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.

The Pearson-Matthews correlation coefficient (usually abbreviated MCC) is considered to be one of the most useful metrics for the performance of a binary classification or hypothesis testing method (for the sake of conciseness we will use the classification terminology throughout, but the concepts and methods discussed in the paper apply verbatim to hypothesis testing as well). For multinary classification tasks (with more than two classes) the existing extension of MCC, commonly called the $\text{R}_{\text{K}}$ metric, has also been successfully used in many applications. The present paper begins with an introductory discussion on certain aspects of MCC. Then we go on to discuss the topic of multinary classification that is the main focus of this paper and which, despite its practical and theoretical importance, appears to be less developed than the topic of binary classification. Our discussion of the $\text{R}_{\text{K}}$ is followed by the introduction of two other metrics for multinary classification derived from the multivariate Pearson correlation (MPC) coefficients. We show that both $\text{R}_{\text{K}}$ and the MPC metrics suffer from the problem of not decisively indicating poor classification results when they should, and introduce three new enhanced metrics that do not suffer from this problem. We also present an additional new metric for multinary classification which can be viewed as a direct extension of MCC.

The paper surveys automated scientific discovery, from equation discovery and symbolic regression to autonomous discovery systems and agents. It discusses the individual approaches from a "big picture" perspective and in context, but also discusses open issues and recent topics like the various roles of deep neural networks in this area, aiding in the discovery of human-interpretable knowledge. Further, we will present closed-loop scientific discovery systems, starting with the pioneering work on the Adam system up to current efforts in fields from material science to astronomy. Finally, we will elaborate on autonomy from a machine learning perspective, but also in analogy to the autonomy levels in autonomous driving. The maximal level, level five, is defined to require no human intervention at all in the production of scientific knowledge. Achieving this is one step towards solving the Nobel Turing Grand Challenge to develop AI Scientists: AI systems capable of making Nobel-quality scientific discoveries highly autonomously at a level comparable, and possibly superior, to the best human scientists by 2050.

Data is a central component of machine learning and causal inference tasks. The availability of large amounts of data from sources such as open data repositories, data lakes and data marketplaces creates an opportunity to augment data and boost those tasks' performance. However, augmentation techniques rely on a user manually discovering and shortlisting useful candidate augmentations. Existing solutions do not leverage the synergy between discovery and augmentation, thus under exploiting data. In this paper, we introduce METAM, a novel goal-oriented framework that queries the downstream task with a candidate dataset, forming a feedback loop that automatically steers the discovery and augmentation process. To select candidates efficiently, METAM leverages properties of the: i) data, ii) utility function, and iii) solution set size. We show METAM's theoretical guarantees and demonstrate those empirically on a broad set of tasks. All in all, we demonstrate the promise of goal-oriented data discovery to modern data science applications.

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Autonomous robots are required to reason about the behaviour of dynamic agents in their environment. The creation of models to describe these relationships is typically accomplished through the application of causal discovery techniques. However, as it stands observational causal discovery techniques struggle to adequately cope with conditions such as causal sparsity and non-stationarity typically seen during online usage in autonomous agent domains. Meanwhile, interventional techniques are not always feasible due to domain restrictions. In order to better explore the issues facing observational techniques and promote further discussion of these topics we carry out a benchmark across 10 contemporary observational temporal causal discovery methods in the domain of autonomous driving. By evaluating these methods upon causal scenes drawn from real world datasets in addition to those generated synthetically we highlight where improvements need to be made in order to facilitate the application of causal discovery techniques to the aforementioned use-cases. Finally, we discuss potential directions for future work that could help better tackle the difficulties currently experienced by state of the art techniques.

Most models of decision-making in neuroscience assume an infinite horizon, which yields an optimal solution that integrates evidence up to a fixed decision threshold; however, under most experimental as well as naturalistic behavioral settings, the decision has to be made before some finite deadline, which is often experienced as a stochastic quantity, either due to variable external constraints or internal timing uncertainty. In this work, we formulate this problem as sequential hypothesis testing under a stochastic horizon. We use dynamic programming tools to show that, for a large class of deadline distributions, the Bayes-optimal solution requires integrating evidence up to a threshold that declines monotonically over time. We use numerical simulations to illustrate the optimal policy in the special cases of a fixed deadline and one that is drawn from a gamma distribution.

Initiatives using machine learning cannot be treated in the same manner as projects involving conventional software. It's imperative to move quickly so that you can test things, fix issues and test them again. In other words, you must be able to fail quickly – and do so early on in the process. Waiting until later in this process to find issues can end up being very expensive and time-consuming. When developing software using the traditional method, you use decision logic.

Regeneron isn't the only company eager to derive more value from its data. Despite the enormous amounts of data they collect and the amount of capital they invest in data management solutions, business leaders are still not benefitting from their data. According to IDC research, 83% of CEOs want their organizations to be more data driven, but they struggle with the cultural and technological changes needed to execute an effective data strategy. In response, many organizations, including Regeneron, are turning to a new form of data architecture as a modern approach to data management. In fact, by 2024, more than three-quarters of current data lake users will be investing in this type of hybrid "data lakehouse" architecture to enhance the value generated from their accumulated data, according to Matt Aslett, a research director with Ventana Research.