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.

In statistics and machine learning, detecting dependencies in datasets is a central challenge. We propose a novel neural network model for supervised graph structure learning, i.e., the process of learning a mapping between observational data and their underlying dependence structure. The model is trained with variably shaped and coupled simulated input data and requires only a single forward pass through the trained network for inference. By leveraging structural equation models and employing randomly generated multivariate Chebyshev polynomials for the simulation of training data, our method demonstrates robust generalizability across both linear and various types of non-linear dependencies. We introduce a novel bilinear attention mechanism (BAM) for explicit processing of dependency information, which operates on the level of covariance matrices of transformed data and respects the geometry of the manifold of symmetric positive definite matrices. Empirical evaluation demonstrates the robustness of our method in detecting a wide range of dependencies, excelling in undirected graph estimation and proving competitive in completed partially directed acyclic graph estimation through a novel two-step approach.

Developmental AI is a bootstrapping approach where embodied AIs start with innate competences and learn by interacting with the world. They develop abilities in small steps along a bio-inspired trajectory. However, developmental AIs have not yet reached the abilities of young children. In contrast, mainstream approaches for creating AIs have led to valuable AI systems and impressive feats. These approaches include deep learning and generative approaches (e.g., large language models) and manually constructed symbolic approaches. Manually constructed AIs are brittle even in circumscribed domains. Generative AIs are helpful on average, but they can make strange mistakes and not notice them. They sometimes lack common sense and social alignment. This position paper lays out prospects, gaps, and challenges for augmenting AI mainstream approaches with developmental AI. The ambition is to create data-rich experientially based foundation models and human-compatible, resilient, and trustworthy AIs. This research aims to produce AIs that learn to communicate, establish common ground, read critically, consider the provenance of information, test hypotheses, and collaborate. A virtuous multidisciplinary research cycle has led to developmental AIs with capabilities for multimodal perception, object recognition, and manipulation. Computational models for hierarchical planning, abstraction discovery, curiosity, and language acquisition exist but need to be adapted to an embodied learning approach. They need to bridge competence gaps involving nonverbal communication, speech, reading, and writing. Aspirationally, developmental AIs would learn, share what they learn, and collaborate to achieve high standards. The approach would make the creation of AIs more democratic, enabling more people to train, test, build on, and replicate AIs.

Federated learning (FL) is a machine learning paradigm where the clients possess decentralized training data and the central server handles aggregation and scheduling. Typically, FL algorithms involve clients training their local models using stochastic gradient descent (SGD), which carries drawbacks such as slow convergence and being prone to getting stuck in suboptimal solutions. In this work, we propose a message passing based Bayesian federated learning (BFL) framework to avoid these drawbacks.Specifically, we formulate the problem of deep neural network (DNN) learning and compression and as a sparse Bayesian inference problem, in which group sparse prior is employed to achieve structured model compression. Then, we propose an efficient BFL algorithm called EMTDAMP, where expectation maximization (EM) and turbo deep approximate message passing (TDAMP) are combined to achieve distributed learning and compression. The central server aggregates local posterior distributions to update global posterior distributions and update hyperparameters based on EM to accelerate convergence. The clients perform TDAMP to achieve efficient approximate message passing over DNN with joint prior distribution. We detail the application of EMTDAMP to Boston housing price prediction and handwriting recognition, and present extensive numerical results to demonstrate the advantages of EMTDAMP.

Students' engagements reflect their level of involvement in an ongoing learning process which can be estimated through their interactions with a computer-based learning or assessment system. A pre-requirement for stimulating student engagement lies in the capability to have an approximate representation model for comprehending students' varied (dis)engagement behaviors. In this paper, we utilized model-based clustering for this purpose which generates K mixture Markov models to group students' traces containing their (dis)engagement behavioral patterns. To prevent the Expectation-Maximization (EM) algorithm from getting stuck in a local maxima, we also introduced a K-means-based initialization method named as K-EM. We performed an experimental work on two real datasets using the three variants of the EM algorithm: the original EM, emEM, K-EM; and, non-mixture baseline models for both datasets. The proposed K-EM has shown very promising results and achieved significant performance difference in comparison with the other approaches particularly using the Dataset. Hence, we suggest to perform further experiments using large dataset(s) to validate our method. Additionally, visualization of the resultant clusters through first-order Markov chains reveals very useful insights about (dis)engagement behaviors depicted by the students. We conclude the paper with a discussion on the usefulness of our approach, limitations and potential extensions of this work.