Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings, characterizing probability measures, for example, through densities, can be ill-defined or technically challenging. Motivated by clustering applications, we propose a Gaussian mixture framework for Hilbert-space-valued data based on kernel mean embeddings and develop efficient optimization algorithms for estimation. We establish theoretical guarantees showing that the proposed algorithm is well defined and that the model yields a dense class of approximations in infinite-dimensional spaces. We evaluate the framework through extensive experiments on diverse structures and data geometries, including $L^2$-functional data and random graphs in Laplacian spaces arising in modern medical applications.

Creating high-quality scientific figures can be time-consuming and challenging, even though sketching ideas on paper is relatively easy. Furthermore, recreating existing figures that are not stored in formats preserving semantic information is equally complex.

Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for example when reconstructing clean images from poor signals.

Our tight mechanism-specific bounds outperform tight mechanism-agnostic bounds and classic group privacy results.

If taking a closer look at the MedDRA classification on the system organ level on its website, we can find a claim of "System Organ Classes (SOCs) which are groupings by aetiology (e.g. However, as claimed in the original paper, "It should be noted that we did not perform any preprocessing of our datasets, such as Tab. These datasets appear in MoleculeNet as well. As mentioned in the introduction in the main paper, there are also issues with inconsistent representations and undefined stereochemistry. We list an example for each in Figure 1 and Figure 1.

Thus, in this paper, we seek to establish a new gold standard for small molecule drug discovery benchmarking, W elQrate .

One of the core facets of Bayesianism is in the updating of prior beliefs in light of new evidence$\text{ -- }$so how can we maintain a Bayesian approach if we have no prior beliefs in the first place? This is one of the central challenges in the field of Bayesian deep learning, where it is not clear how to represent beliefs about a prediction task by prior distributions over model parameters. Bridging the fields of Bayesian deep learning and probabilistic meta-learning, we introduce a way to $\textit{learn}$ a weights prior from a collection of datasets by introducing a way to perform per-dataset amortised variational inference. The model we develop can be viewed as a neural process whose latent variable is the set of weights of a BNN and whose decoder is the neural network parameterised by a sample of the latent variable itself. This unique model allows us to study the behaviour of Bayesian neural networks under well-specified priors, use Bayesian neural networks as flexible generative models, and perform desirable but previously elusive feats in neural processes such as within-task minibatching or meta-learning under extreme data-starvation.