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In this paper we obtain quantitative Bernstein-von Mises type bounds on the normal approximation of the posterior distribution in exponential family models when centering either around the posterior mode or around the maximum likelihood estimator. Our bounds, obtained through a version of Stein's method, are non-asymptotic, and data dependent; they are of the correct order both in the total variation and Wasserstein distances, as well as for approximations for expectations of smooth functions of the posterior. All our results are valid for univariate and multivariate posteriors alike, and do not require a conjugate prior setting. We illustrate our findings on a variety of exponential family distributions, including Poisson, multinomial and normal distribution with unknown mean and variance. The resulting bounds have an explicit dependence on the prior distribution and on sufficient statistics of the data from the sample, and thus provide insight into how these factors may affect the quality of the normal approximation. The performance of the bounds is also assessed with simulations.

In this article, we propose a novel spatial global-local spike-and-slab selection prior for image-on-scalar regression. We consider a Bayesian hierarchical Gaussian process model for image smoothing, that uses a flexible Inverse-Wishart process prior to handle within-image dependency, and propose a general global-local spatial selection prior that extends a rich class of well-studied selection priors. Unlike existing constructions, we achieve simultaneous global (i.e, at covariate-level) and local (i.e., at pixel/voxel-level) selection by introducing `participation rate' parameters that measure the probability for the individual covariates to affect the observed images. This along with a hard-thresholding strategy leads to dependency between selections at the two levels, introduces extra sparsity at the local level, and allows the global selection to be informed by the local selection, all in a model-based manner. We design an efficient Gibbs sampler that allows inference for large image data. We show on simulated data that parameters are interpretable and lead to efficient selection. Finally, we demonstrate performance of the proposed model by using data from the Autism Brain Imaging Data Exchange (ABIDE) study. To the best of our knowledge, the proposed model construction is the first in the Bayesian literature to simultaneously achieve image smoothing, parameter estimation and a two-level variable selection for image-on-scalar regression.

Reinforcement learning (RL) techniques have been developed to optimize industrial cooling systems, offering substantial energy savings compared to traditional heuristic policies. A major challenge in industrial control involves learning behaviors that are feasible in the real world due to machinery constraints. For example, certain actions can only be executed every few hours while other actions can be taken more frequently. Without extensive reward engineering and experimentation, an RL agent may not learn realistic operation of machinery. To address this, we use hierarchical reinforcement learning with multiple agents that control subsets of actions according to their operation time scales. Our hierarchical approach achieves energy savings over existing baselines while maintaining constraints such as operating chillers within safe bounds in a simulated HVAC control environment.

Feature transformation aims to extract a good representation (feature) space by mathematically transforming existing features. It is crucial to address the curse of dimensionality, enhance model generalization, overcome data sparsity, and expand the availability of classic models. Current research focuses on domain knowledge-based feature engineering or learning latent representations; nevertheless, these methods are not entirely automated and cannot produce a traceable and optimal representation space. When rebuilding a feature space for a machine learning task, can these limitations be addressed concurrently? In this extension study, we present a self-optimizing framework for feature transformation. To achieve a better performance, we improved the preliminary work by (1) obtaining an advanced state representation for enabling reinforced agents to comprehend the current feature set better; and (2) resolving Q-value overestimation in reinforced agents for learning unbiased and effective policies. Finally, to make experiments more convincing than the preliminary work, we conclude by adding the outlier detection task with five datasets, evaluating various state representation approaches, and comparing different training strategies. Extensive experiments and case studies show that our work is more effective and superior.

Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this work, we first show that BNN+LV suffers from a serious form of non-identifiability: explanatory power can be transferred between the model parameters and latent variables while fitting the data equally well. We demonstrate that as a result, in the limit of infinite data, the posterior mode over the network weights and latent variables is asymptotically biased away from the ground-truth. Due to this asymptotic bias, traditional inference methods may in practice yield parameters that generalize poorly and misestimate uncertainty. Next, we develop a novel inference procedure that explicitly mitigates the effects of likelihood non-identifiability during training and yields high-quality predictions as well as uncertainty estimates. We demonstrate that our inference method improves upon benchmark methods across a range of synthetic and real data-sets.

Variational Bayesian posterior inference often requires simplifying approximations such as mean-field parametrisation to ensure tractability. However, prior work has associated the variational mean-field approximation for Bayesian neural networks with underfitting in the case of small datasets or large model sizes. In this work, we show that invariances in the likelihood function of over-parametrised models contribute to this phenomenon because these invariances complicate the structure of the posterior by introducing discrete and/or continuous modes which cannot be well approximated by Gaussian mean-field distributions. In particular, we show that the mean-field approximation has an additional gap in the evidence lower bound compared to a purpose-built posterior that takes into account the known invariances. Importantly, this invariance gap is not constant; it vanishes as the approximation reverts to the prior. We proceed by first considering translation invariances in a linear model with a single data point in detail. We show that, while the true posterior can be constructed from a mean-field parametrisation, this is achieved only if the objective function takes into account the invariance gap. Then, we transfer our analysis of the linear model to neural networks. Our analysis provides a framework for future work to explore solutions to the invariance problem.

We train graph neural networks on halo catalogues from Gadget N-body simulations to perform field-level likelihood-free inference of cosmological parameters. The catalogues contain $\lesssim$5,000 halos with masses $\gtrsim 10^{10}~h^{-1}M_\odot$ in a periodic volume of $(25~h^{-1}{\rm Mpc})^3$; every halo in the catalogue is characterized by several properties such as position, mass, velocity, concentration, and maximum circular velocity. Our models, built to be permutationally, translationally, and rotationally invariant, do not impose a minimum scale on which to extract information and are able to infer the values of $\Omega_{\rm m}$ and $\sigma_8$ with a mean relative error of $\sim6\%$, when using positions plus velocities and positions plus masses, respectively. More importantly, we find that our models are very robust: they can infer the value of $\Omega_{\rm m}$ and $\sigma_8$ when tested using halo catalogues from thousands of N-body simulations run with five different N-body codes: Abacus, CUBEP$^3$M, Enzo, PKDGrav3, and Ramses. Surprisingly, the model trained to infer $\Omega_{\rm m}$ also works when tested on thousands of state-of-the-art CAMELS hydrodynamic simulations run with four different codes and subgrid physics implementations. Using halo properties such as concentration and maximum circular velocity allow our models to extract more information, at the expense of breaking the robustness of the models. This may happen because the different N-body codes are not converged on the relevant scales corresponding to these parameters.

The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, if not better than, the original dense networks. Sparsity can reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field.