We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global maximum. PES codifies this intractable acquisition function in terms of the expected reduction in the differential entropy of the predictive distribution. This reformulation allows PES to obtain approximations that are both more accurate and efficient than other alternatives such as Entropy Search (ES). Furthermore, PES can easily perform a fully Bayesian treatment of the model hyperparameters while ES cannot. We evaluate PES in both synthetic and realworld applications, including optimization problems in machine learning, finance, biotechnology, and robotics. We show that the increased accuracy of PES leads to significant gains in optimization performance.

Weaknesses: - Central parts of the paper are unclear eg. in line 80 \log P_M (X; \theta) should be the negative cross entropy. The only quantitative results are on adaptation from USPS to MNIST in line 268. However, prior work [1] achieves 96.5% accuracy in comparison to the 55% accuracy achieved by the proposed method. It would be desirable to evaluate the proposed approach on the more complex Facades/Maps/Cityscapes using the MSE metric to facilitate comparison with AlignFlow and [1]. It is unclear how the inductive bias from each of the datasets influence the shared space.

After discussion, all reviewers, and the meta-reviewer, agree that the paper should be accepted. As the authors show, the method in its current form may not scale well to higher dimensions. While a method without this limitation would obviously be preferable, the reviewers agree that this limitation can be addressed in future work, where the connection with GANs that the authors establish may be helpful.

Offline preference alignment for language models such as Direct Preference Optimization (DPO) is favored for its effectiveness and simplicity, eliminating the need for costly reinforcement learning. Various offline algorithms have been developed for different data settings, yet they lack a unified understanding. In this study, we introduce Pior-Informed Preference Alignment (PIPA), a unified, RL-free probabilistic framework that formulates language model preference alignment as a Maximum Likelihood Estimation (MLE) problem with prior constraints. This method effectively accommodates both paired and unpaired data, as well as answer and step-level annotations. We illustrate that DPO and KTO are special cases with different prior constraints within our framework. By integrating different types of prior information, we developed two variations of PIPA: PIPA-M and PIPA-N. Both algorithms demonstrate a $3\sim10\%$ performance enhancement on the GSM8K and MATH benchmarks across all configurations, achieving these gains without additional training or computational costs compared to existing algorithms.

Large Language Models (LLMs) are prone to generating plausible yet incorrect responses, known as hallucinations. Effectively detecting hallucinations is therefore crucial for the safe deployment of LLMs. Recent research has linked hallucinations to model uncertainty, suggesting that hallucinations can be detected by measuring dispersion over answer distributions obtained from a set of samples drawn from a model. While drawing from the distribution over tokens defined by the model is a natural way to obtain samples, in this work, we argue that it is sub-optimal for the purpose of detecting hallucinations. We show that detection can be improved significantly by taking into account model uncertainty in the Bayesian sense. To this end, we propose a very simple and efficient approach that perturbs an appropriate subset of model parameters, or equivalently hidden unit activations, during sampling. We demonstrate its effectiveness across a wide range of datasets and model architectures.

In this work, we present a novel approach to system identification for dynamical systems, based on a specific class of Deep Gaussian Processes (Deep GPs). These models are constructed by interconnecting linear dynamic GPs (equivalent to stochastic linear time-invariant dynamical systems) and static GPs (to model static nonlinearities). Our approach combines the strengths of data-driven methods, such as those based on neural network architectures, with the ability to output a probability distribution. This offers a more comprehensive framework for system identification that includes uncertainty quantification. Using both simulated and real-world data, we demonstrate the effectiveness of the proposed approach.

We propose a construction of coresets based on a predictive view of Bayesian posterior inference (Fong et al., 2024; Fortini and Petrone, 2012). The main attraction of the approach is the model-agnostic nature - the method is valid with any inference model and independent of the specific inference goals, making it highly adaptable for a wide range of applications. Such adaptability is particularly valuable in the context of large-scale datasets, now commonplace in fields like genomics and astronomy. While this explosion of data offers incredible opportunities for discoveries, it also brings significant computational challenges. Tasks that were once straightforward, such as evaluating likelihoods several times have become increasingly difficult, making traditional data processing methods impractical. These obstacles have frequently pushed practitioners toward simpler statistical models that might not capture the full complexity of the data, disregarding expressiveness and flexibility that rich hierarchical and nonparametric models can offer.

Accelerated discovery in materials science demands autonomous systems capable of dynamically formulating and solving design problems. In this work, we introduce a novel framework that leverages Bayesian optimization over a problem formulation space to identify optimal design formulations in line with decision-maker preferences. By mapping various design scenarios to a multi attribute utility function, our approach enables the system to balance conflicting objectives such as ductility, yield strength, density, and solidification range without requiring an exact problem definition at the outset. We demonstrate the efficacy of our method through an in silico case study on a Mo-Nb-Ti-V-W alloy system targeted for gas turbine engine blade applications. The framework converges on a sweet spot that satisfies critical performance thresholds, illustrating that integrating problem formulation discovery into the autonomous design loop can significantly streamline the experimental process. Future work will incorporate human feedback to further enhance the adaptability of the system in real-world experimental settings.

Tractable learning aims to learn probabilistic models where inference is guaranteed to be efficient. However, the particular class of queries that is tractable depends on the model and underlying representation. We propose a tractable learner that guarantees efficient inference for a broader class of queries. It simultaneously learns a Markov network and its tractable circuit representation, in order to guarantee and measure tractability. Our approach differs from earlier work by using Sentential Decision Diagrams (SDD) as the tractable language instead of Arithmetic Circuits (AC).

This paper addresses the problem of learning causal networks with interventions, when each intervention is limited to size k. The paper is generally well-written and addresses a relevant question, as it is generally not feasible to learn the causal structure from observational data alone. Moreover, in some cases, it may also not be possible to perform arbitrarily large interventions, but it is possible to perform interventions over smaller subsets of the variables. The authors prove a number of results around the number of interventions required to learn complete and chordal graphs, and, while I was not able to check all the proofs in detail, the results are as expected (and appear to be correct). The results on chordal graphs are applicable to general causal structures in the sense that application of conditional independence learning and Meek rules results in a chain graph with chordal chain components.