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We consider the one-dimensional outer stochastic Stefan problem with reflection which models the short-time prediction of the price or spread of one volatile asset traded in a financial market. The problem admits maximal solutions as long as the velocity of the moving boundary stays bounded, [3,6,7]. We apply Malliavin calculus on the transformed equation and prove first that its maximal solution u has continuous paths a.s. In the case of the unreflected problem, the previous enables localization of a proper approximating sequence of the maximal solution. Then, we derive there locally the differentiability of maximal $u$ in the Malliavin sense. The novelty of this work, apart from the derivation of continuity of the paths for the maximal solution with reflection, is that for the unreflected case we introduce a localization argument on maximal solutions and define efficiently the relevant sample space. More precisely, we present a methodology suitable for the proof of the expected local only (in the sample space) existence of the Malliavin derivative., Comment: 23 pages

The advent of artificial intelligence has contributed in a groundbreaking transformation of the fashion industry, redefining creativity and innovation in unprecedented ways. This work investigates methodologies for generating tailored fashion descriptions using two distinct Large Language Models and a Stable Diffusion model for fashion image creation. Emphasizing adaptability in AI-driven fashion creativity, we depart from traditional approaches and focus on prompting techniques, such as zero-shot and few-shot learning, as well as Chain-of-Thought (CoT), which results in a variety of colors and textures, enhancing the diversity of the outputs. Central to our methodology is Retrieval-Augmented Generation (RAG), enriching models with insights from fashion sources to ensure contemporary representations. Evaluation combines quantitative metrics such as CLIPscore with qualitative human judgment, highlighting strengths in creativity, coherence, and aesthetic appeal across diverse styles. Among the participants, RAG and few-shot learning techniques are preferred for their ability to produce more relevant and appealing fashion descriptions. Our code is provided at https://github.com/georgiarg/AutoFashion.

Bridging the gap between internal and external validity is crucial for heterogeneous treatment effect estimation. Randomised controlled trials (RCTs), favoured for their internal validity due to randomisation, often encounter challenges in generalising findings due to strict eligibility criteria. Observational studies on the other hand, provide external validity advantages through larger and more representative samples but suffer from compromised internal validity due to unmeasured confounding. Motivated by these complementary characteristics, we propose a novel Bayesian nonparametric approach leveraging multi-task Gaussian processes to integrate data from both RCTs and observational studies. In particular, we introduce a parameter which controls the degree of borrowing between the datasets and prevents the observational dataset from dominating the estimation. The value of the parameter can be either user-set or chosen through a data-adaptive procedure. Our approach outperforms other methods in point predictions across the covariate support of the observational study, and furthermore provides a calibrated measure of uncertainty for the estimated treatment effects, which is crucial when extrapolating. We demonstrate the robust performance of our approach in diverse scenarios through multiple simulation studies and a real-world education randomised trial.

In this work, we study Markov-dependent reflected autoregressive processes. In queueing terms, such processes describe the workload just before a customer arrival, which makes obsolete a fraction of the work already present, and where the interarrival time and the service time depend on a common discrete time Markov chain. Among others, we consider the case where given the state of the underlying Markov chain, the interarrival time and the service time are independent, as well as the case where there is also additional dependence based on the Farlie-Gumbel-Morgenstern copula, the case where the service time depends on the waiting time of the customer, and the modulated shot-noise queue where server's speed is workload proportional. The Laplace-Stieltjes transform of the steady-state workload is derived via a recursive approach. Moreover, we further consider a Markov-modulated version of the reflected autoregressive process with more general structure and obtain the Laplace-Stieltjes transform of the transient distribution of the workload.

Emotion detection in textual data has received growing interest in recent years, as it is pivotal for developing empathetic human-computer interaction systems. This paper introduces a method for categorizing emotions from text, which acknowledges and differentiates between the diversified similarities and distinctions of various emotions. Initially, we establish a baseline by training a transformer-based model for standard emotion classification, achieving state-of-the-art performance. We argue that not all misclassifications are of the same importance, as there are perceptual similarities among emotional classes. We thus redefine the emotion labeling problem by shifting it from a traditional classification model to an ordinal classification one, where discrete emotions are arranged in a sequential order according to their valence levels. Finally, we propose a method that performs ordinal classification in the two-dimensional emotion space, considering both valence and arousal scales. The results show that our approach not only preserves high accuracy in emotion prediction but also significantly reduces the magnitude of errors in cases of misclassification.

Counterfactual explanations (CEs) based on concepts are explanations that consider alternative scenarios to understand which high-level semantic features contributed to particular model predictions. In this work, we propose CEs based on the semantic graphs accompanying input data to achieve more descriptive, accurate, and human-aligned explanations. Building upon state-of-the-art (SoTA) conceptual attempts, we adopt a model-agnostic edit-based approach and introduce leveraging GNNs for efficient Graph Edit Distance (GED) computation. With a focus on the visual domain, we represent images as scene graphs and obtain their GNN embeddings to bypass solving the NP-hard graph similarity problem for all input pairs, an integral part of the CE computation process. We apply our method to benchmark and real-world datasets with varying difficulty and availability of semantic annotations. Testing on diverse classifiers, we find that our CEs outperform previous SoTA explanation models based on semantics, including both white and black-box as well as conceptual and pixel-level approaches. Their superiority is proven quantitatively and qualitatively, as validated by human subjects, highlighting the significance of leveraging semantic edges in the presence of intricate relationships. Our model-agnostic graph-based approach is widely applicable and easily extensible, producing actionable explanations across different contexts.

In this work, we consider extensions of the dual risk model with proportional gains by introducing a dependence structure between gain sizes and gain interrarrival times. Among others, we further consider the case where the proportional parameter is randomly chosen, the case where it is a uniformly random variable, as well as the case where we may have upwards as well as downwards jumps. Moreover, we consider the case with causal dependence structure, as well as the case where the dependence is based on the generalized Farlie-Gumbel-Morgenstern copula. The ruin probability and the distribution of the time to ruin are investigated.

We review the electronic stopping power data within the IAEA database, assessing the abundance and scarcity of available data as a function of energy and collisional systems. Our analysis includes an examination of the experimental values, their evolution in time, the dispersion among data, and trends of the more recent measurements. Additionally, we provide comparisons with SRIM-2013 calculations for select cases of interest. Notably, we identify sparsely measured systems and energy regions, emphasizing the pressing need for new, reliable data and independent theoretical predictions.

Counterfactuals have been established as a popular explainability technique which leverages a set of minimal edits to alter the prediction of a classifier. When considering conceptual counterfactuals on images, the edits requested should correspond to salient concepts present in the input data. At the same time, conceptual distances are defined by knowledge graphs, ensuring the optimality of conceptual edits. In this work, we extend previous endeavors on graph edits as counterfactual explanations by conducting a comparative study which encompasses both supervised and unsupervised Graph Neural Network (GNN) approaches. To this end, we pose the following significant research question: should we represent input data as graphs, which is the optimal GNN approach in terms of performance and time efficiency to generate minimal and meaningful counterfactual explanations for black-box image classifiers?

Current automatic lyrics transcription (ALT) benchmarks focus exclusively on word content and ignore the finer nuances of written lyrics including formatting and punctuation, which leads to a potential misalignment with the creative products of musicians and songwriters as well as listeners' experiences. For example, line breaks are important in conveying information about rhythm, emotional emphasis, rhyme, and high-level structure. To address this issue, we introduce Jam-ALT, a new lyrics transcription benchmark based on the JamendoLyrics dataset. Our contribution is twofold. Firstly, a complete revision of the transcripts, geared specifically towards ALT evaluation by following a newly created annotation guide that unifies the music industry's guidelines, covering aspects such as punctuation, line breaks, spelling, background vocals, and non-word sounds. Secondly, a suite of evaluation metrics designed, unlike the traditional word error rate, to capture such phenomena. We hope that the proposed benchmark contributes to the ALT task, enabling more precise and reliable assessments of transcription systems and enhancing the user experience in lyrics applications such as subtitle renderings for live captioning or karaoke., Comment: 6 pages (3 pages main content); website: https://audioshake.github.io/jam-alt/; data: https://huggingface.co/datasets/audioshake/jam-alt; code: https://github.com/audioshake/alt-eval/

Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Amongst others, we study cases where the interarrival and service times are proportionally dependent with additive and/or subtracting delay, as well as cases cases where interarrival times depends on whether the service duration of the previous arrival exceeds or not a random threshold. Moreover, we study cases where the autoregressive parameter is constant as well as a discrete or a continuous random variable, as well as cases where . More general dependence structures are also discussed. Our primary aim is to investigate a broad class of recursions of autoregressive type for which several independence assumptions are lifted, and for which a detailed exact analysis is provided. We provide expressions for the Laplace transform of the waiting time of a customer in the system in terms of an infinite product of known Laplace transforms. An integer-valued reflected autoregressive process that can be used to model a novel retrial queueing system with orbital searching time to depend on whether the last busy period starts with an empty or a non empty orbit queue, is also discussed. For such a model the probability generating function of the stationary orbit queue length is given as an infinite product of known generating functions. A first attempt towards multidimensional setting is also analyzed. Some additional generalizations with more general dependence structure are also discussed.

We apply state-of-the-art, likelihood-free statistical inference (machine-learning-based) techniques for reconstructing the spectral shape of a gravitational wave background (GWB). We focus on the reconstruction of an arbitrarily shaped signal by the LISA detector, but the method can be easily extended to either template-dependent signals, or to other detectors, as long as a characterisation of the instrumental noise is available. As proof of the technique, we quantify the ability of LISA to reconstruct signals of arbitrary spectral shape (${\it blind}$ reconstruction), considering a diversity of frequency profiles, and including astrophysical backgrounds in some cases. As a teaser of how the method can reconstruct signals characterised by a parameter-dependent template (${\it template}$ reconstruction), we present a dedicated study for power-law signals. While our technique has several advantages with respect to traditional MCMC methods, we validate it with the latter for concrete cases. This work opens the door for both fast and accurate Bayesian parameter estimation of GWBs, with essentially no computational overhead during the inference step. Our set of tools are integrated into the package ${\tt GWBackFinder}$, which is publicly available in https://github.com/AndronikiDimitriou/GWBackFinder., Comment: Typos corrected, some figures replaced, no change of results. Submitted to JCAP. 29 pages plus appendices and references, 12 figures