The recent rapid adoption of large language models (LLMs) highlights the critical need for benchmarking their fairness. Conventional fairness metrics, which focus on discrete accuracy-based evaluations (i.e., prediction correctness), fail to capture the implicit impact of model uncertainty (e.g., higher model confidence about one group over another despite similar accuracy). To address this limitation, we propose an uncertainty-aware fairness metric, UCerf, to enable a fine-grained evaluation of model fairness that is more reflective of the internal bias in model decisions. Furthermore, observing data size, diversity, and clarity issues in current datasets, we introduce a new gender-occupation fairness evaluation dataset with 31,756 samples for co-reference resolution, offering a more diverse and suitable benchmark for modern LLMs. Combining our metric and dataset, we provide insightful comparisons of eight open-source LLMs. For example, Mistral-8B exhibits suboptimal fairness due to high confidence in incorrect predictions, a detail overlooked by Equalized Odds but captured by UCerF. Overall, this work provides a holistic framework for LLM evaluation by jointly assessing fairness and uncertainty, enabling the development of more transparent and accountable AI systems.

The mechanisms behind the success of multi-view self-supervised learning (MVSSL) are not yet fully understood. Contrastive MVSSL methods have been studied through the lens of InfoNCE, a lower bound of the Mutual Information (MI). However, the relation between other MVSSL methods and MI remains unclear. We consider a different lower bound on the MI consisting of an entropy and a reconstruction term (ER), and analyze the main MVSSL families through its lens. Through this ER bound, we show that clustering-based methods such as DeepCluster and SwAV maximize the MI. We also re-interpret the mechanisms of distillation-based approaches such as BYOL and DINO, showing that they explicitly maximize the reconstruction term and implicitly encourage a stable entropy, and we confirm this empirically. We show that replacing the objectives of common MVSSL methods with this ER bound achieves competitive performance, while making them stable when training with smaller batch sizes or smaller exponential moving average (EMA) coefficients.

Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high dimensional data. Many of them rely on a non-parametric nearest neighbours approach which suffers from the curse of dimensionality. We attempt to address that challenge by proposing a novel approach to the problem: Local Intrinsic Dimension estimation using approximate Likelihood (LIDL). Our method relies on an arbitrary density estimation method as its subroutine, and hence tries to sidestep the dimensionality challenge by making use of the recent progress in parametric neural methods for likelihood estimation. We carefully investigate the empirical properties of the proposed method, compare them with our theoretical predictions, show that LIDL yields competitive results on the standard benchmarks for this problem, and that it scales to thousands of dimensions. What is more, we anticipate this approach to improve further with the continuing advances in the density estimation literature.

We show that the standard computational pipeline of probabilistic programming systems (PPSs) can be inefficient for estimating expectations and introduce the concept of expectation programming to address this. In expectation programming, the aim of the backend inference engine is to directly estimate expected return values of programs, as opposed to approximating their conditional distributions. This distinction, while subtle, allows us to achieve substantial performance improvements over the standard PPS computational pipeline by tailoring computation to the expectation we care about. We realize a particular instance of our expectation programming concept, Expectation Programming in Turing (EPT), by extending the PPS Turing to allow so-called target-aware inference to be run automatically. We then verify the statistical soundness of EPT theoretically, and show that it provides substantial empirical gains in practice.

Standard approaches for Bayesian inference focus solely on approximating the posterior distribution. Typically, this approximation is, in turn, used to calculate expectations for one or more target functions—a computational pipeline that is inefficient when the target function(s) are known upfront. We address this inefficiency by introducing a framework for target–aware Bayesian inference (TABI) that estimates these expectations directly. While conventional Monte Carlo estimators have a fundamental limit on the error they can achieve for a given sample size, our TABI framework is able to breach this limit; it can theoretically produce arbitrarily accurate estimators using only three samples, while we show empirically that it can also breach this limit in practice. We utilize our TABI framework by combining it with adaptive importance sampling approaches and show both theoretically and empirically that the resulting estimators are capable of converging faster than the standard $\mathcal{O}(1/N)$ Monte Carlo rate, potentially producing rates as fast as $\mathcal{O}(1/N^2)$. We further combine our TABI framework with amortized inference methods, to produce a method for amortizing the cost of calculating expectations. Finally, we show how TABI can be used to convert any marginal likelihood estimator into a target aware inference scheme and demonstrate the substantial benefits this can yield.

Current approaches to amortizing Bayesian inference focus solely on approximating the posterior distribution. Typically, this approximation is, in turn, used to calculate expectations for one or more target functions{—}a computational pipeline which is inefficient when the target function(s) are known upfront. In this paper, we address this inefficiency by introducing AMCI, a method for amortizing Monte Carlo integration directly. AMCI operates similarly to amortized inference but produces three distinct amortized proposals, each tailored to a different component of the overall expectation calculation. At runtime, samples are produced separately from each amortized proposal, before being combined to an overall estimate of the expectation. We show that while existing approaches are fundamentally limited in the level of accuracy they can achieve, AMCI can theoretically produce arbitrarily small errors for any integrable target function using only a single sample from each proposal at runtime. We further show that it is able to empirically outperform the theoretically optimal selfnormalized importance sampler on a number of example problems. Furthermore, AMCI allows not only for amortizing over datasets but also amortizing over target functions.

Inference amortization methods share information across multiple posterior-inference problems, allowing each to be carried out more efficiently. Generally, they require the inversion of the dependency structure in the generative model, as the modeller must learn a mapping from observations to distributions approximating the posterior. Previous approaches have involved inverting the dependency structure in a heuristic way that fails to capture these dependencies correctly, thereby limiting the achievable accuracy of the resulting approximations. We introduce an algorithm for faithfully, and minimally, inverting the graphical model structure of any generative model. Such inverses have two crucial properties: (a) they do not encode any independence assertions that are absent from the model and; (b) they are local maxima for the number of true independencies encoded. We prove the correctness of our approach and empirically show that the resulting minimally faithful inverses lead to better inference amortization than existing heuristic approaches.