Approximate Bayesian inference typically revolves around computing the posterior parameter distribution. In practice, however, the main object of interest is often a model's predictions rather than its parameters. In this work, we propose to bypass the parameter posterior and focus directly on approximating the posterior predictive distribution. We achieve this by drawing inspiration from self-training within self-supervised and semi-supervised learning. Essentially, we quantify a Bayesian model's predictive uncertainty by refitting on self-predicted data. The idea is strikingly simple: If a model assigns high likelihood to self-predicted data, these predictions are of low uncertainty, and vice versa. This yields a deterministic, sampling-free approximation of the posterior predictive. The modular structure of our Self-Supervised Laplace Approximation (SSLA) further allows us to plug in different prior specifications, enabling classical Bayesian sensitivity (w.r.t. prior choice) analysis. In order to bypass expensive refitting, we further introduce an approximate version of SSLA, called ASSLA. We study (A)SSLA both theoretically and empirically in regression models ranging from Bayesian linear models to Bayesian neural networks. Across a wide array of regression tasks with simulated and real-world datasets, our methods outperform classical Laplace approximations in predictive calibration while remaining computationally efficient.

We study optimal policy learning under combined budget and minimum coverage constraints. We show that the problem admits a knapsack-type structure and that the optimal policy can be characterized by an affine threshold rule involving both budget and coverage shadow prices. We establish that the linear programming relaxation of the combinatorial solution has an O(1) integrality gap, implying asymptotic equivalence with the optimal discrete allocation. Building on this result, we analyze two implementable approaches: a Greedy-Lagrangian (GLC) and a rank-and-cut (RC) algorithm. We show that the GLC closely approximates the optimal solution and achieves near-optimal performance in finite samples. By contrast, RC is approximately optimal whenever the coverage constraint is slack or costs are homogeneous, while misallocation arises only when cost heterogeneity interacts with a binding coverage constraint. Monte Carlo evidence supports these findings.

Conformal prediction constructs prediction sets with finite-sample coverage guarantees, but its calibration stage is structurally constrained to a scalar score function and a single threshold variable -- forcing shapes of prediction sets to be fixed before calibration, typically through data splitting. We introduce multi-variable conformal prediction (MCP), a framework that extends conformal prediction to vector-valued score functions with multiple simultaneous calibration variables. Building on scenario theory as a principled framework for certifying data-driven decisions, MCP unifies prediction set design and calibration into a single optimization problem, eliminating data splitting without sacrificing coverage guarantees. We propose two computationally efficient variants: RemMCP, grounded in constrained optimization with constraint removal, which admits a clean generalization of split conformal prediction; and RelMCP, based on iterative optimization with constraint relaxation, which supports non-convex score functions at the cost of possibly greater conservatism. Through numerical experiments on ellipsoidal and multi-modal prediction sets, we demonstrate that RemMCP and RelMCP consistently meet the target coverage with prediction set sizes smaller than or comparable to those of baselines with data split, while considerably reducing variance across calibration runs -- a direct consequence of using all available data for shape optimization and calibration simultaneously.

We propose and analyze a model-based bootstrap for transition kernels in finite controlled Markov chains (CMCs) with possibly nonstationary or history-dependent control policies, a setting that arises naturally in offline reinforcement learning (RL) when the behavior policy generating the data is unknown. We establish distributional consistency of the bootstrap transition estimator in both a single long-chain regime and the episodic offline RL regime. The key technical tools are a novel bootstrap law of large numbers (LLN) for the visitation counts and a novel use of the martingale central limit theorem (CLT) for the bootstrap transition increments. We extend bootstrap distributional consistency to the downstream targets of offline policy evaluation (OPE) and optimal policy recovery (OPR) via the delta method by verifying Hadamard differentiability of the Bellman operators, yielding asymptotically valid confidence intervals for value and $Q$-functions. Experiments on the RiverSwim problem show that the proposed bootstrap confidence intervals (CIs), especially the percentile CIs, outperform the episodic bootstrap and plug-in CLT CIs, and are often close to nominal ($50\%$, $90\%$, $95\%$) coverage, while the baselines are poorly calibrated at small sample sizes and short episode lengths.

We propose an algorithm to sample from composite log-concave distributions over $\mathbb{R}^d$, i.e., densities of the form $π\propto e^{-f-g}$, assuming access to gradient evaluations of $f$ and a restricted Gaussian oracle (RGO) for $g$. The latter requirement means that we can easily sample from the density $\text{RGO}_{g,h,y}(x) \propto \exp(-g(x) -\frac{1}{2h}||y-x||^2)$, which is the sampling analogue of the proximal operator for $g$. If $f + g$ is $α$-strongly convex and $f$ is $β$-smooth, our sampler achieves $\varepsilon$ error in total variation distance in $\widetilde{\mathcal O}(κ\sqrt d \log^4(1/\varepsilon))$ iterations where $κ:= β/α$, which matches prior state-of-the-art results for the case $g=0$. We further extend our results to cases where (1) $π$ is non-log-concave but satisfies a Poincaré or log-Sobolev inequality, and (2) $f$ is non-smooth but Lipschitz.

Florida students boo graduation speaker who called AI'next Industrial Revolution' Real estate executive got an unexpected earful when she spoke of'living in a time of profound change' Though college graduations usually consist of a speaker giving advice to students, one recent ceremony featured students giving the speaker their opinions - loudly. The University of Central Florida's 2026 graduating class booed as a real estate development executive spoke about how "the rise of artificial intelligence is the next Industrial Revolution" and about "living in a time of profound change". US university's commencement speaker reveals he will pay off students' final-year loans The crowd of students was so loud that Gloria Caulfield paused, turned away from the podium and threw her hands up in the air. As the crowd calmed down, Caulfield proceeded. "Only a few years ago, AI was not a factor in our lives."

Elon Musk tried to take control of OpenAI, even suggesting it could pass to his children when he dies, Sam Altman said on Tuesday. Altman is co-founder and chief executive of the artificial intelligence (AI) company behind ChatGPT. He is being sued by Musk, who accuses him of having looted a charity given OpenAI began as a non-profit. Appearing before a federal jury in Oakland, California, Altman said Musk not only backed the idea of OpenAI becoming a for-profit business, he wanted control of it for the long-run. A particularly hair-raising moment was when my cofounders asked, 'If you have control, what happens when you die?'

Googlebook Is Google's New AI-Powered Laptop Platform Built on Android They won't replace Chromebooks, but Googlebooks have an Android-centered operating system, AI-first features like the Magic Pointer, and a promise of desktop-grade apps. Almost exactly 15 years since Google introduced Chromebooks and ChromeOS --which ushered a wave of cheap, functional, web-based laptops that would come to dominate the US education market--the company has announced a new laptop platform called Googlebook. It's built around artificial intelligence and Android, and while it isn't replacing Chromebooks, it could give the company a more meaningful foothold in the premium computer market. Google announced the platform on The Android Show on YouTube, where it also detailed new features coming in Android 17 and Gemini Intelligence (you can read more about that here). Google is purposefully not sharing the operating system's name yet (it was codenamed Aluminium OS internally); Googlebook is the platform, and Dell, Acer, Asus, HP, and Lenovo have all signed up to produce Googlebooks coming later this fall.

Here's what you need to know, from why the cruise ship outbreak won't spark the next pandemic to how hantavirus spreads. Now that more than 100 passengers aboard a hantavirus -stricken luxury cruise ship have been evacuated, with 18 Americans in biocontainment units in Nebraska and Georgia, health officials around the world are working to monitor more than two dozen individuals who left the cruise and anyone with whom they might have come in close contact. So far, all of the 11 reported hantavirus cases are among passengers or crew on the ship, the World Health Organization's director-general Tedros Adhanom Ghebreyesus said at a press conference in Madrid on Tuesday. That includes three deaths resulting from the virus. Typically, hantaviruses are spread when contaminated rodent droppings and urine are stirred up in the air and breathed in.

GameStop has built up a stake of 5% in eBay and is offering to acquire the company at $125 a share. GameStop has built up a stake of 5% in eBay and is offering to acquire the company at $125 a share. GameStop's $55.5bn bid for eBay rejected as'neither credible nor attractive' Online marketplace takes into account uncertainty around US video games retailer's financing proposal The board of eBay has rejected the US video games retailer GameStop's surprise $55.5bn bid (£41bn) for the online marketplace, describing the proposal as "neither credible nor attractive". Earlier this month, GameStop made an unsolicited bid for eBay, publishing a letter on its website outlining a half-cash, half-stock proposal. This was despite the US games company - which became a global household name during the meme stock craze of 2021 - being worth far less than its takeover target.