Kuhn's framework of scientific progress (Kuhn, 1962) provides a useful framing of the paradigm shifts that have occurred in Artificial Intelligence over the last 60 years. The framework is also useful in understanding what is arguably a new paradigm shift in AI, signaled by the emergence of large pre-trained systems such as GPT-3, on which conversational agents such as ChatGPT are based. Such systems make intelligence a commoditized general purpose technology that is configurable to applications. In this paper, I summarize the forces that led to the rise and fall of each paradigm, and discuss the pressing issues and risks associated with the current paradigm shift in AI.

Machine learning systems have gained widespread use in science, technology, and society. Given the increasing number of high-stakes machine learning applications and the growing complexity of machine learning models, many have advocated for interpretability and explainability to promote understanding and trust in machine learning results (Rasheed et al., 2022, Toreini et al., 2020, Broderick et al., 2023). In response, there has been a recent explosion of research on Interpretable Machine Learning (IML), mostly focusing on new techniques to interpret black-box systems; see Molnar (2022), Lipton (2018), Guidotti et al. (2018), Doshi-Velez & Kim (2017), Du et al. (2019), Murdoch et al. (2019), Carvalho et al. (2019) for recent reviews of the IML and explainable artificial intelligence literature. While most of these interpretability techniques were not necessarily designed for this purpose, they are increasingly being used to mine large and complex data sets to generate new insights (Roscher et al., 2020). These so-called data-driven discoveries are especially important to advance data-rich fields in science, technology, and medicine. While prior reviews focus mainly on IML techniques, we primarily review how IML methods promote data-driven discoveries, challenges associated with this task, and related new research opportunities at the intersection of machine learning and statistics. In the sciences and beyond, IML techniques are routinely employed to make new discoveries from large and complex data sets; to motivate our review on this topic, we highlight several examples. First, feature importance and feature selection in supervised learning are popular forms of interpretation that have led to major discoveries like discovering new genomic biomarkers of diseases (Guyon et al., 2002), discovering physical laws governing dynamical systems (Brunton et al., 2016), and discovering lesions and other abnormalities in radiology (Borjali et al., 2020, Reyes et al., 2020). While most of the IML literature focuses on supervised learning (Molnar, 2022, Lipton, 2018, Guidotti et al., 2018, Doshi-Velez & Kim, 2017), there have been many major scientific discoveries made via unsupervised techniques and we argue that these approaches

We leverage research in natural language processing (NLP), information retrieval, data mining, and human-computer interaction (HCI) and draw concepts from multiple disciplines. For example, efforts in metascience focus on sociological factors that influence the evolution of science,17 such as analyses of information silos that impede mutual understanding and interaction,38 of macro-scale ramifications of the rapid growth in scholarly publications,4 and of current metrics for measuring impact5--work enabled by digitization of scholarly corpora. Metascience research makes important observations about human biases (desideratum 2) but generally does not engage in building computational interventions to augment researchers (desideratum 1). Conversely, work in literature-based discovery33 mines information from literature to generate new predictions (for example, functions of materials or drug targets) but is typically done in isolation from cognitive considerations; however, these techniques have great promise in being used as part of human-augmentation systems. Other work uses machines to automate aspects of science.

Organizations are collecting increasingly large amounts of data for data driven decision making. These data are often dumped into a centralized repository, e.g., a data lake, consisting of thousands of structured and unstructured datasets. Perversely, such mixture of datasets makes the problem of discovering elements (e.g., tables or documents) that are relevant to a user's query or an analytical task very challenging. Despite the recent efforts in data discovery, the problem remains widely open especially in the two fronts of (1) discovering relationships and relatedness across structured and unstructured datasets where existing techniques suffer from either scalability, being customized for a specific problem type (e.g., entity matching or data integration), or demolishing the structural properties on its way, and (2) developing a holistic system for integrating various similarity measurements and sketches in an effective way to boost the discovery accuracy. In this paper, we propose a new data discovery system, named CMDL, for addressing these two limitations. CMDL supports the data discovery process over both structured and unstructured data while retaining the structural properties of tables.

Within enterprises, there is a growing need to intelligently navigate data lakes, specifically focusing on data discovery. Of particular importance to enterprises is the ability to find related tables in data repositories. These tables can be unionable, joinable, or subsets of each other. There is a dearth of benchmarks for these tasks in the public domain, with related work targeting private datasets. In LakeBench, we develop multiple benchmarks for these tasks by using the tables that are drawn from a diverse set of data sources such as government data from CKAN, Socrata, and the European Central Bank. We compare the performance of 4 publicly available tabular foundational models on these tasks. None of the existing models had been trained on the data discovery tasks that we developed for this benchmark; not surprisingly, their performance shows significant room for improvement. The results suggest that the establishment of such benchmarks may be useful to the community to build tabular models usable for data discovery in data lakes.

We explore Reconstruction Robustness (ReRo), which was recently proposed as an upper bound on the success of data reconstruction attacks against machine learning models. Previous research has demonstrated that differential privacy (DP) mechanisms also provide ReRo, but so far, only asymptotic Monte Carlo estimates of a tight ReRo bound have been shown. Directly computable ReRo bounds for general DP mechanisms are thus desirable. In this work, we establish a connection between hypothesis testing DP and ReRo and derive closed-form, analytic or numerical ReRo bounds for the Laplace and Gaussian mechanisms and their subsampled variants.

Tackling the most pressing problems for humanity, such as the climate crisis and the threat of global pandemics, requires accelerating the pace of scientific discovery. While science has traditionally relied on trial and error and even serendipity to a large extent, the last few decades have seen a surge of data-driven scientific discoveries. However, in order to truly leverage large-scale data sets and high-throughput experimental setups, machine learning methods will need to be further improved and better integrated in the scientific discovery pipeline. A key challenge for current machine learning methods in this context is the efficient exploration of very large search spaces, which requires techniques for estimating reducible (epistemic) uncertainty and generating sets of diverse and informative experiments to perform. This motivated a new probabilistic machine learning framework called GFlowNets, which can be applied in the modeling, hypotheses generation and experimental design stages of the experimental science loop. GFlowNets learn to sample from a distribution given indirectly by a reward function corresponding to an unnormalized probability, which enables sampling diverse, high-reward candidates. GFlowNets can also be used to form efficient and amortized Bayesian posterior estimators for causal models conditioned on the already acquired experimental data. Having such posterior models can then provide estimators of epistemic uncertainty and information gain that can drive an experimental design policy. Altogether, here we will argue that GFlowNets can become a valuable tool for AI-driven scientific discovery, especially in scenarios of very large candidate spaces where we have access to cheap but inaccurate measurements or to expensive but accurate measurements. This is a common setting in the context of drug and material discovery, which we use as examples throughout the paper.

Over the past decade, the techniques of topological data analysis (TDA) have grown into prominence to describe the shape of data. In recent years, there has been increasing interest in developing statistical methods and in particular hypothesis testing procedures for TDA. Under the statistical perspective, persistence diagrams -- the central multi-scale topological descriptors of data provided by TDA -- are viewed as random observations sampled from some population or process. In this context, one of the earliest works on hypothesis testing focuses on the two-group permutation-based approach where the associated loss function is defined in terms of within-group pairwise bottleneck or Wasserstein distances between persistence diagrams (Robinson and Turner, 2017). However, in situations where persistence diagrams are large in size and number, the permutation test in question gets computationally more costly to apply. To address this limitation, we instead consider pairwise distances between vectorized functional summaries of persistence diagrams for the loss function. In the present work, we explore the utility of the Betti function in this regard, which is one of the simplest function summaries of persistence diagrams. We introduce an alternative vectorization method for the Betti function based on integration and prove stability results with respect to the Wasserstein distance. Moreover, we propose a new shuffling technique of group labels to increase the power of the test. Through several experimental studies, on both synthetic and real data, we show that the vectorized Betti function leads to competitive results compared to the baseline method involving the Wasserstein distances for the permutation test.

We stand at the foot of a significant inflection in the trajectory of scientific discovery. As society continues on its fast-paced digital transformation, so does humankind's collective scientific knowledge and discourse. We now read and write papers in digitized form, and a great deal of the formal and informal processes of science are captured digitally -- including papers, preprints and books, code and datasets, conference presentations, and interactions in social networks and collaboration and communication platforms. The transition has led to the creation and growth of a tremendous amount of information -- much of which is available for public access -- opening exciting opportunities for computational models and systems that analyze and harness it. In parallel, exponential growth in data processing power has fueled remarkable advances in artificial intelligence, including large neural language models capable of learning powerful representations from unstructured text. Dramatic changes in scientific communication -- such as the advent of the first scientific journal in the 17th century -- have historically catalyzed revolutions in scientific thought. The confluence of societal and computational trends suggests that computer science is poised to ignite a revolution in the scientific process itself.

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.