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Confidence assessments of semantic segmentation algorithms in remote sensing are important. It is a desirable property of models to a priori know if they produce an incorrect output. Evaluations of the confidence assigned to the estimates of models for the task of classification in Earth Observation (EO) are crucial as they can be used to achieve improved semantic segmentation performance and prevent high error rates during inference and deployment. The model we develop, the Confidence Assessments of classification algorithms for Semantic segmentation (CAS) model, performs confidence evaluations at both the segment and pixel levels, and outputs both labels and confidence. The outcome of this work has important applications. The main application is the evaluation of EO Foundation Models on semantic segmentation downstream tasks, in particular land cover classification using satellite Copernicus Sentinel-2 data. The evaluation shows that the proposed model is effective and outperforms other alternative baseline models.

A class of decision problems related to inconsistency proofs for formal theories is used to show that under a constructive interpretation of computational complexity classes, an assumption referred to as the MW thesis implies that one may explicitly construct decision problems in NP which are not algorithmically solvable. In particular, in this interpretation the MW thesis implies P $\neq$ NP. It is argued that MW is a naturally valid, yet also naturally unformalizable principle.

Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to hold for time series due to their temporally correlated nature. In this work, we present a novel use of conformal prediction for time series forecasting that incorporates time series decomposition. This approach allows us to model different temporal components individually. By applying specific conformal algorithms to each component and then merging the obtained prediction intervals, we customize our methods to account for the different exchangeability regimes underlying each component. Our decomposition-based approach is thoroughly discussed and empirically evaluated on synthetic and real-world data. We find that the method provides promising results on well-structured time series, but can be limited by factors such as the decomposition step for more complex data.

Retrieval models are often evaluated on partially-annotated datasets. Each query is mapped to a few relevant texts and the remaining corpus is assumed to be irrelevant. As a result, models that successfully retrieve false negatives are punished in evaluation. Unfortunately, completely annotating all texts for every query is not resource efficient. In this work, we show that using partially-annotated datasets in evaluation can paint a distorted picture. We curate D-MERIT, a passage retrieval evaluation set from Wikipedia, aspiring to contain all relevant passages for each query. Queries describe a group (e.g., ``journals about linguistics'') and relevant passages are evidence that entities belong to the group (e.g., a passage indicating that Language is a journal about linguistics). We show that evaluating on a dataset containing annotations for only a subset of the relevant passages might result in misleading ranking of the retrieval systems and that as more relevant texts are included in the evaluation set, the rankings converge. We propose our dataset as a resource for evaluation and our study as a recommendation for balance between resource-efficiency and reliable evaluation when annotating evaluation sets for text retrieval.

The goal of multi-objective optimisation is to identify the Pareto front surface which is the set obtained by connecting the best trade-off points. Typically this surface is computed by evaluating the objectives at different points and then interpolating between the subset of the best evaluated trade-off points. In this work, we propose to parameterise the Pareto front surface using polar coordinates. More precisely, we show that any Pareto front surface can be equivalently represented using a scalar-valued length function which returns the projected length along any positive radial direction. We then use this representation in order to rigorously develop the theory and applications of stochastic Pareto front surfaces. In particular, we derive many Pareto front surface statistics of interest such as the expectation, covariance and quantiles. We then discuss how these can be used in practice within a design of experiments setting, where the goal is to both infer and use the Pareto front surface distribution in order to make effective decisions. Our framework allows for clear uncertainty quantification and we also develop advanced visualisation techniques for this purpose. Finally we discuss the applicability of our ideas within multivariate extreme value theory and illustrate our methodology in a variety of numerical examples, including a case study with a real-world air pollution data set.

We consider the problem of ranking a set of objects based on their performance when the measurement of said performance is subject to noise. In this scenario, the performance is measured repeatedly, resulting in a range of measurements for each object. If the ranges of two objects do not overlap, then we consider one object as 'better' than the other, and we expect it to receive a higher rank; if, however, the ranges overlap, then the objects are incomparable, and we wish them to be assigned the same rank. Unfortunately, the incomparability relation of ranges is in general not transitive; as a consequence, in general the two requirements cannot be satisfied simultaneously, i.e., it is not possible to guarantee both distinct ranks for objects with separated ranges, and same rank for objects with overlapping ranges. This conflict leads to more than one reasonable way to rank a set of objects. In this paper, we explore the ambiguities that arise when ranking with ties, and define a set of reasonable rankings, which we call partial rankings. We develop and analyse three different methodologies to compute a partial ranking. Finally, we show how performance differences among objects can be investigated with the help of partial ranking.

Making inference with spatial extremal dependence models can be computationally burdensome since they involve intractable and/or censored likelihoods. Building on recent advances in likelihood-free inference with neural Bayes estimators, that is, neural networks that approximate Bayes estimators, we develop highly efficient estimators for censored peaks-over-threshold models that {use data augmentation techniques} to encode censoring information in the neural network {input}. Our new method provides a paradigm shift that challenges traditional censored likelihood-based inference methods for spatial extremal dependence models. Our simulation studies highlight significant gains in both computational and statistical efficiency, relative to competing likelihood-based approaches, when applying our novel estimators to make inference with popular extremal dependence models, such as max-stable, $r$-Pareto, and random scale mixture process models. We also illustrate that it is possible to train a single neural Bayes estimator for a general censoring level, precluding the need to retrain the network when the censoring level is changed. We illustrate the efficacy of our estimators by making fast inference on hundreds-of-thousands of high-dimensional spatial extremal dependence models to assess extreme particulate matter 2.5 microns or less in diameter (${\rm PM}_{2.5}$) concentration over the whole of Saudi Arabia.

Explicit, momentum-based dynamics for optimizing functions defined on Lie groups was recently constructed, based on techniques such as variational optimization and left trivialization. We appropriately add tractable noise to the optimization dynamics to turn it into a sampling dynamics, leveraging the advantageous feature that the trivialized momentum variable is Euclidean despite that the potential function lives on a manifold. We then propose a Lie-group MCMC sampler, by delicately discretizing the resulting kinetic-Langevin-type sampling dynamics. The Lie group structure is exactly preserved by this discretization. Exponential convergence with explicit convergence rate for both the continuous dynamics and the discrete sampler are then proved under $W_2$ distance. Only compactness of the Lie group and geodesically $L$-smoothness of the potential function are needed. To the best of our knowledge, this is the first convergence result for kinetic Langevin on curved spaces, and also the first quantitative result that requires no convexity or, at least not explicitly, any common relaxation such as isoperimetry.

The complexity of BIM software presents significant barriers to the widespread adoption of BIM and model-based design within the Architecture, Engineering, and Construction (AEC) sector. End-users frequently express concerns regarding the additional effort required to create a sufficiently detailed BIM model when compared with conventional 2D drafting. This study explores the potential of sequential recommendation systems to accelerate the BIM modeling process. By treating BIM software commands as recommendable items, we introduce a novel end-to-end approach that predicts the next-best command based on user historical interactions. Our framework extensively preprocesses real-world, large-scale BIM log data, utilizes the transformer architectures from the latest large language models as the backbone network, and ultimately results in a prototype that provides real-time command suggestions within the BIM authoring tool Vectorworks. Subsequent experiments validated that our proposed model outperforms the previous study, demonstrating the immense potential of the recommendation system in enhancing design efficiency.

Hashing has been widely used in approximate nearest search for large-scale database retrieval for its computation and storage efficiency. Deep hashing, which devises convolutional neural network architecture to exploit and extract the semantic information or feature of images, has received increasing attention recently. In this survey, several deep supervised hashing methods for image retrieval are evaluated and I conclude three main different directions for deep supervised hashing methods. Several comments are made at the end. Moreover, to break through the bottleneck of the existing hashing methods, I propose a Shadow Recurrent Hashing(SRH) method as a try. Specifically, I devise a CNN architecture to extract the semantic features of images and design a loss function to encourage similar images projected close. To this end, I propose a concept: shadow of the CNN output. During optimization process, the CNN output and its shadow are guiding each other so as to achieve the optimal solution as much as possible. Several experiments on dataset CIFAR-10 show the satisfying performance of SRH.