This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized zeroth-order Tikhonov regularization, providing a rational justification for the choice of the residual and regularization terms, respectively, from the negative logarithms of the likelihood and prior distributions. In addition to the estimation of model coefficients, the Bayesian interpretation gives access to the full apparatus for Bayesian inference, including the ranking of models, the quantification of model uncertainties and the estimation of unknown (nuisance) hyperparameters. Two Bayesian algorithms, joint maximum \textit{a~posteriori} (JMAP) and variational Bayesian approximation (VBA), are compared to the popular SINDy algorithm for thresholded least-squares regression, by application to several dynamical systems with added noise. For multivariate Gaussian likelihood and prior distributions, the Bayesian formulation gives Gaussian posterior and evidence distributions, in which the numerator terms can be expressed in terms of the Mahalanobis distance or ``Gaussian norm'' $||\vy-\hat{\vy}||^2_{M^{-1}} = (\vy-\hat{\vy})^\top {M^{-1}} (\vy-\hat{\vy})$, where $\vy$ is a vector variable, $\hat{\vy}$ is its estimator and $M$ is the covariance matrix. The posterior Gaussian norm is shown to provide a robust metric for quantitative model selection.

This paper addresses the challenging problem of energy-efficient and uncertainty-aware pose estimation in insect-scale drones, which is crucial for tasks such as surveillance in constricted spaces and for enabling non-intrusive spatial intelligence in smart homes. Since tiny drones operate in highly dynamic environments, where factors like lighting and human movement impact their predictive accuracy, it is crucial to deploy uncertainty-aware prediction algorithms that can account for environmental variations and express not only the prediction but also confidence in the prediction. We address both of these challenges with Compute-in-Memory (CIM) which has become a pivotal technology for deep learning acceleration at the edge. While traditional CIM techniques are promising for energy-efficient deep learning, to bring in the robustness of uncertainty-aware predictions at the edge, we introduce a suite of novel techniques: First, we discuss CIM-based acceleration of Bayesian filtering methods uniquely by leveraging the Gaussian-like switching current of CMOS inverters along with co-design of kernel functions to operate with extreme parallelism and with extreme energy efficiency. Secondly, we discuss the CIM-based acceleration of variational inference of deep learning models through probabilistic processing while unfolding iterative computations of the method with a compute reuse strategy to significantly minimize the workload. Overall, our co-design methodologies demonstrate the potential of CIM to improve the processing efficiency of uncertainty-aware algorithms by orders of magnitude, thereby enabling edge robotics to access the robustness of sophisticated prediction frameworks within their extremely stringent area/power resources.

In this paper, we propose an online algorithm "mspace" for forecasting node features in temporal graphs, which adeptly captures spatial cross-correlation among different nodes as well as the temporal autocorrelation within a node. The algorithm can be used for both probabilistic and deterministic multi-step forecasting, making it applicable for estimation and generation tasks. Comparative evaluations against various baselines, including graph neural network (GNN) based models and classical Kalman filters, demonstrate that mspace performs at par with the state-of-the-art and even surpasses them on some datasets. Importantly, mspace demonstrates consistent robustness across datasets with varying training sizes, a notable advantage over GNN-based methods requiring abundant training samples to learn the spatiotemporal trends in the data effectively. Therefore, employing mspace is advantageous in scenarios where the training sample availability is limited. Additionally, we establish theoretical bounds on multi-step forecasting error of mspace and show that it scales as $O(q)$ for $q$-step forecast.

Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample performance due to distributional uncertainty. In the spirit of distributionally robust optimization, we propose a novel robust criterion by combining insights from Bayesian nonparametric (i.e., Dirichlet Process) theory and recent decision-theoretic models of smooth ambiguity-averse preferences. First, we highlight novel connections with standard regularized empirical risk minimization techniques, among which Ridge and LASSO regressions. Then, we theoretically demonstrate the existence of favorable finite-sample and asymptotic statistical guarantees on the performance of the robust optimization procedure. For practical implementation, we propose and study tractable approximations of the criterion based on well-known Dirichlet Process representations. We also show that the smoothness of the criterion naturally leads to standard gradient-based numerical optimization. Finally, we provide insights into the workings of our method by applying it to high-dimensional sparse linear regression and robust location parameter estimation tasks.

There are now many explainable AI methods for understanding the decisions of a machine learning model. Among these are those based on counterfactual reasoning, which involve simulating features changes and observing the impact on the prediction. This article proposes to view this simulation process as a source of creating a certain amount of knowledge that can be stored to be used, later, in different ways. This process is illustrated in the additive model and, more specifically, in the case of the naive Bayes classifier, whose interesting properties for this purpose are shown.

The performance of Markov chain Monte Carlo samplers strongly depends on the properties of the target distribution such as its covariance structure, the location of its probability mass and its tail behavior. We explore the use of bijective affine transformations of the sample space to improve the properties of the target distribution and thereby the performance of samplers running in the transformed space. In particular, we propose a flexible and user-friendly scheme for adaptively learning the affine transformation during sampling. Moreover, the combination of our scheme with Gibbsian polar slice sampling is shown to produce samples of high quality at comparatively low computational cost in several settings based on real-world data.

This report examines a novel risk associated with current (and projected) AI tools. Making effective decisions about future actions requires us to reason under uncertainty (RUU), and doing so is essential to many critical real world problems. Overfaced by this challenge, there is growing demand for AI tools like LLMs to assist decision-makers. Having evidenced this demand and the incentives behind it, we expose a growing risk: we 1) do not currently sufficiently understand LLM capabilities in this regard, and 2) have no guarantees of performance given fundamental computational explosiveness and deep uncertainty constraints on accuracy. This report provides an exposition of what makes RUU so challenging for both humans and machines, and relates these difficulties to prospective AI timelines and capabilities. Having established this current potential misuse risk, we go on to expose how this seemingly additive risk (more misuse additively contributed to potential harm) in fact has multiplicative properties. Specifically, we detail how this misuse risk connects to a wider network of underlying structural risks (e.g., shifting incentives, limited transparency, and feedback loops) to produce non-linear harms. We go on to provide a solutions roadmap that targets multiple leverage points in the structure of the problem. This includes recommendations for all involved actors (prospective users, developers, and policy-makers) and enfolds insights from areas including Decision-making Under Deep Uncertainty and complex systems theory. We argue this report serves not only to raise awareness (and subsequently mitigate/correct) of a current, novel AI risk, but also awareness of the underlying class of structural risks by illustrating how their interconnected nature poses twin-dangers of camouflaging their presence, whilst amplifying their potential effects.

Extracting meaningful information from high-dimensional data poses a formidable modeling challenge, particularly when the data is obscured by noise or represented through different modalities. In this research, we propose a novel non-parametric modeling approach, leveraging the Gaussian Process (GP), to characterize high-dimensional data by mapping it to a latent low-dimensional manifold. This model, named the Latent Discriminative Generative Decoder (LDGD), utilizes both the data (or its features) and associated labels (such as category or stimulus) in the manifold discovery process. To infer the latent variables, we derive a Bayesian solution, allowing LDGD to effectively capture inherent uncertainties in the data while enhancing the model's predictive accuracy and robustness. We demonstrate the application of LDGD on both synthetic and benchmark datasets. Not only does LDGD infer the manifold accurately, but its prediction accuracy in anticipating labels surpasses state-of-the-art approaches. We have introduced inducing points to reduce the computational complexity of Gaussian Processes (GPs) for large datasets. This enhancement facilitates batch training, allowing for more efficient processing and scalability in handling extensive data collections. Additionally, we illustrate that LDGD achieves higher accuracy in predicting labels and operates effectively with a limited training dataset, underscoring its efficiency and effectiveness in scenarios where data availability is constrained. These attributes set the stage for the development of non-parametric modeling approaches in the analysis of high-dimensional data; especially in fields where data are both high-dimensional and complex.

This paper proposes a model learning Semi-parametric relationships in an Expert Bayesian Network (SEBN) with linear parameter and structure constraints. We use Gaussian Processes and a Horseshoe prior to introduce minimal nonlinear components. To prioritize modifying the expert graph over adding new edges, we optimize differential Horseshoe scales. In real-world datasets with unknown truth, we generate diverse graphs to accommodate user input, addressing identifiability issues and enhancing interpretability. Evaluation on synthetic and UCI Liver Disorders datasets, using metrics like structural Hamming Distance and test likelihood, demonstrates our models outperform state-of-the-art semi-parametric Bayesian Network model.

Conventional retransmission (ARQ) protocols are designed with the goal of ensuring the correct reception of all the individual transmitter's packets at the receiver. When the transmitter is a learner communicating with a teacher, this goal is at odds with the actual aim of the learner, which is that of eliciting the most relevant label information from the teacher. Taking an active learning perspective, this paper addresses the following key protocol design questions: (i) Active batch selection: Which batch of inputs should be sent to the teacher to acquire the most useful information and thus reduce the number of required communication rounds? (ii) Batch encoding: Can batches of data points be combined to reduce the communication resources required at each communication round? Specifically, this work introduces Communication-Constrained Bayesian Active Knowledge Distillation (CC-BAKD), a novel protocol that integrates Bayesian active learning with compression via a linear mix-up mechanism. Comparisons with existing active learning protocols demonstrate the advantages of the proposed approach.