We propose a novel tomographic method, nonlinear Gaussian process tomography (nonlinear GPT) that employs the Laplace approximation to ensure the non-negative physical quantity, such as the emissivity of plasma optical diagnostics. This new method implements a logarithmic Gaussian process (log-GP) to model plasma distribution more naturally, thereby expanding the limitations of standard GPT, which are restricted to linear problems and may yield non-physical negative values. The effectiveness of the proposed log-GP tomography is demonstrated through a case study using the Ring Trap 1 (RT-1) device, where log-GPT outperforms existing methods, standard GPT, and the Minimum Fisher Information (MFI) methods in terms of reconstruction accuracy. The result highlights the effectiveness of nonlinear GPT for imposing physical constraints in applications to an inverse problem.

Recently there has been a proliferation of intrinsic motivation (IM) reward-shaping methods to learn in complex and sparse-reward environments. These methods can often inadvertently change the set of optimal policies in an environment, leading to suboptimal behavior. Previous work on mitigating the risks of reward shaping, particularly through potential-based reward shaping (PBRS), has not been applicable to many IM methods, as they are often complex, trainable functions themselves, and therefore dependent on a wider set of variables than the traditional reward functions that PBRS was developed for. We present an extension to PBRS that we prove preserves the set of optimal policies under a more general set of functions than has been previously proven. We also present {\em Potential-Based Intrinsic Motivation} (PBIM) and {\em Generalized Reward Matching} (GRM), methods for converting IM rewards into a potential-based form that are useable without altering the set of optimal policies. Testing in the MiniGrid DoorKey and Cliff Walking environments, we demonstrate that PBIM and GRM successfully prevent the agent from converging to a suboptimal policy and can speed up training. Additionally, we prove that GRM is sufficiently general as to encompass all potential-based reward shaping functions. This paper expands on previous work introducing the PBIM method, and provides an extension to the more general method of GRM, as well as additional proofs, experimental results, and discussion.

Conditional density estimation (CDE) goes beyond regression by modeling the full conditional distribution, providing a richer understanding of the data than just the conditional mean in regression. This makes CDE particularly useful in critical application domains. However, interpretable CDE methods are understudied. Current methods typically employ kernel-based approaches, using kernel functions directly for kernel density estimation or as basis functions in linear models. In contrast, despite their conceptual simplicity and visualization suitability, tree-based methods -- which are arguably more comprehensible -- have been largely overlooked for CDE tasks. Thus, we propose the Conditional Density Tree (CDTree), a fully non-parametric model consisting of a decision tree in which each leaf is formed by a histogram model. Specifically, we formalize the problem of learning a CDTree using the minimum description length (MDL) principle, which eliminates the need for tuning the hyperparameter for regularization. Next, we propose an iterative algorithm that, although greedily, searches the optimal histogram for every possible node split. Our experiments demonstrate that, in comparison to existing interpretable CDE methods, CDTrees are both more accurate (as measured by the log-loss) and more robust against irrelevant features. Further, our approach leads to smaller tree sizes than existing tree-based models, which benefits interpretability.

We consider the problem of detecting, isolating and classifying elephant calls in continuously recorded audio. Such automatic call characterisation can assist conservation efforts and inform environmental management strategies. In contrast to previous work in which call detection was performed at a segment level, we perform call detection at a frame level which implicitly also allows call endpointing, the isolation of a call in a longer recording. For experimentation, we employ two annotated datasets, one containing Asian and the other African elephant vocalisations. We evaluate several shallow and deep classifier models, and show that the current best performance can be improved by using an audio spectrogram transformer (AST), a neural architecture which has not been used for this purpose before, and which we have configured in a novel sequence-to-sequence manner. We also show that using transfer learning by pre-training leads to further improvements both in terms of computational complexity and performance. Finally, we consider sub-call classification using an accepted taxonomy of call types, a task which has not previously been considered. We show that also in this case the transformer architectures provide the best performance. Our best classifiers achieve an average precision (AP) of 0.962 for framewise binary call classification, and an area under the receiver operating characteristic (AUC) of 0.957 and 0.979 for call classification with 5 classes and sub-call classification with 7 classes respectively. All of these represent either new benchmarks (sub-call classifications) or improvements on previously best systems. We conclude that a fully-automated elephant call detection and subcall classification system is within reach. Such a system would provide valuable information on the behaviour and state of elephant herds for the purposes of conservation and management.

We introduce a generic, compositional and interpretable class of generative world models that supports open-ended learning agents. This is a sparse class of Bayesian networks capable of approximating a broad range of stochastic processes, which provide agents with the ability to learn world models in a manner that may be both interpretable and computationally scalable. This approach integrating Bayesian structure learning and intrinsically motivated (model-based) planning enables agents to actively develop and refine their world models, which may lead to developmental learning and more robust, adaptive behavior.

Selecting cost-effective optimal sensor configurations for subsequent inference of parameters in black-box stochastic systems faces significant computational barriers. We propose a novel and robust approach, modelling the joint distribution over input parameters and solution with a joint energy-based model, trained on simulation data. Unlike existing simulation-based inference approaches, which must be tied to a specific set of point evaluations, we learn a functional representation of parameters and solution. This is used as a resolution-independent plug-and-play surrogate for the joint distribution, which can be conditioned over any set of points, permitting an efficient approach to sensor placement. We demonstrate the validity of our framework on a variety of stochastic problems, showing that our method provides highly informative sensor locations at a lower computational cost compared to conventional approaches.

Several popular variational bounds involving importance weighting ideas have been proposed to generalize and improve on the Evidence Lower BOund (ELBO) in the context of maximum likelihood optimization, such as the Importance Weighted Auto-Encoder (IWAE) and the Variational R\'enyi (VR) bounds. The methodology to learn the parameters of interest using these bounds typically amounts to running gradient-based variational inference algorithms that incorporate the reparameterization trick. However, the way the choice of the variational bound impacts the outcome of variational inference algorithms can be unclear. Recently, the VR-IWAE bound was introduced as a variational bound that unifies the ELBO, IWAE and VR bounds methodologies. In this paper, we provide two analyses for the reparameterized and doubly-reparameterized gradient estimators of the VR-IWAE bound, which reveal the advantages and limitations of these gradient estimators while enabling us to compare of the ELBO, IWAE and VR bounds methodologies. Our work advances the understanding of importance weighted variational inference methods and we illustrate our theoretical findings empirically.

The log-linear model has received a significant amount of theoretical attention in previous decades and remains the fundamental tool used for learning probability distributions over discrete variables. Despite its large popularity in statistical mechanics and high-dimensional statistics, the vast majority of such energy-based modeling approaches only focus on the two-variable relationships, such as Boltzmann machines and Markov graphical models. Although these approaches have easier-to-solve structure learning problems and easier-to-optimize parametric distributions, they often ignore the rich structure which exists in the higher-order interactions between different variables. Using more recent tools from the field of information geometry, we revisit the classical formulation of the log-linear model with a focus on higher-order mode interactions, going beyond the 1-body modes of independent distributions and the 2-body modes of Boltzmann distributions. This perspective allows us to define a complete decomposition of the KL error. This then motivates the formulation of a sparse selection problem over the set of possible mode interactions. In the same way as sparse graph selection allows for better generalization, we find that our learned distributions are able to more efficiently use the finite amount of data which is available in practice. On both synthetic and real-world datasets, we demonstrate our algorithm's effectiveness in maximizing the log-likelihood for the generative task and also the ease of adaptability to the discriminative task of classification.

Bayesian Optimal Experimental Design (BOED) is a powerful tool to reduce the cost of running a sequence of experiments. When based on the Expected Information Gain (EIG), design optimization corresponds to the maximization of some intractable expected {\it contrast} between prior and posterior distributions. Scaling this maximization to high dimensional and complex settings has been an issue due to BOED inherent computational complexity. In this work, we introduce an {\it expected posterior} distribution with cost-effective sampling properties and provide a tractable access to the EIG contrast maximization via a new EIG gradient expression. Diffusion-based samplers are used to compute the dynamics of the expected posterior and ideas from bi-level optimization are leveraged to derive an efficient joint sampling-optimization loop, without resorting to lower bound approximations of the EIG. The resulting efficiency gain allows to extend BOED to the well-tested generative capabilities of diffusion models. By incorporating generative models into the BOED framework, we expand its scope and its use in scenarios that were previously impractical. Numerical experiments and comparison with state-of-the-art methods show the potential of the approach.

The emerging zero-shot capabilities of Large Language Models (LLMs) have led to their applications in areas extending well beyond natural language processing tasks. In reinforcement learning, while LLMs have been extensively used in text-based environments, their integration with continuous state spaces remains understudied. In this paper, we investigate how pre-trained LLMs can be leveraged to predict in context the dynamics of continuous Markov decision processes. We identify handling multivariate data and incorporating the control signal as key challenges that limit the potential of LLMs' deployment in this setup and propose Disentangled In-Context Learning (DICL) to address them. We present proof-of-concept applications in two reinforcement learning settings: model-based policy evaluation and data-augmented off-policy reinforcement learning, supported by theoretical analysis of the proposed methods. Our experiments further demonstrate that our approach produces well-calibrated uncertainty estimates. We release the code at https://github.com/abenechehab/dicl.