Large language models (LLMs) trained on huge corpora of text datasets demonstrate intriguing capabilities, achieving state-of-the-art performance on tasks they were not explicitly trained for. The precise nature of LLM capabilities is often mysterious, and different prompts can elicit different capabilities through in-context learning. We propose a framework that enables us to analyze in-context learning dynamics to understand latent concepts underlying LLMs' behavioral patterns. This provides a more nuanced understanding than success-or-failure evaluation benchmarks, but does not require observing internal activations as a mechanistic interpretation of circuits would. Inspired by the cognitive science of human randomness perception, we use random binary sequences as context and study dynamics of in-context learning by manipulating properties of context data, such as sequence length. In the latest GPT-3.5+ models, we find emergent abilities to generate seemingly random numbers and learn basic formal languages, with striking in-context learning dynamics where model outputs transition sharply from seemingly random behaviors to deterministic repetition.

Federated learning is a new learning paradigm that decouples data collection and model training via multi-party computation and model aggregation. As a flexible learning setting, federated learning has the potential to integrate with other learning frameworks. We conduct a focused survey of federated learning in conjunction with other learning algorithms. Specifically, we explore various learning algorithms to improve the vanilla federated averaging algorithm and review model fusion methods such as adaptive aggregation, regularization, clustered methods, and Bayesian methods. Following the emerging trends, we also discuss federated learning in the intersection with other learning paradigms, termed federated X learning, where X includes multitask learning, meta-learning, transfer learning, unsupervised learning, and reinforcement learning. This survey reviews the state of the art, challenges, and future directions.

Unobserved confounding is common in many applications, making causal inference from observational data challenging. As a remedy, causal sensitivity analysis is an important tool to draw causal conclusions under unobserved confounding with mathematical guarantees. In this paper, we propose NeuralCSA, a neural framework for generalized causal sensitivity analysis. Unlike previous work, our framework is compatible with (i) a large class of sensitivity models, including the marginal sensitivity model, f-sensitivity models, and Rosenbaum's sensitivity model; (ii) different treatment types (i.e., binary and continuous); and (iii) different causal queries, including (conditional) average treatment effects and simultaneous effects on multiple outcomes. The generality of \frameworkname is achieved by learning a latent distribution shift that corresponds to a treatment intervention using two conditional normalizing flows. We provide theoretical guarantees that NeuralCSA is able to infer valid bounds on the causal query of interest and also demonstrate this empirically using both simulated and real-world data.

Standard regularized training procedures correspond to maximizing a posterior distribution over parameters, known as maximum a posteriori (MAP) estimation. However, model parameters are of interest only insomuch as they combine with the functional form of a model to provide a function that can make good predictions. Moreover, the most likely parameters under the parameter posterior do not generally correspond to the most likely function induced by the parameter posterior. In fact, we can re-parametrize a model such that any setting of parameters can maximize the parameter posterior. As an alternative, we investigate the benefits and drawbacks of directly estimating the most likely function implied by the model and the data. We show that this procedure leads to pathological solutions when using neural networks and prove conditions under which the procedure is well-behaved, as well as a scalable approximation. Under these conditions, we find that function-space MAP estimation can lead to flatter minima, better generalization, and improved robustness to overfitting.

This study proposes the first Bayesian approach for learning high-dimensional linear Bayesian networks. The proposed approach iteratively estimates each element of the topological ordering from backward and its parent using the inverse of a partial covariance matrix. The proposed method successfully recovers the underlying structure when Bayesian regularization for the inverse covariance matrix with unequal shrinkage is applied. Specifically, it shows that the number of samples $n = \Omega( d_M^2 \log p)$ and $n = \Omega(d_M^2 p^{2/m})$ are sufficient for the proposed algorithm to learn linear Bayesian networks with sub-Gaussian and 4m-th bounded-moment error distributions, respectively, where $p$ is the number of nodes and $d_M$ is the maximum degree of the moralized graph. The theoretical findings are supported by extensive simulation studies including real data analysis. Furthermore the proposed method is demonstrated to outperform state-of-the-art frequentist approaches, such as the BHLSM, LISTEN, and TD algorithms in synthetic data.

In the field of equation learning, exhaustively considering all possible equations derived from a basis function dictionary is infeasible. Sparse regression and greedy algorithms have emerged as popular approaches to tackle this challenge. However, the presence of multicollinearity poses difficulties for sparse regression techniques, and greedy steps may inadvertently exclude terms of the true equation, leading to reduced identification accuracy. In this article, we present an approach that strikes a balance between comprehensiveness and efficiency in equation learning. Inspired by stepwise regression, our approach combines the coefficient of determination, $R^2$, and the Bayesian model evidence, $p(\boldsymbol y|\mathcal M)$, in a novel way. Our procedure is characterized by a comprehensive search with just a minor reduction of the model space at each iteration step. With two flavors of our approach and the adoption of $p(\boldsymbol y|\mathcal M)$ for bi-directional stepwise regression, we present a total of three new avenues for equation learning. Through three extensive numerical experiments involving random polynomials and dynamical systems, we compare our approach against four state-of-the-art methods and two standard approaches. The results demonstrate that our comprehensive search approach surpasses all other methods in terms of identification accuracy. In particular, the second flavor of our approach establishes an efficient overfitting penalty solely based on $R^2$, which achieves highest rates of exact equation recovery.

Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from sequential simulation using neural network-based conditional density estimators by minimizing a specific loss function. The SNPE method proposed by Lueckmann et al. (2017) used a calibration kernel to boost the sample weights around the observed data, resulting in a concentrated loss function. However, the use of calibration kernels may increase the variances of both the empirical loss and its gradient, making the training inefficient. To improve the stability of SNPE, this paper proposes to use an adaptive calibration kernel and several variance reduction techniques. The proposed method greatly speeds up the process of training, and provides a better approximation of the posterior than the original SNPE method and some existing competitors as confirmed by numerical experiments.

Car following (CF) models are fundamental to describing traffic dynamics. However, the CF behavior of human drivers is highly stochastic and nonlinear. As a result, identifying the "best" CF model has been challenging and controversial despite decades of research. Introduction of automated vehicles has further complicated this matter as their CF controllers remain proprietary, though their behavior appears different than human drivers. This paper develops a stochastic learning approach to integrate multiple CF models, rather than relying on a single model. The framework is based on approximate Bayesian computation that probabilistically concatenates a pool of CF models based on their relative likelihood of describing observed behavior. The approach, while data-driven, retains physical tractability and interpretability. Evaluation results using two datasets show that the proposed approach can better reproduce vehicle trajectories for both human-driven and automated vehicles than any single CF model considered.

Electroanatomical mapping is a technique used in cardiology to create a detailed 3D map of the electrical activity in the heart. It is useful for diagnosis, treatment planning and real time guidance in cardiac ablation procedures to treat arrhythmias like atrial fibrillation. A probabilistic machine learning model trained on a library of CT/MRI scans of the heart can be used during electroanatomical mapping to generate a patient-specific 3D model of the chamber being mapped. The use of probabilistic machine learning models under a Bayesian framework provides a way to quantify uncertainty in results and provide a natural framework of interpretability of the model. Here we introduce a Bayesian approach to surface reconstruction of cardiac chamber models from a sparse 3D point cloud data acquired during electroanatomical mapping. We show how probabilistic graphical models trained on segmented CT/MRI data can be used to generate cardiac chamber models from few acquired locations thereby reducing procedure time and x-ray exposure. We show how they provide insight into what the neural network learns from the segmented CT/MRI images used to train the network, which provides explainability to the resulting cardiac chamber models generated by the model.

Computational models are powerful tools for understanding human cognition and behavior. They let us express our theories clearly and precisely, and offer predictions that can be subtle and often counter-intuitive. However, this same richness and ability to surprise means our scientific intuitions and traditional tools are ill-suited to designing experiments to test and compare these models. To avoid these pitfalls and realize the full potential of computational modeling, we require tools to design experiments that provide clear answers about what models explain human behavior and the auxiliary assumptions those models must make. Bayesian optimal experimental design (BOED) formalizes the search for optimal experimental designs by identifying experiments that are expected to yield informative data. In this work, we provide a tutorial on leveraging recent advances in BOED and machine learning to find optimal experiments for any kind of model that we can simulate data from, and show how by-products of this procedure allow for quick and straightforward evaluation of models and their parameters against real experimental data. As a case study, we consider theories of how people balance exploration and exploitation in multi-armed bandit decision-making tasks. We validate the presented approach using simulations and a real-world experiment. As compared to experimental designs commonly used in the literature, we show that our optimal designs more efficiently determine which of a set of models best account for individual human behavior, and more efficiently characterize behavior given a preferred model. At the same time, formalizing a scientific question such that it can be adequately addressed with BOED can be challenging and we discuss several potential caveats and pitfalls that practitioners should be aware of. We provide code and tutorial notebooks to replicate all analyses.