The estimation of uncertainties associated with predictions from quantitative structure-activity relationship (QSAR) models can accelerate the drug discovery process by identifying promising experiments and allowing an efficient allocation of resources. Several computational tools exist that estimate the predictive uncertainty in machine learning models. However, deviations from the i.i.d. setting have been shown to impair the performance of these uncertainty quantification methods. We use a real-world pharmaceutical dataset to address the pressing need for a comprehensive, large-scale evaluation of uncertainty estimation methods in the context of realistic distribution shifts over time. We investigate the performance of several uncertainty estimation methods, including ensemble-based and Bayesian approaches. Furthermore, we use this real-world setting to systematically assess the distribution shifts in label and descriptor space and their impact on the capability of the uncertainty estimation methods. Our study reveals significant shifts over time in both label and descriptor space and a clear connection between the magnitude of the shift and the nature of the assay. Moreover, we show that pronounced distribution shifts impair the performance of popular uncertainty estimation methods used in QSAR models. This work highlights the challenges of identifying uncertainty quantification methods that remain reliable under distribution shifts introduced by real-world data.

Fuzzy implication functions are a key area of study in fuzzy logic, extending the classical logical conditional to handle truth degrees in the interval $[0,1]$. While existing literature often focuses on a limited number of families, in the last ten years many new families have been introduced, each defined by specific construction methods and having different key properties. This survey aims to provide a comprehensive and structured overview of the diverse families of fuzzy implication functions, emphasizing their motivations, properties, and potential applications. By organizing the information schematically, this document serves as a valuable resource for both theoretical researchers seeking to avoid redundancy and practitioners looking to select appropriate operators for specific applications.

The successful application of modern machine learning for time series classification is often hampered by limitations in quality and quantity of available training data. To overcome these limitations, available domain expert knowledge in the form of parametrised mechanistic dynamical models can be used whenever it is available and time series observations may be represented as an element from a given class of parametrised dynamical models. This makes the learning process interpretable and allows the modeller to deal with sparsely and irregularly sampled data in a natural way. However, the internal processes of a dynamical model are often only partially observed. This can lead to ambiguity regarding which particular model realization best explains a given time series observation. This problem is well-known in the literature, and a dynamical model with this issue is referred to as structurally unidentifiable. Training a classifier that incorporates knowledge about a structurally unidentifiable dynamical model can negatively influence classification performance. To address this issue, we employ structural identifiability analysis to explicitly relate parameter configurations that are associated with identical system outputs. Using the derived relations in classifier training, we demonstrate that this method significantly improves the classifier's ability to generalize to unseen data on a number of example models from the biomedical domain. This effect is especially pronounced when the number of training instances is limited. Our results demonstrate the importance of accounting for structural identifiability, a topic that has received relatively little attention from the machine learning community.

Summary and Contributions: Quite a bit of recent research on deep density estimation under the normalizing flows umbrella has focused on efficiently computing (a restricted form of) the Jacobian term that appears in the objective. Such models operate with a set of transformations where the computation of this term is easy. While arbitrary distributions can be learned by such methods, the features that are learned are quite skewered which can prevent learning a proper disentangled representation. This paper presents a conceptually simple method to optimize for exact maximum likelihood in such models. In particular, the authors consider a transform from the observed to the latent space which is parameterized by fully connected networks with the only constraint that the weight matrices are invertible. Since the parameters of the transformation are matrices, the authors use properties of Riemannian geometry of matrix spaces to derive updates in terms of the relative gradient.

The focus of the work is deep density estimation (also called normalizing flows). Particularly, the authors focus on the generative model x f(s) as defined in (1) where the observation (x) is described as the invertible non-linear function (f) of a latent variable (s). They take a maximum-likelihood perspective (2) where g_{\theta}, the approximation of the inverse of f, is the composition of g_1 \sigma_1(W_1 \cdot), ..., g_L \sigma_L(W_L \cdot) invertible and differentiable component functions. They propose to use the relative gradient method to optimize \theta to speed up computations. Deep density estimation is an important problem in machine learning.

Thompson Sampling with Approximate Inference This paper investigates the performance of Thompson sampling, when the sampled distribution does not match the "problem" distribution exactly. The authors clearly explain some settings where mismatched sampling distributions can cause linear regret. The authors support their analysis with some expository "toy" experiments. There are several things to like about this paper: - This paper is one of the first to provide a clear analysis of Thompson sampling in the regime of imperfect inference. It seems like another solution that would "intuitively work" is to artificially expand the "prior" of the Thompson sampling procedure, but in a way that would concentrate away with data.

This submission was diligently evaluated, and the main problem that was identified was clarity. An additional expert reviewer was asked to checked the proofs. I am suggesting acceptance, given that the authors put a serious effort into rewriting. The reviewers did a great job in identifying where the improvements are needed, please do take advantage of that. Furthermore, for the final version, please take a look at this paper: https://link.springer.com/chapter/10.1007%2F978-3-319-46379-7_22 .

Convergence of existing Stein variational methods is known to suffer in high dimensions due to the locality of the kernel. The authors address this problem by exploiting the structure of the posterior distribution. Concretely, they propose to perform Stein gradient steps in a low-dimensional projection subspace. The basis of the projection space is derived from the expected Hessian of the log-likelihood, where the expectation is adaptively approximated by an empirical estimate. The introduced projection scheme and the corresponding Stein gradient steps are well motivated and presented. A theoretical analysis is presented to bound the bias introduced by the projection.

Knowledge of the primordial matter density field from which the large-scale structure of the Universe emerged over cosmic time is of fundamental importance for cosmology. However, reconstructing these cosmological initial conditions from late-time observations is a notoriously difficult task, which requires advanced cosmological simulators and sophisticated statistical methods to explore a multi-million-dimensional parameter space. We show how simulation-based inference (SBI) can be used to tackle this problem and to obtain data-constrained realisations of the primordial dark matter density field in a simulation-efficient way with general non-differentiable simulators. Our method is applicable to full high-resolution dark matter $N$-body simulations and is based on modelling the posterior distribution of the constrained initial conditions to be Gaussian with a diagonal covariance matrix in Fourier space. As a result, we can generate thousands of posterior samples within seconds on a single GPU, orders of magnitude faster than existing methods, paving the way for sequential SBI for cosmological fields. Furthermore, we perform an analytical fit of the estimated dependence of the covariance on the wavenumber, effectively transforming any point-estimator of initial conditions into a fast sampler. We test the validity of our obtained samples by comparing them to the true values with summary statistics and performing a Bayesian consistency test.

Simulation-based calibration checking (SBC) refers to the validation of an inference algorithm and model implementation through repeated inference on data simulated from a generative model. In the original and commonly used approach, the generative model uses parameters drawn from the prior, and thus the approach is testing whether the inference works for simulated data generated with parameter values plausible under that prior. This approach is natural and desirable when we want to test whether the inference works for a wide range of datasets we might observe. However, after observing data, we are interested in answering whether the inference works conditional on that particular data. In this paper, we propose posterior SBC and demonstrate how it can be used to validate the inference conditionally on observed data. We illustrate the utility of posterior SBC in three case studies: (1) A simple multilevel model; (2) a model that is governed by differential equations; and (3) a joint integrative neuroscience model which is approximated via amortized Bayesian inference with neural networks.