. In fact, ICA comes to rescue the traditional tools when one aims at assessing non-Gaussian sources from data, often not available for direct measurement. Frequently, ICA and KPCA are more powerful tools for solving challenging tasks than PCA since they exploit high-order statistics from data. All these methods require some simplifications to allow a simple online implementation when coping with streaming data. This monograph describes some state-of-the-art solutions for PCA, KPCA, and ICA, emphasizing their online deployments. Many online PCA and, more recently, KPCA techniques were proposed based on Hebbian learning rules and fixed-point iterative equations. Notably, online KPCA solutions also include data selection strategies to define a compact dictionary over which the kernel components are expanded. The complexity of these dictionaries is controlled by simply setting a single hyperparameter. In both cases, the online extensions proposed rely on simple equations, can track nonstationary environments, and require reduced storage, enabling its use in real-time applications operating in low-cost embedded hardware. This monograph discusses the state-of-the-art online PCA and KPCA techniques in a unified and principled manner, presenting solutions that achieve a higher convergence speed and accuracy in many applications, particularly image processing. Besides, this work also explains how to remove various artifacts from data records based on blind source separation (BSS) by ICA, splitting feature identification from feature separation. Herein, three FastICA online hardware architectures and implementation for biomedical signal processing are addressed. The main features are summarized as follows: 1) energy-efficient FastICA using the early determination scheme; 2) cost-effective variable-channel FastICA using the Gram-Schmidt-based whitening algorithm; and 3) moving-window-based online FastICA algorithm with limited memory. The post-layout simulation results with artificial and EEG data validate the design concepts. In summary, this monograph presents the leading algorithmic solutions for PCA, KPCA, ICA, Iterative PCA, Online KPCA, and Online ICA, focusing on approaches amenable to process streaming signals. Furthermore, it provides some insights into how to choose the right solution for practical systems. Along the way, some implementation examples are provided in a variety of areas.
In the current noisy intermediate-scale quantum (NISQ) era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parameterized, and the parameters are tuned via classical optimization based on data and on measurements of the outputs of the circuit. Parameterized quantum circuits (PQCs) can efficiently address combinatorial optimization problems, implement probabilistic generative models, and carry out inference (classification and regression). This monograph provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra. It first describes the necessary background, concepts, and tools necessary to describe quantum operations and measurements. Then, it covers parameterized quantum circuits, the variational quantum eigensolver, as well as unsupervised and supervised quantum machine learning formulations.
