We propose a scalable variational Bayes method for statistical inference for a single or low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field approximation to the nuisance coordinates and carefully modelling the conditional distribution of the target given the nuisance. This requires only a preprocessing step and preserves the computational advantages of mean-field variational Bayes, while ensuring accurate and reliable inference for the target parameter, including for uncertainty quantification. We investigate the numerical performance of our algorithm, showing that it performs competitively with existing methods. We further establish accompanying theoretical guarantees for estimation and uncertainty quantification in the form of a Bernstein--von Mises theorem.

Large Language Models (LLMs) often suffer from overconfidence during inference, particularly when adapted to downstream domain-specific tasks with limited data. Previous work addresses this issue by employing approximate Bayesian estimation after the LLMs are trained, enabling them to quantify uncertainty. However, such post-training approaches' performance is severely limited by the parameters learned during training. In this paper, we go beyond post-training Bayesianization and propose Bayesian Low-Rank Adaptation by Backpropagation (BLoB), an algorithm that continuously and jointly adjusts both the mean and covariance of LLM parameters throughout the whole fine-tuning process. Our empirical results verify the effectiveness of BLoB in terms of generalization and uncertainty estimation, when evaluated on both in-distribution and out-of-distribution data.

Robots navigating in crowded areas should negotiate free space with humans rather than fully controlling collision avoidance, as this can lead to freezing behavior. Game theory provides a framework for the robot to reason about potential cooperation from humans for collision avoidance during path planning. In particular, the mixed strategy Nash equilibrium captures the negotiation behavior under uncertainty, making it well suited for crowd navigation. However, computing the mixed strategy Nash equilibrium is often prohibitively expensive for real-time decision-making. In this paper, we propose an iterative Bayesian update scheme over probability distributions of trajectories. The algorithm simultaneously generates a stochastic plan for the robot and probabilistic predictions of other pedestrians' paths. We prove that the proposed algorithm is equivalent to solving a mixed strategy game for crowd navigation, and the algorithm guarantees the recovery of the global Nash equilibrium of the game. We name our algorithm Bayes' Rule Nash Equilibrium (BRNE) and develop a real-time model prediction crowd navigation framework. Since BRNE is not solving a general-purpose mixed strategy Nash equilibrium but a tailored formula specifically for crowd navigation, it can compute the solution in real-time on a low-power embedded computer. We evaluate BRNE in both simulated environments and real-world pedestrian datasets. BRNE consistently outperforms non-learning and learning-based methods regarding safety and navigation efficiency. It also reaches human-level crowd navigation performance in the pedestrian dataset benchmark. Lastly, we demonstrate the practicality of our algorithm with real humans on an untethered quadruped robot with fully onboard perception and computation.

Mathematical equivalence between statistical mechanics and machine learning theory has been known since the 20th century, and researches based on such equivalence have provided novel methodology in both theoretical physics and statistical learning theory. For example, algebraic approach in statistical mechanics such as operator algebra enables us to analyze phase transition phenomena mathematically. In this paper, for theoretical physicists who are interested in artificial intelligence, we review and prospect algebraic researches in machine learning theory. If a learning machine has hierarchical structure or latent variables, then the random Hamiltonian cannot be expressed by any quadratic perturbation because it has singularities. To study an equilibrium state defined by such a singular random Hamiltonian, algebraic approach is necessary to derive asymptotic form of the free energy and the generalization error. We also introduce the most recent advance, in fact, theoretical foundation for alignment of artificial intelligence is now being constructed based on algebraic learning theory. This paper is devoted to the memory of Professor Huzihiro Araki who is a pioneer founder of algebraic research in both statistical mechanics and quantum field theory.

With the prevailing efforts to combat the coronavirus disease 2019 (COVID-19) pandemic, there are still uncertainties that are yet to be discovered about its spread, future impact, and resurgence. In this paper, we present a three-stage data-driven approach to distill the hidden information about COVID-19. The first stage employs a Bayesian network structure learning method to identify the causal relationships among COVID-19 symptoms and their intrinsic demographic variables. As a second stage, the output from the Bayesian network structure learning, serves as a useful guide to train an unsupervised machine learning (ML) algorithm that uncovers the similarities in patients' symptoms through clustering. The final stage then leverages the labels obtained from clustering to train a demographic symptom identification (DSID) model which predicts a patient's symptom class and the corresponding demographic probability distribution. We applied our method on the COVID-19 dataset obtained from the Centers for Disease Control and Prevention (CDC) in the United States. Results from the experiments show a testing accuracy of 99.99%, as against the 41.15% accuracy of a heuristic ML method. This strongly reveals the viability of our Bayesian network and ML approach in understanding the relationship between the virus symptoms, and providing insights on patients' stratification towards reducing the severity of the virus.

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs, we obtain the exact minimax quantile risk for a rich family of error functions and establish the minimaxity of OLS. This improves on the lower bounds obtained by Lecué and Mendelson (2016) and Mendelson (2017) for the special case of square error, and provides us with a lower bound on the minimax quantile risk over larger sets of distributions. Under the square error and a fourth moment assumption on the distribution of inputs, we show that this lower bound is tight over a larger class of problems. Specifically, we prove a matching upper bound on the worst-case quantile risk of a variant of the procedure proposed by Lecué and Lerasle (2020), thereby establishing its minimaxity, up to absolute constants. We illustrate the usefulness of our approach by extending this result to all p-th power error functions for p (2,). Along the way, we develop a generic analogue to the classical Bayesian method for lower bounding the minimax risk when working with the quantile risk, as well as a tight characterization of the quantiles of the smallest eigenvalue of the sample covariance matrix.

Large language models (LLMs) can adapt to new tasks through in-context learning (ICL) based on a few examples presented in dialogue history without any model parameter update. Despite such convenience, the performance of ICL heavily depends on the quality of the in-context examples presented, which makes the in-context example selection approach a critical choice. This paper proposes a novel Bayesian in-Context example Selection method (ByCS) for ICL. Extending the inference probability conditioned on in-context examples based on Bayes' theorem, ByCS focuses on the inverse inference conditioned on test input. Following the assumption that accurate inverse inference probability (likelihood) will result in accurate inference probability (posterior), in-context examples are selected based on their inverse inference results. Diverse and extensive cross-tasking and cross-modality experiments are performed with speech, text, and image examples. Experimental results show the efficacy and robustness of our ByCS method on various models, tasks and modalities.

Instruction Fine-Tuning enhances pre-trained language models from basic next-word prediction to complex instruction-following. However, existing One-off Instruction Fine-Tuning (One-off IFT) method, applied on a diverse instruction, may not effectively boost models' adherence to instructions due to the simultaneous handling of varying instruction complexities. To improve this, Phased Instruction Fine-Tuning (Phased IFT) is proposed, based on the idea that learning to follow instructions is a gradual process. It assesses instruction difficulty using GPT-4, divides the instruction data into subsets of increasing difficulty, and uptrains the model sequentially on these subsets. Experiments with Llama-2 7B/13B/70B, Llama3 8/70B and Mistral-7B models using Alpaca data show that Phased IFT significantly outperforms One-off IFT, supporting the progressive alignment hypothesis and providing a simple and efficient way to enhance large language models. Codes and datasets from our experiments are freely available at https://github.com/xubuvd/PhasedSFT.

Causal discovery is crucial for understanding complex systems and informing decisions. While observational data can uncover causal relationships under certain assumptions, it often falls short, making active interventions necessary. Current methods, such as Bayesian and graph-theoretical approaches, do not prioritize decision-making and often rely on ideal conditions or information gain, which is not directly related to hypothesis testing. We propose a novel Bayesian optimization-based method inspired by Bayes factors that aims to maximize the probability of obtaining decisive and correct evidence. Our approach uses observational data to estimate causal models under different hypotheses, evaluates potential interventions pre-experimentally, and iteratively updates priors to refine interventions. We demonstrate the effectiveness of our method through various experiments. Our contributions provide a robust framework for efficient causal discovery through active interventions, enhancing the practical application of theoretical advancements.

We present an approach for estimating the fraction of text in a large corpus which is likely to be substantially modified or produced by a large language model (LLM). Our maximum likelihood model leverages expert-written and AI-generated reference texts to accurately and efficiently examine real-world LLM-use at the corpus level. We apply this approach to a case study of scientific peer review in AI conferences that took place after the release of ChatGPT: ICLR 2024, NeurIPS 2023, CoRL 2023 and EMNLP 2023. Our results suggest that between 6.5% and 16.9% of text submitted as peer reviews to these conferences could have been substantially modified by LLMs, i.e. beyond spell-checking or minor writing updates. The circumstances in which generated text occurs offer insight into user behavior: the estimated fraction of LLM-generated text is higher in reviews which report lower confidence, were submitted close to the deadline, and from reviewers who are less likely to respond to author rebuttals. We also observe corpus-level trends in generated text which may be too subtle to detect at the individual level, and discuss the implications of such trends on peer review. We call for future interdisciplinary work to examine how LLM use is changing our information and knowledge practices.