Rank aggregation combines information from ordered lists ranking items by preference. Classical parametric models for such data, including the Mallows and Plackett-Luce models, assume the orders concentrate around one or more complete consensus rankings. Recent work relaxes the total-order assumption by allowing the consensus structure to be a partial order (poset), allowing for incomparabilities in preferences. However, in many applications preference data exhibit group structure. We introduce hierarchical partial order (HPO) models, which extend poset-based models to accommodate grouped data through a hierarchy of latent posets. This framework, which parallels mixture model extensions of the Mallows and Plackett-Luce models, enables principled sharing of information across groups while preserving partial-order structure. We show that the Plackett-Luce model and its hierarchical variants are special cases of HPO-models. We develop a hierarchical clustering extension (HCPO) for unsupervised clustering in settings where group labels are unknown. Bayesian inference for the latent poset hierarchy is performed using Markov chain Monte Carlo methods. Experiments on synthetic and real-world datasets, including pairwise acoustic preference data and LLM agent traces, demonstrate that the proposed HPO and HCPO models outperform existing approaches in both predictive performance and structural interpretability.

Learning effective policies for adaptive data acquisition remains challenging: posterior-based methods rely on surrogate models and posterior approximations that can be misspecified or biased, while direct policy-learning methods map from historical observations and fail to exploit available model representations, making learning harder. We introduce policy learning with belief representations (POLAR), based on the insight that optimal data acquisition depends on the observation history only through a sufficient belief state. Specifically, POLAR decouples representation learning from policy learning by leveraging pretrained predictive foundation models as belief-state encoders, training a policy head on top of their representations. This yields a simple, unified amortised policy learning framework for Bayesian experimental design, Bayesian optimisation, and active learning, differing only in the task-specific utility used to train the policy. Empirically, we find that POLAR outperforms state-of-the-art amortised methods across diverse tasks while requiring far fewer training samples, demonstrating a significant step in the scalability and efficiency of amortised data acquisition.

Mean Field Variational Inference (MFVI) is widely understood to underestimate posterior variance. By analysing conjugate Bayesian Linear Regression (BLR), we show that this characterization is incomplete: while MFVI underestimates the variance in parameter space, it can overestimate the predictive variance compared to the exact posterior. We show that if the MFVI posterior underestimates predictive variances in some directions, it necessarily overestimates them in others. Crucially, this overestimation occurs in directions where the training data concentrates. This leads to the surprising result that, for a test point drawn from the training distribution, MFVI's expected predictive variance exceeds that of the exact posterior. We demonstrate a pathological case of this effect, where the MFVI posterior fails to reduce predictive variance compared to the prior on in distribution data. We connect these results to the Cold Posterior Effect, arguing that varying the temperature can correct this overestimation, yielding predictions closer to those of the exact posterior. We validate our theory on synthetic and real-world regression tasks.

I've spent 30 years in recruitment - this is how to get a job If you've sent off dozens of job applications and heard nothing back, the silence can be as infuriating as a rejection. Part of the problem is the shrinking number of entry-level jobs. Reed, the recruitment firm, says that graduate vacancies on its website have fallen from around 180,000 three or four years ago to 50,000. James Reed, chair and chief executive of Reed, has spent 30 years watching how employers make decisions and, like many, is frustrated at how difficult the process has become. Here, the recruitment veteran gives some pointers on how to get noticed in a tough jobs market.

Image caption, Elon Musk has repeatedly boasted of Tesla's self-driving capabilities. Jennifer Barbour filed her lawsuit in a local court on Tuesday, just days after her 76-year-old mother Martha Avila died from injuries she sustained after a Tesla Model 3 sped into their shared home . The Tesla driver told police that he was using the car's autonomous or full self-driving technology at the time of the crash. In the lawsuit Barbour accuses Elon Musk's electric vehicle company of defective design and negligence by promoting technology that is unsafe, while Musk on social media denied the technology was to blame. Tesla was approached for comment.

New Scotland Yard, the headquarters of the Metropolitan police whose pilot with Palantir focuses on detecting misconduct by officers. New Scotland Yard, the headquarters of the Metropolitan police whose pilot with Palantir focuses on detecting misconduct by officers. Mayor's office grants extra 12 months to run pilot while London force procures long-term supplier Wed 24 Jun 2026 18.14 EDTLast modified on Wed 24 Jun 2026 18.50 EDT The Metropolitan police have been granted a 12-month extension to a pilot project with the spy-tech firm Palantir while the force carries out a procurement process. The development comes weeks after the mayor of London, Sadiq Khan, blocked a £50m deal between the Met and the US company to automate intelligence analysis in criminal investigations. Last month the mayor's office said there had been a "clear and serious breach" of procurement rules and said police had seriously considered only one supplier. Palantir's lawyers subsequently wrote to the Mayor's Office for Policing and Crime (Mopac) saying they intended to challenge the decision in court, the Times reported.

Is the war entering a new phase? A multi-storey apartment has been hit with what Russian-installed authorities called a Ukrainian drone strike in the Donetsk region. The area is in a Russian-controlled part of Ukraine. European heatwave, scorching weather triggers UK'red' warning Rubio: US'completely aligned' with Gulf allies on Iran

The AI arms race between China and the US has researchers on both sides worried about a "Chernobyl moment." Just over a week ago, I attended a major artificial intelligence conference in Zhongguancun, Beijing's bustling high-tech district. It was packed with fascinating sessions touching on everything from recursive self-improvement--the idea that models can tweak their own code and advance indefinitely--to humanoid robots. And it featured a few legends of computing, including Whitfield Diffie, co-inventor of public-key cryptography, and Andrew Barto, who won the Turing Award with Rich Sutton for his pioneering work on reinforcement learning. But I left with one takeaway above all else: The US and China should put their fierce AI rivalry to the side.

Sci-fi columnist Emily H. Wilson rounds up her favourite reads of the year to date - and highlights one particular book as her top pick The best science-fiction book of the year so far has only just been published. The End of Everything, by M. John Harrison, is about half the length of a regular novel, but it's so powerful and complete that there is nothing slight about it. I consumed it in one greedy gulp before getting up one morning. Our main characters, Phillip and his grandmother Marnie, live along the south coast of England in the wake of an alien invasion. Since the iGhetti began to appear, the European mainland seems to have disappeared, and it has become very hard indeed to work out what is real and what isn't. Strange, dangerous artefacts wash up out of the sea.

The scroll was recovered from the library of a luxury Roman villa in Herculaneum, near Naples, that was blasted by heat and buried under ash in AD79. The scroll was recovered from the library of a luxury Roman villa in Herculaneum, near Naples, that was blasted by heat and buried under ash in AD79. The surviving part of an ancient scroll that was burnt to a crisp when Mount Vesuvius erupted nearly 2,000 years ago has been virtually unwrapped and read with help from artificial intelligence. Researchers uncovered 20 columns of previously hidden text covering more than a metre of charred papyrus without physically unrolling the scroll. The age of the scroll, named PHerc 1667, makes it one of the oldest in a collection of hundreds recovered from the library of a luxury Roman villa in Herculaneum that was blasted by heat and buried under ash in the volcanic eruption that destroyed nearby Pompeii in AD79.