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.

Distributions in spatial model often exhibit localized features. Intuitively, this locality implies a low intrinsic dimensionality, which can be exploited for efficient approximation and computation of complex distributions. However, existing approximation theory mainly considers the joint distributions, which does not guarantee that the marginal errors are small. In this work, we establish a dimension independent error bound for the marginals of approximate distributions. This $\ell_\infty$-approximation error is obtained using Stein's method, and we propose a $\delta$-locality condition that quantifies the degree of localization in a distribution. We also show how $\delta$-locality can be derived from different conditions that characterize the distribution's locality. Our $\ell_\infty$ bound motivates the localization of existing approximation methods to respect the locality. As examples, we show how to use localized likelihood-informed subspace method and localized score matching, which not only avoid dimension dependence in the approximation error, but also significantly reduce the computational cost due to the local and parallel implementation based on the localized structure.

As complex machine learning models continue to find applications in high-stakes decision-making scenarios, it is crucial that we can explain and understand their predictions. Post-hoc explanation methods provide useful insights by identifying important features in an input $\mathbf{x}$ with respect to the model output $f(\mathbf{x})$. In this work, we formalize and study two precise notions of feature importance for general machine learning models: sufficiency and necessity. We demonstrate how these two types of explanations, albeit intuitive and simple, can fall short in providing a complete picture of which features a model finds important. To this end, we propose a unified notion of importance that circumvents these limitations by exploring a continuum along a necessity-sufficiency axis. Our unified notion, we show, has strong ties to other popular definitions of feature importance, like those based on conditional independence and game-theoretic quantities like Shapley values. Crucially, we demonstrate how a unified perspective allows us to detect important features that could be missed by either of the previous approaches alone.

Monitoring networks increasingly aim to assimilate data from a large number of diverse sensors covering many sensing modalities. Bayesian optimal experimental design (OED) seeks to identify data, sensor configurations, or experiments which can optimally reduce uncertainty and hence increase the performance of a monitoring network. Information theory guides OED by formulating the choice of experiment or sensor placement as an optimization problem that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge and models of expected observation data. Therefore, within the context of seismo-acoustic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types, and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize a sensor network's ability to locate seismic events from arrival time data of detected seismic phases at the regional-scale. Bayesian OED requires four elements: 1) A likelihood function that describes the distribution of detection and travel time data from the sensor network, 2) A Bayesian solver that uses a prior and likelihood to identify the posterior distribution of seismic events given the data, 3) An algorithm to compute EIG about seismic events over a dataset of hypothetical prior events, 4) An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we explore many relevant questions to monitoring such as: how to trade off sensor fidelity and earth model uncertainty; how sensor types, number, and locations influence uncertainty; and how prior models and constraints influence sensor placement.

Stein Variational Gradient Descent (SVGD) is a highly efficient method to sample from an unnormalized probability distribution. However, the SVGD update relies on gradients of the log-density, which may not always be available. Existing gradient-free versions of SVGD make use of simple Monte Carlo approximations or gradients from surrogate distributions, both with limitations. To improve gradient-free Stein variational inference, we combine SVGD steps with evolution strategy (ES) updates. Our results demonstrate that the resulting algorithm generates high-quality samples from unnormalized target densities without requiring gradient information. Compared to prior gradient-free SVGD methods, we find that the integration of the ES update in SVGD significantly improves the performance on multiple challenging benchmark problems.

We propose a scalable kinetic Langevin dynamics algorithm for sampling parameter spaces of big data and AI applications. Our scheme combines a symmetric forward/backward sweep over minibatches with a symmetric discretization of Langevin dynamics. For a particular Langevin splitting method (UBU), we show that the resulting Symmetric Minibatch Splitting-UBU (SMS-UBU) integrator has bias $O(h^2 d^{1/2})$ in dimension $d>0$ with stepsize $h>0$, despite only using one minibatch per iteration, thus providing excellent control of the sampling bias as a function of the stepsize. We apply the algorithm to explore local modes of the posterior distribution of Bayesian neural networks (BNNs) and evaluate the calibration performance of the posterior predictive probabilities for neural networks with convolutional neural network architectures for classification problems on three different datasets (Fashion-MNIST, Celeb-A and chest X-ray). Our results indicate that BNNs sampled with SMS-UBU can offer significantly better calibration performance compared to standard methods of training and stochastic weight averaging.

Reasoning is key to many decision making processes. It requires consolidating a set of rule-like premises that are often associated with degrees of uncertainty and observations to draw conclusions. In this work, we address both the case where premises are specified as numeric probabilistic rules and situations in which humans state their estimates using words expressing degrees of certainty. Existing probabilistic reasoning datasets simplify the task, e.g., by requiring the model to only rank textual alternatives, by including only binary random variables, or by making use of a limited set of templates that result in less varied text. In this work, we present QUITE, a question answering dataset of real-world Bayesian reasoning scenarios with categorical random variables and complex relationships. QUITE provides high-quality natural language verbalizations of premises together with evidence statements and expects the answer to a question in the form of an estimated probability. We conduct an extensive set of experiments, finding that logic-based models outperform out-of-the-box large language models on all reasoning types (causal, evidential, and explaining-away). Our results provide evidence that neuro-symbolic models are a promising direction for improving complex reasoning. We release QUITE and code for training and experiments on Github.

Bayesian optimisation for real-world problems is often performed interactively with human experts, and integrating their domain knowledge is key to accelerate the optimisation process. We consider a setup where experts provide advice on the next query point through binary accept/reject recommendations (labels). Experts' labels are often costly, requiring efficient use of their efforts, and can at the same time be unreliable, requiring careful adjustment of the degree to which any expert is trusted. We introduce the first principled approach that provides two key guarantees. (1) Handover guarantee: similar to a no-regret property, we establish a sublinear bound on the cumulative number of experts' binary labels. Initially, multiple labels per query are needed, but the number of expert labels required asymptotically converges to zero, saving both expert effort and computation time. (2) No-harm guarantee with data-driven trust level adjustment: our adaptive trust level ensures that the convergence rate will not be worse than the one without using advice, even if the advice from experts is adversarial. Unlike existing methods that employ a user-defined function that hand-tunes the trust level adjustment, our approach enables data-driven adjustments. Real-world applications empirically demonstrate that our method not only outperforms existing baselines, but also maintains robustness despite varying labelling accuracy, in tasks of battery design with human experts.

Predicting future trajectories of nearby objects, especially under occlusion, is a crucial task in autonomous driving and safe robot navigation. Prior works typically neglect to maintain uncertainty about occluded objects and only predict trajectories of observed objects using high-capacity models such as Transformers trained on large datasets. While these approaches are effective in standard scenarios, they can struggle to generalize to the long-tail, safety-critical scenarios. In this work, we explore a conceptual framework unifying trajectory prediction and occlusion reasoning under the same class of structured probabilistic generative model, namely, switching dynamical systems. We then present some initial experiments illustrating its capabilities using the Waymo open dataset.

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, a consensus on the correct measurement of predictive uncertainty remains elusive. In this work, we return to first principles to develop a fundamental framework of information-theoretic predictive uncertainty measures. Our proposed framework categorizes predictive uncertainty measures according to two factors: (I) The predicting model (II) The approximation of the true predictive distribution. Examining all possible combinations of these two factors, we derive a set of predictive uncertainty measures that includes both known and newly introduced ones. We empirically evaluate these measures in typical uncertainty estimation settings, such as misclassification detection, selective prediction, and out-of-distribution detection. The results show that no single measure is universal, but the effectiveness depends on the specific setting. Thus, our work provides clarity about the suitability of predictive uncertainty measures by clarifying their implicit assumptions and relationships.