Causal graph discovery is a significant problem with applications across various disciplines. However, with observational data alone, the underlying causal graph can only be recovered up to its Markov equivalence class, and further assumptions or interventions are necessary to narrow down the true graph. This work addresses the causal discovery problem under the setting of stochastic interventions with the natural goal of minimizing the number of interventions performed. We propose the following stochastic intervention model which subsumes existing adaptive noiseless interventions in the literature while capturing scenarios such as fat-hand interventions and CRISPR gene knockouts: any intervention attempt results in an actual intervention on a random subset of vertices, drawn from a distribution dependent on attempted action. Under this model, we study the two fundamental problems in causal discovery of verification and search and provide approximation algorithms with polylogarithmic competitive ratios and provide some preliminary experimental results.

We introduce a set of gradient-flow-guided adaptive importance sampling (IS) transformations to stabilize Monte-Carlo approximations of point-wise leave one out cross-validated (LOO) predictions for Bayesian classification models. One can leverage this methodology for assessing model generalizability by for instance computing a LOO analogue to the AIC or computing LOO ROC/PRC curves and derived metrics like the AUROC and AUPRC. By the calculus of variations and gradient flow, we derive two simple nonlinear single-step transformations that utilize gradient information to shift a model's pre-trained full-data posterior closer to the target LOO posterior predictive distributions. In doing so, the transformations stabilize importance weights. Because the transformations involve the gradient of the likelihood function, the resulting Monte Carlo integral depends on Jacobian determinants with respect to the model Hessian. We derive closed-form exact formulae for these Jacobian determinants in the cases of logistic regression and shallow ReLU-activated artificial neural networks, and provide a simple approximation that sidesteps the need to compute full Hessian matrices and their spectra. We test the methodology on an $n\ll p$ dataset that is known to produce unstable LOO IS weights.

To find New Physics or to refine our knowledge of the Standard Model at the LHC is an enterprise that involves many factors. We focus on taking advantage of available information and pour our effort in re-thinking the usual data-driven ABCD method to improve it and to generalize it using Bayesian Machine Learning tools. We propose that a dataset consisting of a signal and many backgrounds is well described through a mixture model. Signal, backgrounds and their relative fractions in the sample can be well extracted by exploiting the prior knowledge and the dependence between the different observables at the event-by-event level with Bayesian tools. We show how, in contrast to the ABCD method, one can take advantage of understanding some properties of the different backgrounds and of having more than two independent observables to measure in each event. In addition, instead of regions defined through hard cuts, the Bayesian framework uses the information of continuous distribution to obtain soft-assignments of the events which are statistically more robust. To compare both methods we use a toy problem inspired by $pp\to hh\to b\bar b b \bar b$, selecting a reduced and simplified number of processes and analysing the flavor of the four jets and the invariant mass of the jet-pairs, modeled with simplified distributions. Taking advantage of all this information, and starting from a combination of biased and agnostic priors, leads us to a very good posterior once we use the Bayesian framework to exploit the data and the mutual information of the observables at the event-by-event level. We show how, in this simplified model, the Bayesian framework outperforms the ABCD method sensitivity in obtaining the signal fraction in scenarios with $1\%$ and $0.5\%$ true signal fractions in the dataset. We also show that the method is robust against the absence of signal.

The prior drift is crucial in Continual Test-Time Adaptation (CTTA) methods that only use unlabeled test data, as it can cause significant error propagation. In this paper, we introduce VCoTTA, a variational Bayesian approach to measure uncertainties in CTTA. At the source stage, we transform a pre-trained deterministic model into a Bayesian Neural Network (BNN) via a variational warm-up strategy, injecting uncertainties into the model. During the testing time, we employ a mean-teacher update strategy using variational inference for the student model and exponential moving average for the teacher model. Our novel approach updates the student model by combining priors from both the source and teacher models. The evidence lower bound is formulated as the cross-entropy between the student and teacher models, along with the Kullback-Leibler (KL) divergence of the prior mixture. Experimental results on three datasets demonstrate the method's effectiveness in mitigating prior drift within the CTTA framework.

How can individuals exchange information to learn from each other despite their privacy needs and security concerns? For example, consider individuals deliberating a contentious topic and being concerned about divulging their private experiences. Preserving individual privacy and enabling efficient social learning are both important desiderata but seem fundamentally at odds with each other and very hard to reconcile. We do so by controlling information leakage using rigorous statistical guarantees that are based on differential privacy (DP). Our agents use log-linear rules to update their beliefs after communicating with their neighbors. Adding DP randomization noise to beliefs provides communicating agents with plausible deniability with regard to their private information and their network neighborhoods. We consider two learning environments one for distributed maximum-likelihood estimation given a finite number of private signals and another for online learning from an infinite, intermittent signal stream. Noisy information aggregation in the finite case leads to interesting tradeoffs between rejecting low-quality states and making sure all high-quality states are accepted in the algorithm output. Our results flesh out the nature of the trade-offs in both cases between the quality of the group decision outcomes, learning accuracy, communication cost, and the level of privacy protections that the agents are afforded.

Graph Laplacian learning, also known as network topology inference, is a problem of great interest to multiple communities. In Gaussian graphical models (GM), graph learning amounts to endowing covariance selection with the Laplacian structure. In graph signal processing (GSP), it is essential to infer the unobserved graph from the outputs of a filtering system. In this paper, we study the problem of learning Cartesian product graphs under Laplacian constraints. The Cartesian graph product is a natural way for modeling higher-order conditional dependencies and is also the key for generalizing GSP to multi-way tensors. We establish statistical consistency for the penalized maximum likelihood estimation (MLE) of a Cartesian product Laplacian, and propose an efficient algorithm to solve the problem. We also extend our method for efficient joint graph learning and imputation in the presence of structural missing values. Experiments on synthetic and real-world datasets demonstrate that our method is superior to previous GSP and GM methods.

In this paper, we propose a novel approach to Bayesian Experimental Design (BED) for non-exchangeable data that formulates it as risk-sensitive policy optimization. We develop the Inside-Out SMC^2 algorithm that uses a nested sequential Monte Carlo (SMC) estimator of the expected information gain and embeds it into a particle Markov chain Monte Carlo (pMCMC) framework to perform gradient-based policy optimization. This is in contrast to recent approaches that rely on biased estimators of the expected information gain (EIG) to amortize the cost of experiments by learning a design policy in advance. Numerical validation on a set of dynamical systems showcases the efficacy of our method in comparison to other state-of-the-art strategies.

Large language models (LLMs) have been extensively studied for their abilities to generate convincing natural language sequences, however their utility for quantitative information retrieval is less well understood. In this paper we explore the feasibility of LLMs as a mechanism for quantitative knowledge retrieval to aid data analysis tasks such as elicitation of prior distributions for Bayesian models and imputation of missing data. We present a prompt engineering framework, treating an LLM as an interface to a latent space of scientific literature, comparing responses in different contexts and domains against more established approaches. Implications and challenges of using LLMs as 'experts' are discussed.

Several approaches to graphically representing context-specific relations among jointly distributed categorical variables have been proposed, along with structure learning algorithms. While existing optimization-based methods have limited scalability due to the large number of context-specific models, the constraint-based methods are more prone to error than even constraint-based DAG learning algorithms since more relations must be tested. We present a hybrid algorithm for learning context-specific models that scales to hundreds of variables while testing no more constraints than standard DAG learning algorithms. Scalable learning is achieved through a combination of an order-based MCMC algorithm and sparsity assumptions analogous to those typically invoked for DAG models. To implement the method, we solve a special case of an open problem recently posed by Alon and Balogh. The method is shown to perform well on synthetic data and real world examples, in terms of both accuracy and scalability.

Machine learning models in modern mass-market applications are often updated over time. One of the foremost challenges faced is that, despite increasing overall performance, these updates may flip specific model predictions in unpredictable ways. In practice, researchers quantify the number of unstable predictions between models pre and post update -- i.e., predictive churn. In this paper, we study this effect through the lens of predictive multiplicity -- i.e., the prevalence of conflicting predictions over the set of near-optimal models (the Rashomon set). We show how traditional measures of predictive multiplicity can be used to examine expected churn over this set of prospective models -- i.e., the set of models that may be used to replace a baseline model in deployment. We present theoretical results on the expected churn between models within the Rashomon set from different perspectives. And we characterize expected churn over model updates via the Rashomon set, pairing our analysis with empirical results on real-world datasets -- showing how our approach can be used to better anticipate, reduce, and avoid churn in consumer-facing applications. Further, we show that our approach is useful even for models enhanced with uncertainty awareness.