The dominant approach in recent literature on causal discovery from interventional data is optimization of a model score. Although the scoring is straightforward in the sense that the optimization over DAGs refers to fully specified joint models for all observational and interventional data, the optimization landscape is very high-dimensional, making score-based algorithms infeasible for graphs with hundreds/thousands of nodes that are common in biological applications. This makes causal discovery difficult, in addition to many other challenges that remain such as departing from restrictive genericity assumptions on the underlying distributions and developing methodology for high-dimensional settings. In this article, to address these challenges, we depart from a score-based strategy and leverage special properties of polytrees to obtain a highly scalable "local" approach that learns from low-dimensional marginals. Our methods yield fast and consistent algorithms to learn linear Gaussian polytrees from interventional data.

In this paper, we present new high-probability PAC-Bayes bounds for different types of losses. Firstly, for losses with a bounded range, we recover a strengthened version of Catoni's bound that holds uniformly for all parameter values. This leads to new fast rate and mixed rate bounds that are interpretable and tighter than previous bounds in the literature. In particular, the fast rate bound is equivalent to the Seeger--Langford bound. Secondly, for losses with more general tail behaviors, we introduce two new parameter-free bounds: a PAC-Bayes Chernoff analogue when the loss' cumulative generating function is bounded, and a bound when the loss' second moment is bounded. These two bounds are obtained using a new technique based on a discretization of the space of possible events for the "in probability" parameter optimization problem. This technique is both simpler and more general than previous approaches optimizing over a grid on the parameters' space. Finally, we extend all previous results to anytime-valid bounds using a simple technique applicable to any existing bound.

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many applications, particularly in physical sciences and engineering, but also in areas such as geostatistics and neuroscience, invariance to symmetries is one of the most fundamental forms of prior information one can consider. The invariance of a Gaussian process' covariance to such symmetries gives rise to the most natural generalization of the concept of stationarity to such spaces. In this work, we develop constructive and practical techniques for building stationary Gaussian processes on a very large class of non-Euclidean spaces arising in the context of symmetries. Our techniques make it possible to (i) calculate covariance kernels and (ii) sample from prior and posterior Gaussian processes defined on such spaces, both in a practical manner. This work is split into two parts, each involving different technical considerations: part I studies compact spaces, while part II studies non-compact spaces possessing certain structure. Our contributions make the non-Euclidean Gaussian process models we study compatible with well-understood computational techniques available in standard Gaussian process software packages, thereby making them accessible to practitioners.

Using a fully Bayesian approach, Gaussian Process regression is extended to include marginalisation over the kernel choice and kernel hyperparameters. In addition, Bayesian model comparison via the evidence enables direct kernel comparison. The calculation of the joint posterior was implemented with a transdimensional sampler which simultaneously samples over the discrete kernel choice and their hyperparameters by embedding these in a higher-dimensional space, from which samples are taken using nested sampling. This method was explored on synthetic data from exoplanet transit light curve simulations. The true kernel was recovered in the low noise region while no kernel was preferred for larger noise. Furthermore, inference of the physical exoplanet hyperparameters was conducted. In the high noise region, either the bias in the posteriors was removed, the posteriors were broadened or the accuracy of the inference was increased. In addition, the uncertainty in mean function predictive distribution increased due to the uncertainty in the kernel choice. Subsequently, the method was extended to marginalisation over mean functions and noise models and applied to the inference of the present-day Hubble parameter, $H_0$, from real measurements of the Hubble parameter as a function of redshift, derived from the cosmologically model-independent cosmic chronometer and {\Lambda}CDM-dependent baryon acoustic oscillation observations. The inferred $H_0$ values from the cosmic chronometers, baryon acoustic oscillations and combined datasets are $H_0$ = 66$\pm$6 km/s/Mpc, $H_0$ = 67$\pm$10 km/s/Mpc and $H_0$ = 69$\pm$6 km/s/Mpc, respectively. The kernel posterior of the cosmic chronometers dataset prefers a non-stationary linear kernel. Finally, the datasets are shown to be not in tension with ln(R)=12.17$\pm$0.02.

Modern generative machine learning models demonstrate surprising ability to create realistic outputs far beyond their training data, such as photorealistic artwork, accurate protein structures, or conversational text. These successes suggest that generative models learn to effectively parametrize and sample arbitrarily complex distributions. Beginning half a century ago, foundational works in nonlinear dynamics used tools from information theory to infer properties of chaotic attractors from time series, motivating the development of algorithms for parametrizing chaos in real datasets. In this perspective, we aim to connect these classical works to emerging themes in large-scale generative statistical learning. We first consider classical attractor reconstruction, which mirrors constraints on latent representations learned by state space models of time series. We next revisit early efforts to use symbolic approximations to compare minimal discrete generators underlying complex processes, a problem relevant to modern efforts to distill and interpret black-box statistical models. Emerging interdisciplinary works bridge nonlinear dynamics and learning theory, such as operator-theoretic methods for complex fluid flows, or detection of broken detailed balance in biological datasets. We anticipate that future machine learning techniques may revisit other classical concepts from nonlinear dynamics, such as transinformation decay and complexity-entropy tradeoffs.

Social behavior, defined as the process by which individuals act and react in response to others, is crucial for the function of societies and holds profound implications for mental health. To fully grasp the intricacies of social behavior and identify potential therapeutic targets for addressing social deficits, it is essential to understand its core principles. Although machine learning algorithms have made it easier to study specific aspects of complex behavior, current methodologies tend to focus primarily on single-animal behavior. In this study, we introduce LISBET (seLf-supervIsed Social BEhavioral Transformer), a model designed to detect and segment social interactions. Our model eliminates the need for feature selection and extensive human annotation by using self-supervised learning to detect and quantify social behaviors from dynamic body parts tracking data. LISBET can be used in hypothesis-driven mode to automate behavior classification using supervised finetuning, and in discovery-driven mode to segment social behavior motifs using unsupervised learning. We found that motifs recognized using the discovery-driven approach not only closely match the human annotations but also correlate with the electrophysiological activity of dopaminergic neurons in the Ventral Tegmental Area (VTA). We hope LISBET will help the community improve our understanding of social behaviors and their neural underpinnings.

Stateful policies play an important role in reinforcement learning, such as handling partially observable environments, enhancing robustness, or imposing an inductive bias directly into the policy structure. The conventional method for training stateful policies is Backpropagation Through Time (BPTT), which comes with significant drawbacks, such as slow training due to sequential gradient propagation and the occurrence of vanishing or exploding gradients. The gradient is often truncated to address these issues, resulting in a biased policy update. We present a novel approach for training stateful policies by decomposing the latter into a stochastic internal state kernel and a stateless policy, jointly optimized by following the stateful policy gradient. We introduce different versions of the stateful policy gradient theorem, enabling us to easily instantiate stateful variants of popular reinforcement learning and imitation learning algorithms. Furthermore, we provide a theoretical analysis of our new gradient estimator and compare it with BPTT. We evaluate our approach on complex continuous control tasks, e.g., humanoid locomotion, and demonstrate that our gradient estimator scales effectively with task complexity while offering a faster and simpler alternative to BPTT.

The ability to invent new tools has been identified as an important facet of our ability as a species to problem solve in dynamic and novel environments. While the use of tools by artificial agents presents a challenging task and has been widely identified as a key goal in the field of autonomous robotics, far less research has tackled the invention of new tools by agents. In this paper, (1) we articulate the distinction between tool discovery and tool innovation by providing a minimal description of the two concepts under the formalism of active inference. We then (2) apply this description to construct a toy model of tool innovation by introducing the notion of tool affordances into the hidden states of the agent's probabilistic generative model. This particular state factorisation facilitates the ability to not just discover tools but invent them through the offline induction of an appropriate tool property. We discuss the implications of these preliminary results and outline future directions of research.

Mislabeled, duplicated, or biased data in real-world scenarios can lead to prolonged training and even hinder model convergence. Traditional solutions prioritizing easy or hard samples lack the flexibility to handle such a variety simultaneously. Recent work has proposed a more reasonable data selection principle by examining the data's impact on the model's generalization loss. However, its practical adoption relies on less principled approximations and additional holdout data. This work solves these problems by leveraging a lightweight Bayesian treatment and incorporating off-the-shelf zero-shot predictors built on large-scale pre-trained models. The resulting algorithm is efficient and easy to implement. We perform extensive empirical studies on challenging benchmarks with considerable data noise and imbalance in the online batch selection scenario, and observe superior training efficiency over competitive baselines. Notably, on the challenging Web-Vision benchmark, our method can achieve similar predictive performance with significantly fewer training iterations than leading data selection methods.

Offline reinforcement learning (RL) has received considerable attention in recent years due to its attractive capability of learning policies from offline datasets without environmental interactions. Despite some success in the single-agent setting, offline multi-agent RL (MARL) remains to be a challenge. The large joint state-action space and the coupled multi-agent behaviors pose extra complexities for offline policy optimization. Most existing offline MARL studies simply apply offline data-related regularizations on individual agents, without fully considering the multi-agent system at the global level. In this work, we present OMIGA, a new offline m ulti-agent RL algorithm with implicit global-to-local v alue regularization. OMIGA provides a principled framework to convert global-level value regularization into equivalent implicit local value regularizations and simultaneously enables in-sample learning, thus elegantly bridging multi-agent value decomposition and policy learning with offline regularizations. Based on comprehensive experiments on the offline multi-agent MuJoCo and StarCraft II micro-management tasks, we show that OMIGA achieves superior performance over the state-of-the-art offline MARL methods in almost all tasks.