Complex adaptive agents consistently achieve their goals by solving problems that seem to require an understanding of causal information, information pertaining to the causal relationships that exist among elements of combined agent-environment systems. Causal cognition studies and describes the main characteristics of causal learning and reasoning in human and non-human animals, offering a conceptual framework to discuss cognitive performances based on the level of apparent causal understanding of a task. Despite the use of formal intervention-based models of causality, including causal Bayesian networks, psychological and behavioural research on causal cognition does not yet offer a computational account that operationalises how agents acquire a causal understanding of the world. Machine and reinforcement learning research on causality, especially involving disentanglement as a candidate process to build causal representations, represent on the one hand a concrete attempt at designing causal artificial agents that can shed light on the inner workings of natural causal cognition. In this work, we connect these two areas of research to build a unifying framework for causal cognition that will offer a computational perspective on studies of animal cognition, and provide insights in the development of new algorithms for causal reinforcement learning in AI.

However, the well-established methods for obtaining posterior distributions of likely parameters such as Markov chain Monte Carlo (MCMC) sampling [1] become infeasible with highly parameterized machine learning function representations, such as neural networks (NNs). The curse of dimensionality in this uncertainty quantification (UQ) setting is tied to the cost of sampling the posterior sufficiently to determine its covariance structure and generate representative push-forward realizations. In this work, our goal is to obtain a high-dimensional posterior distribution over a large number of random variables representing model parameters, which is particularly useful when limited amount of training data is available. One of the simplest ways to obtain the approximate posterior is to implement MCMC methods. However, this approach is challenged by the number of parameters typically present in NNs and it is difficult to converge samples to those representative of the posterior, even for models with moderate dimensionality. There has been enormous progress made to approximate high-dimensional posterior distributions using variational inference methods [2]. However, these methods restrict the approximate posterior to a certain parametric family and find the best approximate posterior through optimization. To surmount these issues, Liu and Wang [3] recently proposed a non-parametric variational inference method called Stein variational gradient descent (SVGD).

Randomized algorithms exploit stochasticity to reduce computational complexity. One important example is random feature regression (RFR) that accelerates Gaussian process regression (GPR). RFR approximates an unknown function with a random neural network whose hidden weights and biases are sampled from a probability distribution. Only the final output layer is fit to data. In randomized algorithms like RFR, the hyperparameters that characterize the sampling distribution greatly impact performance, yet are not directly accessible from samples. This makes optimization of hyperparameters via standard (gradient-based) optimization tools inapplicable. Inspired by Bayesian ideas from GPR, this paper introduces a random objective function that is tailored for hyperparameter tuning of vector-valued random features. The objective is minimized with ensemble Kalman inversion (EKI). EKI is a gradient-free particle-based optimizer that is scalable to high-dimensions and robust to randomness in objective functions. A numerical study showcases the new black-box methodology to learn hyperparameter distributions in several problems that are sensitive to the hyperparameter selection: two global sensitivity analyses, integrating a chaotic dynamical system, and solving a Bayesian inverse problem from atmospheric dynamics. The success of the proposed EKI-based algorithm for RFR suggests its potential for automated optimization of hyperparameters arising in other randomized algorithms.

Bayes nets are extensively used in practice to efficiently represent joint probability distributions over a set of random variables and capture dependency relations. In a seminal paper, Chickering et al. (JMLR 2004) showed that given a distribution $P$, that is defined as the marginal distribution of a Bayes net, it is $\mathsf{NP}$-hard to decide whether there is a parameter-bounded Bayes net that represents $P$. They called this problem LEARN. In this work, we extend the $\mathsf{NP}$-hardness result of LEARN and prove the $\mathsf{NP}$-hardness of a promise search variant of LEARN, whereby the Bayes net in question is guaranteed to exist and one is asked to find such a Bayes net. We complement our hardness result with a positive result about the sample complexity that is sufficient to recover a parameter-bounded Bayes net that is close (in TV distance) to a given distribution $P$, that is represented by some parameter-bounded Bayes net, generalizing a degree-bounded sample complexity result of Brustle et al. (EC 2020).

In many real-world settings, an agent must learn to act in environments where no reward signal can be specified, but a set of expert demonstrations is available. Imitation learning (IL) is a popular framework for learning policies from such demonstrations. However, in some cases, differences in observability between the expert and the agent can give rise to an imitation gap such that the expert's policy is not optimal for the agent and a naive application of IL can fail catastrophically. In particular, if the expert observes the Markov state and the agent does not, then the expert will not demonstrate the information-gathering behavior needed by the agent but not the expert. In this paper, we propose a Bayesian solution to the Imitation Gap (BIG), first using the expert demonstrations, together with a prior specifying the cost of exploratory behavior that is not demonstrated, to infer a posterior over rewards with Bayesian inverse reinforcement learning (IRL). BIG then uses the reward posterior to learn a Bayes-optimal policy. Our experiments show that BIG, unlike IL, allows the agent to explore at test time when presented with an imitation gap, whilst still learning to behave optimally using expert demonstrations when no such gap exists.

International Journal of Forecasting, 2024.], a generalised exponential smoothing model was proposed that is able to capture strong trends and volatility in time series. This method achieved state-of-the-art performance in many forecasting tasks, but its fitting proce dure, which is based on the NUTS sampler, is very computationally expensive. In this work, w e propose several modifications to the original model, as well as a bespoke Gibbs sampler for p osterior exploration; these changes improve sampling time by an order of magnitude, thus rendering the model much more practically relevant. The new model, and sampler, are evalu ated on the M3 dataset and are shown to be competitive, or superior, in terms of accuracy to the original method, while being substantially faster to run.

A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced with theoretical ground, algorithm design and experimental validation. This method simulates an interacting particle system (IPS) where particles, i.e. the freely-moving negative charges and spatially-fixed positive charges with magnitudes proportional to the target distribution, interact with each other via attraction and repulsion induced by the resulting electric fields described by Poisson's equation. The IPS evolves towards a steady-state where the distribution of negative charges conforms to the target distribution. This physics-inspired method offers deterministic, gradient-free sampling and inference, achieving comparable performance as other particle-based and MCMC methods in benchmark tasks of inferring complex densities, Bayesian logistic regression and dynamical system identification. A discrete-time, discrete-space algorithmic design, readily extendable to continuous time and space, is provided for usage in more general inference problems occurring in probabilistic machine learning scenarios such as Bayesian inference, generative modelling, and beyond.

Dynamic Bayesian Networks (DBNs) are a class of Probabilistic Graphical Models that enable the modeling of a Markovian dynamic process through defining the kernel transition by the DAG structure of the graph found to fit a dataset. There are a number of structure learners than enable one to find the structure of a DBN to fit data, each of which with its own set of particular advantages and disadvantages. The structure of a DBN itself presents transparent criteria in order to identify causal discovery between variables. However, without the presence of large quantities of data, identifying a ground truth causal structure becomes unrealistic in practice. However, one can consider a procedure by which a set of graphs identifying structure are computed as approximate noisy solutions, and subsequently amortized in a broader statistical procedure fitting a mixture of DBNs. Each component of the mixture presents an alternative hypothesis on the causal structure. From the mixture weights, one can also compute the Bayes Factors comparing the preponderance of evidence between different models. This presents a natural opportunity for the development of Empirical Bayesian methods.

Partially observed stochastic reaction network (SRN) modeling the dynamics of a population of interacting species, such as chemical molecules participating in multiple reactions, is the fundamental building block of multi-scale bioprocess mechanistic model characterizing the causal interdependences from molecular-to macro-kinetics. It plays a critical role to: (1) facilitate digital twin development and support mechanism learning for biomanufacturing processes; (2) allow us to probe critical latent state based on partially observed information; and (3) serve as a fundamental model for a biofoundry platform [1] that can integrate heterogeneous online and offline measures collected from different manufacturing processes and speed up the bioprocess development with much less experiments. Model inference on the SRN mechanistic model based on heterogeneous data also helps to strengthen the theoretical foundations of federated learning on bioprocess mechanisms, through which we can train and advance knowledge. The SRN mechanistic model has three key features that make the model inference challenging. First, the continuoustime state transition model, representing the evolution of concentration or number of molecules, is highly nonlinear.

A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the cumulative intensity function) in the likelihood resulting in doubly intractable posterior distribution. Here, we propose a nonparametric Bayesian approach for estimating the intensity function of an inhomogeneous Poisson process without reliance on large data augmentation or approximations of the likelihood function. We propose to jointly model the intensity and the cumulative intensity function as a transformed Gaussian process, allowing us to directly bypass the need of approximating the cumulative intensity function in the likelihood. We propose an exact MCMC sampler for posterior inference and evaluate its performance on simulated data. We demonstrate the utility of our method in three real-world scenarios including temporal and spatial event data, as well as aggregated time count data collected at multiple resolutions. Finally, we discuss extensions of our proposed method to other point processes.