In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance parameter. By contrast, for Bayesian classification we use a categorical distribution with no mechanism to represent our beliefs about aleatoric uncertainty. Our work shows that explicitly accounting for aleatoric uncertainty significantly improves the performance of Bayesian neural networks. We note that many standard benchmarks, such as CIFAR, have essentially no aleatoric uncertainty. Moreover, we show data augmentation in approximate inference has the effect of softening the likelihood, leading to underconfidence and profoundly misrepresenting our honest beliefs about aleatoric uncertainty. Accordingly, we find that a cold posterior, tempered by a power greater than one, often more honestly reflects our beliefs about aleatoric uncertainty than no tempering -- providing an explicit link between data augmentation and cold posteriors. We show that we can match or exceed the performance of posterior tempering by using a Dirichlet observation model, where we explicitly control the level of aleatoric uncertainty, without any need for tempering.

Home absence detection is an emerging field on smart home installations. Identifying whether or not the residents of the house are present, is important in numerous scenarios. Possible scenarios include but are not limited to: elderly people living alone, people suffering from dementia, home quarantine. The majority of published papers focus on either pressure / door sensors or cameras in order to detect outing events. Although the aforementioned approaches provide solid results, they are intrusive and require modifications for sensor placement. In our work, appliance electrical use is investigated as a means for detecting the presence or absence of residents. The energy use is the result of power disaggregation, a non intrusive / non invasive sensing method. Since a dataset providing energy data and ground truth for home absence is not available, artificial outing events were introduced on the UK-DALE dataset, a well known dataset for Non Intrusive Load Monitoring (NILM). Several machine learning algorithms were evaluated using the generated dataset. Benchmark results have shown that home absence detection using appliance power consumption is feasible.

Optimization strategies driven by machine learning, such as Bayesian optimization, are being explored across experimental sciences as an efficient alternative to traditional design of experiment. When combined with automated laboratory hardware and high-performance computing, these strategies enable next-generation platforms for autonomous experimentation. However, the practical application of these approaches is hampered by a lack of flexible software and algorithms tailored to the unique requirements of chemical research. One such aspect is the pervasive presence of constraints in the experimental conditions when optimizing chemical processes or protocols, and in the chemical space that is accessible when designing functional molecules or materials. Although many of these constraints are known a priori, they can be interdependent, non-linear, and result in non-compact optimization domains. In this work, we extend our experiment planning algorithms Phoenics and Gryffin such that they can handle arbitrary known constraints via an intuitive and flexible interface. We benchmark these extended algorithms on continuous and discrete test functions with a diverse set of constraints, demonstrating their flexibility and robustness. In addition, we illustrate their practical utility in two simulated chemical research scenarios: the optimization of the synthesis of o-xylenyl Buckminsterfullerene adducts under constrained flow conditions, and the design of redox active molecules for flow batteries under synthetic accessibility constraints. The tools developed constitute a simple, yet versatile strategy to enable model-based optimization with known experimental constraints, contributing to its applicability as a core component of autonomous platforms for scientific discovery.

Embarrassingly parallel Markov Chain Monte Carlo (MCMC) exploits parallel computing to scale Bayesian inference to large datasets by using a two-step approach. First, MCMC is run in parallel on (sub)posteriors defined on data partitions. Then, a server combines local results. While efficient, this framework is very sensitive to the quality of subposterior sampling. Common sampling problems such as missing modes or misrepresentation of low-density regions are amplified -- instead of being corrected -- in the combination phase, leading to catastrophic failures. In this work, we propose a novel combination strategy to mitigate this issue. Our strategy, Parallel Active Inference (PAI), leverages Gaussian Process (GP) surrogate modeling and active learning. After fitting GPs to subposteriors, PAI (i) shares information between GP surrogates to cover missing modes; and (ii) uses active sampling to individually refine subposterior approximations. We validate PAI in challenging benchmarks, including heavy-tailed and multi-modal posteriors and a real-world application to computational neuroscience. Empirical results show that PAI succeeds where previous methods catastrophically fail, with a small communication overhead.

This paper proposes using a sparse-structured multivariate Gaussian to provide a closed-form approximator for the output of probabilistic ensemble models used for dense image prediction tasks. This is achieved through a convolutional neural network that predicts the mean and covariance of the distribution, where the inverse covariance is parameterised by a sparsely structured Cholesky matrix. Similarly to distillation approaches, our single network is trained to maximise the probability of samples from pre-trained probabilistic models, in this work we use a fixed ensemble of networks. Once trained, our compact representation can be used to efficiently draw spatially correlated samples from the approximated output distribution. Importantly, this approach captures the uncertainty and structured correlations in the predictions explicitly in a formal distribution, rather than implicitly through sampling alone. This allows direct introspection of the model, enabling visualisation of the learned structure. Moreover, this formulation provides two further benefits: estimation of a sample probability, and the introduction of arbitrary spatial conditioning at test time. We demonstrate the merits of our approach on monocular depth estimation and show that the advantages of our approach are obtained with comparable quantitative performance.

Black-box variational inference (BBVI) now sees widespread use in machine learning and statistics as a fast yet flexible alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, stochastic optimization methods for BBVI remain unreliable and require substantial expertise and hand-tuning to apply effectively. In this paper, we propose Robust, Automated, and Accurate BBVI (RAABBVI), a framework for reliable BBVI optimization. RAABBVI is based on rigorously justified automation techniques, includes just a small number of intuitive tuning parameters, and detects inaccurate estimates of the optimal variational approximation. RAABBVI adaptively decreases the learning rate by detecting convergence of the fixed--learning-rate iterates, then estimates the symmetrized Kullback--Leiber (KL) divergence between the current variational approximation and the optimal one. It also employs a novel optimization termination criterion that enables the user to balance desired accuracy against computational cost by comparing (i) the predicted relative decrease in the symmetrized KL divergence if a smaller learning were used and (ii) the predicted computation required to converge with the smaller learning rate. We validate the robustness and accuracy of RAABBVI through carefully designed simulation studies and on a diverse set of real-world model and data examples.

This paper concerns differentially private Bayesian estimation of the parameters of a population distribution, when a statistic of a sample from that population is shared in noise to provide differential privacy. This work mainly addresses two problems: (1) What statistic of the sample should be shared privately? For the first question, i.e., the one about statistic selection, we promote using the Fisher information. We find out that, the statistic that is most informative in a non-privacy setting may not be the optimal choice under the privacy restrictions. We provide several examples to support that point. We consider several types of data sharing settings and propose several Monte Carlo-based numerical estimation methods for calculating the Fisher information for those settings. The second question concerns inference: (2) Based on the shared statistics, how could we perform effective Bayesian inference? We propose several Markov chain Monte Carlo (MCMC) algorithms for sampling from the posterior distribution of the parameter given the noisy statistic. The proposed MCMC algorithms can be preferred over one another depending on the problem. For example, when the shared statistics is additive and added Gaussian noise, a simple Metropolis-Hasting algorithm that utilizes the central limit theorem is a decent choice. We propose more advanced MCMC algorithms for several other cases of practical relevance. Our numerical examples involve comparing several candidate statistics to be shared privately. For each statistic, we perform Bayesian estimation based on the posterior distribution conditional on the privatized version of that statistic. We demonstrate that, the relative performance of a statistic, in terms of the mean squared error of the Bayesian estimator based on the corresponding privatized statistic, is adequately predicted by the Fisher information of the privatized statistic.

We propose a multi-tone decomposition algorithm that can find the frequencies, amplitudes and phases of the fundamental sinusoids in a noisy observation sequence. Under independent identically distributed Gaussian noise, our method utilizes a maximum likelihood approach to estimate the relevant tone parameters from the contaminated observations. When estimating $M$ number of sinusoidal sources, our algorithm successively estimates their frequencies and jointly optimizes their amplitudes and phases. Our method can also be implemented as a blind source separator in the absence of the information about $M$. The computational complexity of our algorithm is near-linear, i.e., $\tilde{O}(N)$.

Many existing conditional score-based data generation methods utilize Bayes' theorem to decompose the gradients of a log posterior density into a mixture of scores. These methods facilitate the training procedure of conditional score models, as a mixture of scores can be separately estimated using a score model and a classifier. However, our analysis indicates that the training objectives for the classifier in these methods may lead to a serious score mismatch issue, which corresponds to the situation that the estimated scores deviate from the true ones. Such an issue causes the samples to be misled by the deviated scores during the diffusion process, resulting in a degraded sampling quality. To resolve it, we formulate a novel training objective, called Denoising Likelihood Score Matching (DLSM) loss, for the classifier to match the gradients of the true log likelihood density. Our experimental evidence shows that the proposed method outperforms the previous methods on both Cifar-10 and Cifar-100 benchmarks noticeably in terms of several key evaluation metrics. We thus conclude that, by adopting DLSM, the conditional scores can be accurately modeled, and the effect of the score mismatch issue is alleviated. Score-based generative models are probabilistic generative models that estimate score functions, i.e., the gradients of the log density for some given data distributions.

Conditional Neural Processes~(CNPs) bridge neural networks with probabilistic inference to approximate functions of Stochastic Processes under meta-learning settings. Given a batch of non-{\it i.i.d} function instantiations, CNPs are jointly optimized for in-instantiation observation prediction and cross-instantiation meta-representation adaptation within a generative reconstruction pipeline. There can be a challenge in tying together such two targets when the distribution of function observations scales to high-dimensional and noisy spaces. Instead, noise contrastive estimation might be able to provide more robust representations by learning distributional matching objectives to combat such inherent limitation of generative models. In light of this, we propose to equip CNPs by 1) aligning prediction with encoded ground-truth observation, and 2) decoupling meta-representation adaptation from generative reconstruction. Specifically, two auxiliary contrastive branches are set up hierarchically, namely in-instantiation temporal contrastive learning~({\tt TCL}) and cross-instantiation function contrastive learning~({\tt FCL}), to facilitate local predictive alignment and global function consistency, respectively. We empirically show that {\tt TCL} captures high-level abstraction of observations, whereas {\tt FCL} helps identify underlying functions, which in turn provides more efficient representations. Our model outperforms other CNPs variants when evaluating function distribution reconstruction and parameter identification across 1D, 2D and high-dimensional time-series.