Training energy-based models (EBMs) with maximum likelihood estimation on high-dimensional data can be both challenging and time-consuming. As a result, there a noticeable gap in sample quality between EBMs and other generative frameworks like GANs and diffusion models. To close this gap, inspired by the recent efforts of learning EBMs by maximimizing diffusion recovery likelihood (DRL), we propose cooperative diffusion recovery likelihood (CDRL), an effective approach to tractably learn and sample from a series of EBMs defined on increasingly noisy versons of a dataset, paired with an initializer model for each EBM. At each noise level, the initializer model learns to amortize the sampling process of the EBM, and the two models are jointly estimated within a cooperative training framework. Samples from the initializer serve as starting points that are refined by a few sampling steps from the EBM. With the refined samples, the EBM is optimized by maximizing recovery likelihood, while the initializer is optimized by learning from the difference between the refined samples and the initial samples. We develop a new noise schedule and a variance reduction technique to further improve the sample quality. Combining these advances, we significantly boost the FID scores compared to existing EBM methods on CIFAR-10 and ImageNet 32x32, with a 2x speedup over DRL. In addition, we extend our method to compositional generation and image inpainting tasks, and showcase the compatibility of CDRL with classifier-free guidance for conditional generation, achieving similar trade-offs between sample quality and sample diversity as in diffusion models.

A crucial design decision for any robot learning pipeline is the choice of policy representation: what type of model should be used to generate the next set of robot actions? Owing to the inherent multi-modal nature of many robotic tasks, combined with the recent successes in generative modeling, researchers have turned to state-of-the-art probabilistic models such as diffusion models for policy representation. In this work, we revisit the choice of energy-based models (EBM) as a policy class. We show that the prevailing folklore -- that energy models in high dimensional continuous spaces are impractical to train -- is false. We develop a practical training objective and algorithm for energy models which combines several key ingredients: (i) ranking noise contrastive estimation (R-NCE), (ii) learnable negative samplers, and (iii) non-adversarial joint training. We prove that our proposed objective function is asymptotically consistent and quantify its limiting variance. On the other hand, we show that the Implicit Behavior Cloning (IBC) objective is actually biased even at the population level, providing a mathematical explanation for the poor performance of IBC trained energy policies in several independent follow-up works. We further extend our algorithm to learn a continuous stochastic process that bridges noise and data, modeling this process with a family of EBMs indexed by scale variable. In doing so, we demonstrate that the core idea behind recent progress in generative modeling is actually compatible with EBMs. Altogether, our proposed training algorithms enable us to train energy-based models as policies which compete with -- and even outperform -- diffusion models and other state-of-the-art approaches in several challenging multi-modal benchmarks: obstacle avoidance path planning and contact-rich block pushing.

Whether and how data scientists, statisticians and modellers should be accountable for the AI systems they develop remains a controversial and highly debated topic, especially given the complexity of AI systems and the difficulties in comparing and synthesising competing claims arising from their deployment for data analysis. This paper proposes to address this issue by decreasing the opacity and heightening the accountability of decision making using AI systems, through the explicit acknowledgement of the statistical foundations that underpin their development and the ways in which these dictate how their results should be interpreted and acted upon by users. In turn, this enhances (1) the responsiveness of the models to feedback, (2) the quality and meaning of uncertainty on their outputs and (3) their transparency to evaluation. To exemplify this approach, we extend Posterior Belief Assessment to offer a route to belief ownership from complex and competing AI structures. We argue that this is a significant way to bring ethical considerations into mathematical reasoning, and to implement ethical AI in statistical practice. We demonstrate these ideas within the context of competing models used to advise the UK government on the spread of the Omicron variant of COVID-19 during December 2021.

Pool-based active learning (AL) is a promising technology for increasing data-efficiency of machine learning models. However, surveys show that performance of recent AL methods is very sensitive to the choice of dataset and training setting, making them unsuitable for general application. In order to tackle this problem, the field Learning Active Learning (LAL) suggests to learn the active learning strategy itself, allowing it to adapt to the given setting. In this work, we propose a novel LAL method for classification that exploits symmetry and independence properties of the active learning problem with an Attentive Conditional Neural Process model. Our approach is based on learning from a myopic oracle, which gives our model the ability to adapt to non-standard objectives, such as those that do not equally weight the error on all data points. We experimentally verify that our Neural Process model outperforms a variety of baselines in these settings. Finally, our experiments show that our model exhibits a tendency towards improved stability to changing datasets. However, performance is sensitive to choice of classifier and more work is necessary to reduce the performance the gap with the myopic oracle and to improve scalability. We present our work as a proof-of-concept for LAL on nonstandard objectives and hope our analysis and modelling considerations inspire future LAL work.

While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learnt representations meaningful. For this the typical approach is to regularize the learned representation through prior probability distributions. However such priors are usually unavailable or ad hoc. To deal with this, we propose a dynamics-constrained representation learning framework. Instead of using predefined probabilities, we restrict the latent representation to follow specific dynamics, which is a more natural constraint for representation learning in dynamical systems. Our belief stems from a fundamental observation in physics that though different systems can have different marginalized probability distributions, they typically obey the same dynamics, such as Newton's and Schrodinger's equations. We validate our framework for different systems including a real-world fluorescent DNA movie dataset. We show that our algorithm can uniquely identify an uncorrelated, isometric and meaningful latent representation.

Count data play a critical role in medical research, such as heart disease. The Poisson regression model is a common technique for evaluating the impact of a set of covariates on the count responses. The mixture of Poisson regression models with experts is a practical tool to exploit the covariates, not only to handle the heterogeneity in the Poisson regressions but also to learn the mixing structure of the population. Multicollinearity is one of the most common challenges with regression models, leading to ill-conditioned design matrices of Poisson regression components and expert classes. The maximum likelihood method produces unreliable and misleading estimates for the effects of the covariates in multicollinearity. In this research, we develop Ridge and Liu-type methods as two shrinkage approaches to cope with the ill-conditioned design matrices of the mixture of Poisson regression models with experts. Through various numerical studies, we demonstrate that the shrinkage methods offer more reliable estimates for the coefficients of the mixture model in multicollinearity while maintaining the classification performance of the ML method. The shrinkage methods are finally applied to a heart study to analyze the heart disease rate stages.

We conduct a detailed investigation of tempered posteriors and uncover a number of crucial and previously undiscussed points. Contrary to previous results, we first show that for realistic models and datasets and the tightly controlled case of the Laplace approximation to the posterior, stochasticity does not in general improve test accuracy. The coldest temperature is often optimal. One might think that Bayesian models with some stochasticity can at least obtain improvements in terms of calibration. However, we show empirically that when gains are obtained this comes at the cost of degradation in test accuracy. We then discuss how targeting Frequentist metrics using Bayesian models provides a simple explanation of the need for a temperature parameter $\lambda$ in the optimization objective. Contrary to prior works, we finally show through a PAC-Bayesian analysis that the temperature $\lambda$ cannot be seen as simply fixing a misspecified prior or likelihood.

In the simulation of physical systems, an increase in model complexity directly corresponds to an increase in the simulation time, posing substantial limitations to the use of such models for critical applications that depend on timesensitive decisions. Therefore, fast emulators learned by data-driven architectures and integrated in algorithms for the solution of forward and inverse problems are becoming increasingly successful. On one hand, several contributions in the literature have proposed architectures for physics-based emulators designed to limit the number of model evaluations during training. These include, for example, physics-informed neural networks (PINN) [1], deep operator networks (DeepONet) [2], and transformers-based architectures [3]. On the other hand, generative approaches have been the subject of significant recent research due to their flexibility to quantify uncertainty in the predicted outputs. Unlike traditional deep learning tasks, generative models focus on capturing a distributional characterization of the latent variables, providing an improved understanding, and a superior way to interact with a given system. Examples in this context include Gaussian Processes [4], Bayesian networks [5], generative adversarial networks (GAN) [6], diffusion models [7], optimal transport [8], normalizing flow [9, 10] and Variational Auto-Encoders (VAE) [11]. When using data-driven emulators in the context of inverse problems, other difficulties arise. Inverse problem are often ill-posed as a result of non-uniqueness of solutions, or of ill-conditioning due to high-dimensionality, data-sparsity, noise-corruption, and nonlinear response of the physical systems [12, 13, 14, 15, 16].

This article studies the infinite-width limit of deep feedforward neural networks whose weights are dependent, and modelled via a mixture of Gaussian distributions. Each hidden node of the network is assigned a nonnegative random variable that controls the variance of the outgoing weights of that node. We make minimal assumptions on these per-node random variables: they are iid and their sum, in each layer, converges to some finite random variable in the infinite-width limit. Under this model, we show that each layer of the infinite-width neural network can be characterised by two simple quantities: a non-negative scalar parameter and a L\'evy measure on the positive reals. If the scalar parameters are strictly positive and the L\'evy measures are trivial at all hidden layers, then one recovers the classical Gaussian process (GP) limit, obtained with iid Gaussian weights. More interestingly, if the L\'evy measure of at least one layer is non-trivial, we obtain a mixture of Gaussian processes (MoGP) in the large-width limit. The behaviour of the neural network in this regime is very different from the GP regime. One obtains correlated outputs, with non-Gaussian distributions, possibly with heavy tails. Additionally, we show that, in this regime, the weights are compressible, and some nodes have asymptotically non-negligible contributions, therefore representing important hidden features. Many sparsity-promoting neural network models can be recast as special cases of our approach, and we discuss their infinite-width limits; we also present an asymptotic analysis of the pruning error. We illustrate some of the benefits of the MoGP regime over the GP regime in terms of representation learning and compressibility on simulated, MNIST and Fashion MNIST datasets.

We present the effect of adapting to human preferences on trust in a human-robot teaming task. The team performs a task in which the robot acts as an action recommender to the human. It is assumed that the behavior of the human and the robot is based on some reward function they try to optimize. We use a new human trust-behavior model that enables the robot to learn and adapt to the human's preferences in real-time during their interaction using Bayesian Inverse Reinforcement Learning. We present three strategies for the robot to interact with a human: a non-learner strategy, in which the robot assumes that the human's reward function is the same as the robot's, a non-adaptive learner strategy that learns the human's reward function for performance estimation, but still optimizes its own reward function, and an adaptive-learner strategy that learns the human's reward function for performance estimation and also optimizes this learned reward function. Results show that adapting to the human's reward function results in the highest trust in the robot.