Current Legal Judgment Prediction (LJP) is constrained by its reliance on post-hoc judicial materials, increasing the likelihood that models perform retrospective classification rather than true forecasting. This paper empirically investigates shortcut learning in this context by studying claim-level outcome prediction in UK Employment Tribunal (UKET) decisions. Using a corpus of 33,158 individual claims, we predict outcomes from claim texts and LLM-extracted case summaries, evaluating models ranging from interpretable TF-IDF-based classifiers to black-box LLMs. While headline predictive performance figures appear strong, we demonstrate that such performance in LJP systems trained on post-hoc judicial text can be driven by the retrospective nature of the source material. Stratifying the test data by human judgments of leakage reveals that performance increases where outcome-revealing cues are embedded in the narrative. Moreover, a model trained on just the 4

Legal citation detection in court judgments underpins reliable precedent mapping, citation analytics, and document retrieval. Extracting references to legislation and case law in the United Kingdom is especially challenging: citation styles have evolved over centuries, and judgments routinely cite foreign or historical authorities. We conduct the first systematic comparison of three modelling paradigms on this task using the Cambridge Law Corpus: (i) rule‐based regular expressions; (ii) transformer-based encoders (BERT, RoBERTa, LEGAL‐BERT, ModernBERT); and (iii) large language models (GPT‐4.1). We produced a gold‐standard high-quality corpus of 190 court judgments containing 45,179 fine-grained annotations for UK and non-UK legislation and case references. ModernBERT achieves a macro-averaged F1 of 93.3%, only marginally ahead of the other encoder-only models, yet significantly outperforming the strongest regular-expression baseline (35.42% F1) and GPT-4.1 (76.57% F1).

Estimating population parameters in finite populations of text documents can be challenging when obtaining the labels for the target variable requires manual annotation. To address this problem, we combine predictions from a transformer encoder neural network with well-established survey sampling estimators using the model predictions as an auxiliary variable. The applicability is demonstrated in Swedish hate crime statistics based on Swedish police reports. Estimates of the yearly number of hate crimes and the police's under-reporting are derived using the Hansen-Hurwitz estimator, difference estimation, and stratified random sampling estimation. We conclude that if labeled training data is available, the proposed method can provide very efficient estimates with reduced time spent on manual annotation.

Leave-one-out cross-validation (LOO-CV) is a popular method for comparing Bayesian models based on their estimated predictive performance on new, unseen, data. As leave-one-out cross-validation is based on finite observed data, there is uncertainty about the expected predictive performance on new data. By modeling this uncertainty when comparing two models, we can compute the probability that one model has a better predictive performance than the other. Modeling this uncertainty well is not trivial, and for example, it is known that the commonly used standard error estimate is often too small. We study the properties of the Bayesian LOO-CV estimator and the related uncertainty estimates when comparing two models. We provide new results of the properties both theoretically in the linear regression case and empirically for multiple different models and discuss the challenges of modeling the uncertainty. We show that problematic cases include: comparing models with similar predictions, misspecified models, and small data. In these cases, there is a weak connection in the skewness of the individual leave-one-out terms and the distribution of the error of the Bayesian LOO-CV estimator. We show that it is possible that the problematic skewness of the error distribution, which occurs when the models make similar predictions, does not fade away when the data size grows to infinity in certain situations. Based on the results, we also provide practical recommendations for the users of Bayesian LOO-CV for model comparison.

The general applicability and robustness of posterior inference algorithms is critical to widely used probabilistic programming languages such as Stan, PyMC, Pyro, and Turing.jl. When designing a new inference algorithm, whether it involves Monte Carlo sampling or variational approximation, the fundamental problem is evaluating its accuracy and efficiency across a range of representative target posteriors. To solve this problem, we propose posteriordb, 1 a database of models and data sets defining target densities along with reference Monte Carlo draws. We further provide a guide to the best practices in using posteriordb for algorithm evaluation and comparison. To provide a wide range of realistic posteriors, posteriordb currently comprises 120 representative models with data, and has been instrumental in developing several inference algorithms.

Quantifying uncertainty in word embeddings is crucial for reliable inference from textual data. However, existing Bayesian methods such as Hamiltonian Monte Carlo (HMC) and mean-field variational inference (MFVI) are either computationally infeasible for large data or rely on restrictive assumptions. We propose a scalable Gibbs sampler using Polya-Gamma augmentation as well as Laplace approximation and compare them with MFVI and HMC for word embeddings. In addition, we address non-identifiability in word embeddings. Our Gibbs sampler and HMC correctly estimate uncertainties, while MFVI does not, and Laplace approximation only does so on large sample sizes, as expected. Applying the Gibbs sampler to the US Congress and the Movielens datasets, we demonstrate the feasibility on larger real data. Finally, as a result of having draws from the full posterior, we show that the posterior mean of word embeddings improves over maximum a posteriori (MAP) estimates in terms of hold-out likelihood, especially for smaller sampling sizes, further strengthening the need for posterior sampling of word embeddings.

Hate crimes, driven by biases against specific demographic groups, harm not only individuals but undermine the security, trust, and cohesion of entire communities. Accurately identifying such crimes remains a significant challenge due to under-reporting, limited training, and the complexity of determining bias motivations. In this paper, we analyze the results of a text classification model developed to improve the precision of hate crime statistics and identification in Sweden. Empirical results indicate the model outperforms traditional manual police classification of hate crimes, achieving higher precision across various crime types and regions. We further disaggregate performance to pinpoint persistent challenges and highlight categories where both human and machine decision-makers struggle. While the model focuses on statistical estimation rather than direct case-level decision-making, we discuss the broader implications of algorithmic transparency, accountability, and explainability. Ultimately, this research illustrates how transformer-based neural networks can responsibly bolster the detection and understanding of hate crimes, informing policies to better protect vulnerable communities.

In recent years, more and more large data sets have become available. Data accuracy, the absence of verifiable errors in data, is crucial for these large materials to enable high-quality research, downstream applications, and model training. This results in the problem of how to curate or improve data accuracy in such large and growing data, especially when the data is too large for manual curation to be feasible. This paper presents a unified procedure for iterative and continuous improvement of data sets. We provide theoretical guarantees that data accuracy tests speed up error reduction and, most importantly, that the proposed approach will, asymptotically, eliminate all errors in data with probability one. We corroborate the theoretical results with simulations and a real-world use case.

Algorithmic discrimination is a critical concern as machine learning models are used in high-stakes decision-making in legally protected contexts. Although substantial research on algorithmic bias and discrimination has led to the development of fairness metrics, several critical legal issues remain unaddressed in practice. The paper addresses three key shortcomings in prevailing ML fairness paradigms: (1) the narrow reliance on prediction or outcome disparity as evidence for discrimination, (2) the lack of nuanced evaluation of estimation error and assumptions that the true causal structure and data-generating process are known, and (3) the overwhelming dominance of US-based analyses which has inadvertently fostered some misconceptions regarding lawful modelling practices in other jurisdictions. To address these gaps, we introduce a novel decision-theoretic framework grounded in anti-discrimination law of the United Kingdom, which has global influence and aligns closely with European and Commonwealth legal systems. We propose the "conditional estimation parity" metric, which accounts for estimation error and the underlying data-generating process, aligning with UK legal standards. We apply our formalism to a real-world algorithmic discrimination case, demonstrating how technical and legal reasoning can be aligned to detect and mitigate unlawful discrimination. Our contributions offer actionable, legally-grounded guidance for ML practitioners, policymakers, and legal scholars seeking to develop non-discriminatory automated decision systems that are legally robust.

Sociologists increasingly discuss the need for more formal ways of measuring meaning from digital text archives.We bring to attention the seeded topic model, a semi-supervised and scalable extension to the standard topic model, that allows the infusion of social science domain knowledge to the computational learning of meaning structures. Seed words help crystallize topics around known concepts, issues, or ideas, while allowing for topic models' basic functionality of finding associations in text data based on word co-occurrences. The method allows identification of discourses on predefined themes over time and the measuring of a theme's shared interpretation via its associations to other frequently co-occurring topics. Illustrating this theoretically informed method, we extract longitudinal measures of the Swedish understanding of immigration in a vast newspaper corpus containing millions of news articles from 1945 to 2019.

National identification numbers (NIN) and similar identification code systems are widely used for uniquely identifying individuals and organizations in Finland, Sweden, and many other countries. To increase the general understanding of such techniques of identification, openly available methods and tools for NIN analysis and validation are needed. The hetu and sweidnumbr R packages provide functions for extracting embedded information, checking the validity, and generating random but valid numbers in the context of Finnish and Swedish NINs and other identification codes. In this article, we demonstrate these functions from both packages and provide theoretical context and motivation on the importance of the subject matter. Our work contributes to the growing toolkit of standardized methods for computational social science research, epidemiology, demographic studies, and other register-based inquiries.

When evaluating and comparing models using leave-one-out cross-validation (LOO-CV), the uncertainty of the estimate is typically assessed using the variance of the sampling distribution. Considering the uncertainty is important, as the variability of the estimate can be high in some cases. Previous studies show that no general unbiased variance estimator can be constructed, that would apply for any utility or loss measure and any model. We show that it is possible to construct an unbiased estimator considering a specific predictive performance measure and model. We demonstrate an unbiased sampling distribution variance estimator for the Bayesian normal model with fixed model variance using the expected log pointwise predictive density (elpd) utility score. This example demonstrates that it is possible to obtain improved, problem-specific, unbiased estimators for assessing the uncertainty in LOO-CV estimation.

We introduce the Cambridge Law Corpus (CLC), a dataset for legal AI research. It consists of over 250 000 court cases from the UK. Most cases are from the 21st century, but the corpus includes cases as old as the 16th century. This paper presents the first release of the corpus, containing the raw text and meta-data. Together with the corpus, we provide annotations on case outcomes for 638 cases, done by legal experts. Using our annotated data, we have trained and evaluated case outcome extraction with GPT-3, GPT-4 and RoBERTa models to provide benchmarks. We include an extensive legal and ethical discussion to address the potentially sensitive nature of this material. As a consequence, the corpus will only be released for research purposes under certain restrictions.

We introduce probabilistic embeddings using Laplacian priors (PELP). The proposed model enables incorporating graph side-information into static word embeddings. We theoretically show that the model unifies several previously proposed embedding methods under one umbrella. PELP generalises graph-enhanced, group, dynamic, and cross-lingual static word embeddings. PELP also enables any combination of these previous models in a straightforward fashion. Furthermore, we empirically show that our model matches the performance of previous models as special cases. In addition, we demonstrate its flexibility by applying it to the comparison of political sociolects over time. Finally, we provide code as a TensorFlow implementation enabling flexible estimation in different settings.

As large corpora of digitized text become increasingly available, researchers are rediscovering textual data’s potential fruitfulness for inquiries into social and cultural phenomena. Although textual corpora promise to enrich our knowledge of the social world, avoiding problems related to data quality remains a challenge to related empirical research. Hence, evaluating the quality of a corpus will be pivotal for future social scientific inquiries. The authors propose a conceptual framework for total corpus quality, incorporating three crucial dimensions: total corpus error, corpus comparability, and corpus reproducibility. These dimensions affect the validity and reliability of inferences drawn from textual data. In addition, the authors’ framework provides insights toward evaluating and improving studies on the basis of large-scale textual analyses. After outlining this framework, the authors then illustrate an application of the total corpus quality framework by an example case study using digitized newspaper articles to study topic salience over 75 years.

We consider nearest neighbor weighted random walks on the $d$-dimensional box $[n]^d$ that are governed by some function $g:[0,1] \ra [0,\iy)$, by which we mean that standing at $x$, a neighbor $y$ of $x$ is picked at random and the walk then moves there with probability $(1/2)g(n^{-1}y)/(g(n^{-1}y)+g(n^{-1}x))$. We do this for $g$ of the form $f^{m_n}$ for some function $f$ which assumed to be analytically well-behaved and where $m_n \ra \iy$ as $n \ra \iy$. This class of walks covers an abundance of interesting special cases, e.g., the mean-field Potts model, posterior collapsed Gibbs sampling for Latent Dirichlet allocation and certain Bayesian posteriors for models in nuclear physics. The following are among the results of this paper: \begin{itemize} \item If $f$ is unimodal with negative definite Hessian at its global maximum, then the mixing time of the random walk is $O(n\log n)$. \item If $f$ is multimodal, then the mixing time is exponential in $n$, but we show that there is a simulated annealing scheme governed by $f^K$ for an increasing sequence of $K$ that mixes in time $O(n^2)$. Using a varying step size that decreases with $K$, this can be taken down to $O(n\log n)$. \item If the process is studied on a general graph rather than the $d$-dimensional box, a simulated annealing scheme expressed in terms of conductances of the underlying network, works similarly. \end{itemize} Several examples are given, including the ones mentioned above.

Recently, new methods for model assessment, based on subsampling and posterior approximations, have been proposed for scaling leave-one-out cross-validation (LOO) to large datasets. Although these methods work well for estimating predictive performance for individual models, they are less powerful in model comparison. We propose an efficient method for estimating differences in predictive performance by combining fast approximate LOO surrogates with exact LOO subsampling using the difference estimator and supply proofs with regards to scaling characteristics. The resulting approach can be orders of magnitude more efficient than previous approaches, as well as being better suited to model comparison.