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.

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.