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Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often intractable and model simulation may be computationally burdensome. Fortunately, in many of these situations, it is possible to adopt a surrogate model or approximate likelihood function. It may be convenient to conduct Bayesian inference directly with the surrogate, but this can result in bias and poor uncertainty quantification. In this paper we propose a new method for adjusting approximate posterior samples to reduce bias and produce more accurate uncertainty quantification. We do this by optimizing a transform of the approximate posterior that maximizes a scoring rule. Our approach requires only a (fixed) small number of complex model simulations and is numerically stable. We demonstrate good performance of the new method on several examples of increasing complexity.

Vision foundation models are a new frontier in Geospatial Artificial Intelligence (GeoAI), an interdisciplinary research area that applies and extends AI for geospatial problem solving and geographic knowledge discovery, because of their potential to enable powerful image analysis by learning and extracting important image features from vast amounts of geospatial data. This paper evaluates the performance of the first-of-its-kind geospatial foundation model, IBM-NASA's Prithvi, to support a crucial geospatial analysis task: flood inundation mapping. This model is compared with convolutional neural network and vision transformer-based architectures in terms of mapping accuracy for flooded areas. A benchmark dataset, Sen1Floods11, is used in the experiments, and the models' predictability, generalizability, and transferability are evaluated based on both a test dataset and a dataset that is completely unseen by the model. Results show the good transferability of the Prithvi model, highlighting its performance advantages in segmenting flooded areas in previously unseen regions. The findings also indicate areas for improvement for the Prithvi model in terms of adopting multi-scale representation learning, developing more end-to-end pipelines for high-level image analysis tasks, and offering more flexibility in terms of input data bands.

Generative diffusion models have achieved spectacular performance in many areas of generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, in this paper we show that many aspects of these models can be understood using the tools of equilibrium statistical mechanics. Using this reformulation, we show that generative diffusion models undergo second-order phase transitions corresponding to symmetry breaking phenomena. We argue that this lead to a form of instability that lies at the heart of their generative capabilities and that can be described by a set of mean field critical exponents. We conclude by analyzing recent work connecting diffusion models and associative memory networks in view of the thermodynamic formulations.

Bayesian optimal design of experiments is a well-established approach to planning experiments. Briefly, a probability distribution, known as a statistical model, for the responses is assumed which is dependent on a vector of unknown parameters. A utility function is then specified which gives the gain in information for estimating the true value of the parameters using the Bayesian posterior distribution. A Bayesian optimal design is given by maximising the expectation of the utility with respect to the joint distribution given by the statistical model and prior distribution for the true parameter values. The approach takes account of the experimental aim via specification of the utility and of all assumed sources of uncertainty via the expected utility. However, it is predicated on the specification of the statistical model. Recently, a new type of statistical inference, known as Gibbs (or General Bayesian) inference, has been advanced. This is Bayesian-like, in that uncertainty on unknown quantities is represented by a posterior distribution, but does not necessarily rely on specification of a statistical model. Thus the resulting inference should be less sensitive to misspecification of the statistical model. The purpose of this paper is to propose Gibbs optimal design: a framework for optimal design of experiments for Gibbs inference. The concept behind the framework is introduced along with a computational approach to find Gibbs optimal designs in practice. The framework is demonstrated on exemplars including linear models, and experiments with count and time-to-event responses.

In models of opinion dynamics, many parameters -- either in the form of constants or in the form of functions -- play a critical role in describing, calibrating, and forecasting how opinions change with time. When examining a model of opinion dynamics, it is beneficial to infer its parameters using empirical data. In this paper, we study an example of such an inference problem. We consider a mean-field bounded-confidence model with an unknown interaction kernel between individuals. This interaction kernel encodes how individuals with different opinions interact and affect each other's opinions. Because it is often difficult to quantitatively measure opinions as empirical data from observations or experiments, we assume that the available data takes the form of partial observations of a cumulative distribution function of opinions. We prove that certain measurements guarantee a precise and unique inference of the interaction kernel and propose a numerical method to reconstruct an interaction kernel from a limited number of data points. Our numerical results suggest that the error of the inferred interaction kernel decays exponentially as we strategically enlarge the data set.

When multiple self-adaptive systems share the same environment and have common goals, they may coordinate their adaptations at runtime to avoid conflicts and to satisfy their goals. There are two approaches to coordination. (1) Logically centralized, where a supervisor has complete control over the individual self-adaptive systems. Such approach is infeasible when the systems have different owners or administrative domains. (2) Logically decentralized, where coordination is achieved through direct interactions. Because the individual systems have control over the information they share, decentralized coordination accommodates multiple administrative domains. However, existing techniques do not account simultaneously for both local concerns, e.g., preferences, and shared concerns, e.g., conflicts, which may lead to goals not being achieved as expected. Our idea to address this shortcoming is to express both types of concerns within the same constraint optimization problem. We propose CoADAPT, a decentralized coordination technique introducing two types of constraints: preference constraints, expressing local concerns, and consistency constraints, expressing shared concerns. At runtime, the problem is solved in a decentralized way using distributed constraint optimization algorithms implemented by each self-adaptive system. As a first step in realizing CoADAPT, we focus in this work on the coordination of adaptation planning strategies, traditionally addressed only with centralized techniques. We show the feasibility of CoADAPT in an exemplar from cloud computing and analyze experimentally its scalability.

In the present work we propose and study a time discrete scheme for the following chemotaxis-consumption model (for any $s\ge 1$), $$ \partial_t u - \Delta u = - \nabla \cdot (u \nabla v), \quad \partial_t v - \Delta v = - u^s v \quad \hbox{in $(0,T)\times \Omega$,}$$ endowed with isolated boundary conditions and initial conditions, where $(u,v)$ model cell density and chemical signal concentration. The proposed scheme is defined via a reformulation of the model, using the auxiliary variable $z = \sqrt{v + \alpha^2}$ combined with a Backward Euler scheme for the $(u,z)$-problem and a upper truncation of $u$ in the nonlinear chemotaxis and consumption terms. Then, two different ways of retrieving an approximation for the function $v$ are provided. We prove the existence of solution to the time discrete scheme and establish uniform in time \emph{a priori} estimates, yielding the convergence of the scheme towards a weak solution $(u,v)$ of the chemotaxis-consumption model.

We propose a method to detect model misspecifications in nonlinear causal additive and potentially heteroscedastic noise models. We aim to identify predictor variables for which we can infer the causal effect even in cases of such misspecification. We develop a general framework based on knowledge of the multivariate observational data distribution and we then propose an algorithm for finite sample data, discuss its asymptotic properties, and illustrate its performance on simulated and real data.

Most state-of-the-art machine learning techniques revolve around the optimisation of loss functions. Defining appropriate loss functions is therefore critical to successfully solving problems in this field. We present a survey of the most commonly used loss functions for a wide range of different applications, divided into classification, regression, ranking, sample generation and energy based modelling. Overall, we introduce 33 different loss functions and we organise them into an intuitive taxonomy. Each loss function is given a theoretical backing and we describe where it is best used. This survey aims to provide a reference of the most essential loss functions for both beginner and advanced machine learning practitioners.