In contrast to popular decision-making frameworks such as reinforcement learning, which are built upon appealing to decision-theoretic notions such as Maximum Expected Utility, we instead construct an agent by trying to minimise the expected number of bits needed to losslessly describe general agent-environment interactions. The appeal with this approach is that if we can construct a good universal coding scheme for arbitrary agent interactions, one could simply sample from this coding distribution to generate a control policy. However when considering general agents, whose goal is to work well across multiple environments, this question turns out to be surprisingly subtle. Naive approaches which do not discriminate between actions and observations fail, and are subject to the self-delusion problem [Ortega et al., 2021]. In this work, we will adopt a universal source coding perspective to this question, and showcase its efficacy by applying it to the challenging non-stationary stochastic bandit problem. In the passive case, namely, sequential prediction of observations under the logarithmic loss, there is a well developed universal source coding literature for dealing with non-stationary sources under various types of non-stationarity. The most influential idea for modelling piecewise stationary sources is the transition diagram technique of Willems [1996]. This technique performs Bayesian model averaging over all possible partitions of a sequence of data, cleverly exploiting dynamic programming to yield an algorithm which has both quadratic time complexity and provable regret guarantees.

We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions. Fits to these models give us a way to cluster data with distributions of unknown form, including strongly non-Gaussian or multimodal distributions, and return both a division of the data and an estimate of the distributions, effectively performing clustering and density estimation within each cluster at the same time. We describe two fitting methods, one using an expectation-maximization (EM) algorithm and the other a Bayesian non-parametric method using a collapsed Gibbs sampler. The former is numerically efficient, but gives only point estimates of the probability densities. The latter is more computationally demanding but returns a full Bayesian posterior and also an estimate of the number of components. We demonstrate our methods with a selection of illustrative applications and give code implementing both algorithms.

The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable information that can be integrated into a decision pipeline. Rather than seeing the lack of certitude and inherent randomness of GAI as a problem, we view it as an opportunity. Indeed, variable answers to given prompts can be leveraged to construct a prior distribution which reflects assuredness of AI predictions. This prior distribution may be combined with tailored datasets for a fully Bayesian analysis with an AI-driven prior. In this paper, we explore such a possibility within a non-parametric Bayesian framework. The basic idea consists of assigning a Dirichlet process prior distribution on the data-generating distribution with AI generative model as its baseline. Hyper-parameters of the prior can be tuned out-of-sample to assess the informativeness of the AI prior. Posterior simulation is achieved by computing a suitably randomized functional on an augmented data that consists of observed (labeled) data as well as fake data whose labels have been imputed using AI. This strategy can be parallelized and rapidly produces iid samples from the posterior by optimization as opposed to sampling from conditionals. Our method enables (predictive) inference and uncertainty quantification leveraging AI predictions in a coherent probabilistic manner.

We propose a scalable inference algorithm for Bayes posteriors defined on a reproducing kernel Hilbert space (RKHS). Given a likelihood function and a Gaussian random element representing the prior, the corresponding Bayes posterior measure $\Pi_{\text{B}}$ can be obtained as the stationary distribution of an RKHS-valued Langevin diffusion. We approximate the infinite-dimensional Langevin diffusion via a projection onto the first $M$ components of the Kosambi-Karhunen-Lo\`eve expansion. Exploiting the thus obtained approximate posterior for these $M$ components, we perform inference for $\Pi_{\text{B}}$ by relying on the law of total probability and a sufficiency assumption. The resulting method scales as $O(M^3+JM^2)$, where $J$ is the number of samples produced from the posterior measure $\Pi_{\text{B}}$. Interestingly, the algorithm recovers the posterior arising from the sparse variational Gaussian process (SVGP) (see Titsias, 2009) as a special case, owed to the fact that the sufficiency assumption underlies both methods. However, whereas the SVGP is parametrically constrained to be a Gaussian process, our method is based on a non-parametric variational family $\mathcal{P}(\mathbb{R}^M)$ consisting of all probability measures on $\mathbb{R}^M$. As a result, our method is provably close to the optimal $M$-dimensional variational approximation of the Bayes posterior $\Pi_{\text{B}}$ in $\mathcal{P}(\mathbb{R}^M)$ for convex and Lipschitz continuous negative log likelihoods, and coincides with SVGP for the special case of a Gaussian error likelihood.

Interferometric Synthetic Aperture Radar (InSAR) technology uses satellite radar to detect surface deformation patterns and monitor earthquake impacts on buildings. While vital for emergency response planning, extracting multi-class building damage classifications from InSAR data faces challenges: overlapping damage signatures with environmental noise, computational complexity in multi-class scenarios, and the need for rapid regional-scale processing. Our novel multi-class variational causal Bayesian inference framework with quadratic variational bounds provides rigorous approximations while ensuring efficiency. By integrating InSAR observations with USGS ground failure models and building fragility functions, our approach separates building damage signals while maintaining computational efficiency through strategic pruning. Evaluation across five major earthquakes (Haiti 2021, Puerto Rico 2020, Zagreb 2020, Italy 2016, Ridgecrest 2019) shows improved damage classification accuracy (AUC: 0.94-0.96), achieving up to 35.7% improvement over existing methods. Our approach maintains high accuracy (AUC > 0.93) across all damage categories while reducing computational overhead by over 40% without requiring extensive ground truth data.

Modern applications are increasingly built as vast, intricate, distributed systems. These systems comprise various software modules, often developed by different teams using different programming languages and deployed across hundreds to thousands of machines, sometimes spanning multiple data centers. Given the ir scale and complexity, these applications are often designed to tolerate failures and performance issues through inbuilt failure recovery techniques (e.g., hardware or software redundancy) or extern al methods (e.g., health check - based restarts). Computer systems experience frequent failures despite every effort: performance degradations and violations of reliability and K ey Performance Indicators (K PI s) are inevitable. These failures, depending on their nature, can lead to catastrophic incidents impacting critical systems and customers. Swift and accurate root cause identification is thus essential to avert significant incidents impacting both service quality and end users. In this complex landscape, observability platforms that provide deep insights into system behavior and help identify performance bottlenecks are not just helpful -- they are essential for maintaining reliability, ensuring optimal performance, and quickly resolving issues in production. The ability to reason a bout these systems in real - time is critical to ensuring the scalability and stability of modern services. To aid in these investigations, observability platforms that collect various telemetry data t o inform about application behavior and its underlying infrastructure are getting popular .

This study addresses the critical issue of reliability for AI-assisted medical diagnosis. We focus on the selection prediction approach that allows the diagnosis system to abstain from providing the decision if it is not confident in the diagnosis. Such selective prediction (or abstention) approaches are usually based on the modeling predictive uncertainty of machine learning models involved. This study explores uncertainty quantification in machine learning models for medical text analysis, addressing diverse tasks across multiple datasets. We focus on binary mortality prediction from textual data in MIMIC-III, multi-label medical code prediction using ICD-10 codes from MIMIC-IV, and multi-class classification with a private outpatient visits dataset. Additionally, we analyze mental health datasets targeting depression and anxiety detection, utilizing various text-based sources, such as essays, social media posts, and clinical descriptions. In addition to comparing uncertainty methods, we introduce HUQ-2, a new state-of-the-art method for enhancing reliability in selective prediction tasks. Our results provide a detailed comparison of uncertainty quantification methods. They demonstrate the effectiveness of HUQ-2 in capturing and evaluating uncertainty, paving the way for more reliable and interpretable applications in medical text analysis.

For a long time, the authorship of the Federalist Papers had been a subject of inquiry and debate, not only by linguists and historians but also by statisticians. In what was arguably the first Bayesian case study, Mosteller and Wallace (1963) provided the first statistical evidence for attributing all disputed papers to Madison. Our paper revisits this historical dataset but from a lens of modern language models, both small and large. We review some of the more popular Large Language Model (LLM) tools and examine them from a statistical point of view in the context of text classification. We investigate whether, without any attempt to fine-tune, the general embedding constructs can be useful for stylometry and attribution. We explain differences between various word/phrase embeddings and discuss how to aggregate them in a document. Contrary to our expectations, we exemplify that dimension expansion with word embeddings may not always be beneficial for attribution relative to dimension reduction with topic embeddings. Our experiments demonstrate that default LLM embeddings (even after manual fine-tuning) may not consistently improve authorship attribution accuracy. Instead, Bayesian analysis with topic embeddings trained on ``function words" yields superior out-of-sample classification performance. This suggests that traditional (small) statistical language models, with their interpretability and solid theoretical foundation, can offer significant advantages in authorship attribution tasks. The code used in this analysis is available at github.com/sowonjeong/slm-to-llm

In statistics, generalized linear models (GLMs) are widely used for modeling data and can expressively capture potential nonlinear dependence of the model's outcomes on its covariates. Within the broad family of GLMs, those with binary outcomes, which include logistic and probit regressions, are motivated by common tasks such as binary classification with (possibly) non-separable data. In addition, in modern machine learning and statistics, data is often high-dimensional yet has a low intrinsic dimension, making sparsity constraints in models another reasonable consideration. In this work, we propose to use and analyze an iterative hard thresholding (projected gradient descent on the ReLU loss) algorithm, called binary iterative hard thresholding (BIHT), for parameter estimation in sparse GLMs with binary outcomes. We establish that BIHT is statistically efficient and converges to the correct solution for parameter estimation in a general class of sparse binary GLMs. Unlike many other methods for learning GLMs, including maximum likelihood estimation, generalized approximate message passing, and GLM-tron (Kakade et al. 2011; Bahmani et al. 2016), BIHT does not require knowledge of the GLM's link function, offering flexibility and generality in allowing the algorithm to learn arbitrary binary GLMs. As two applications, logistic and probit regression are additionally studied. In this regard, it is shown that in logistic regression, the algorithm is in fact statistically optimal in the sense that the order-wise sample complexity matches (up to logarithmic factors) the lower bound obtained previously. To the best of our knowledge, this is the first work achieving statistical optimality for logistic regression in all noise regimes with a computationally efficient algorithm. Moreover, for probit regression, our sample complexity is on the same order as that obtained for logistic regression.

Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to characterize these dynamics. These models use Gaussian Process (GP) priors to capture the nonlinear dependence of circuit dynamics on task and behavioral variables. Conditioned on these covariates, the data is modeled with linear dynamics. This allows for transparent interpretation and tractable Bayesian inference. We find that CLDS models can perform well even in severely data-limited regimes (e.g. one trial per condition) due to their Bayesian formulation and ability to share statistical power across nearby task conditions. In example applications, we apply CLDS to model thalamic neurons that nonlinearly encode heading direction and to model motor cortical neurons during a cued reaching task