The Na\"ive Bayes has proven to be a tractable and efficient method for classification in multivariate analysis. However, features are usually correlated, a fact that violates the Na\"ive Bayes' assumption of conditional independence, and may deteriorate the method's performance. Moreover, datasets are often characterized by a large number of features, which may complicate the interpretation of the results as well as slow down the method's execution. In this paper we propose a sparse version of the Na\"ive Bayes classifier that is characterized by three properties. First, the sparsity is achieved taking into account the correlation structure of the covariates. Second, different performance measures can be used to guide the selection of features. Third, performance constraints on groups of higher interest can be included. Our proposal leads to a smart search, which yields competitive running times, whereas the flexibility in terms of performance measure for classification is integrated. Our findings show that, when compared against well-referenced feature selection approaches, the proposed sparse Na\"ive Bayes obtains competitive results regarding accuracy, sparsity and running times for balanced datasets. In the case of datasets with unbalanced (or with different importance) classes, a better compromise between classification rates for the different classes is achieved.

Forecast aggregation combines the predictions of multiple agents into a more accurate prediction. With forecast aggregation, decision-makers can reduce error, diversify risk and enhance accuracy based on the collective knowledge of agents compared to any single agent, thereby advancing the common good. Forecast aggregation is commonly used in many domains to generate more informed predictions for various variables, such as weather in weather forecasting, the spread of infectious diseases in public health, the outcome of games in sports, fuel prices in energy, and GDP growth in economics. In practice, one crucial challenge of forecast aggregation is that the aggregator may not have full knowledge of the information structure and the agents. Without this prior knowledge, the aggregator cannot employ Bayes rules to combine the forecasts optimally. Traditional prior-free aggregation methods, such as simple averaging, are especially bad on some information structures. For example, in weather forecasting, assume the prior probability of raining tomorrow is 30%, and there are two agents who will receive a conditionally independent binary signal (Low or High). Agents will report their posterior, which is 10% given the Low signal and 50% given the High signal. When both agents report 50%, the simple averaging will also output 50%.

The loss function is explained by the game theory, the logic is clear and the formula is simple and clear. Thus avoid the use of maximum likelihood estimation to explain the loss function and eliminate the need for Monte Carlo methods to solve the normalized denominator. Assuming that the bridge-type population follows a Boltzmann distribution, a neural network is constructed to represent the energy function. Use Langevin dynamics technology to generate a new sample with low energy value, thus a generative model of bridge-type based on energy is established. Train energy function on symmetric structured image dataset of three span beam bridge, arch bridge, cable-stayed bridge, and suspension bridge to accurately calculate the energy values of real and fake samples. Sampling from latent space, using gradient descent algorithm, the energy function transforms the sampling points into low energy score samples, thereby generating new bridge types different from the dataset. Due to unstable and slow training in this attempt, the possibility of generating new bridge types is rare and the image definition of generated images is low.

In recent years, the question of the reliability of Machine Learning (ML) methods has acquired significant importance, and the analysis of the associated uncertainties has motivated a growing amount of research. However, most of these studies have applied standard error analysis to ML models, and in particular Deep Neural Network (DNN) models, which represent a rather significant departure from standard scientific modelling. It is therefore necessary to integrate the standard error analysis with a deeper epistemological analysis of the possible differences between DNN models and standard scientific modelling and the possible implications of these differences in the assessment of reliability. This article offers several contributions. First, it emphasises the ubiquitous role of model assumptions (both in ML and traditional Science) against the illusion of theory-free science. Secondly, model assumptions are analysed from the point of view of their (epistemic) complexity, which is shown to be language-independent. It is argued that the high epistemic complexity of DNN models hinders the estimate of their reliability and also their prospect of long-term progress. Some potential ways forward are suggested. Thirdly, this article identifies the close relation between a model's epistemic complexity and its interpretability, as introduced in the context of responsible AI. This clarifies in which sense, and to what extent, the lack of understanding of a model (black-box problem) impacts its interpretability in a way that is independent of individual skills. It also clarifies how interpretability is a precondition for assessing the reliability of any model, which cannot be based on statistical analysis alone. This article focuses on the comparison between traditional scientific models and DNN models. But, Random Forest and Logistic Regression models are also briefly considered.

Machine unlearning (MU) is gaining increasing attention due to the need to remove or modify predictions made by machine learning (ML) models. While training models have become more efficient and accurate, the importance of unlearning previously learned information has become increasingly significant in fields such as privacy, security, and fairness. This paper presents a comprehensive survey of MU, covering current state-of-the-art techniques and approaches, including data deletion, perturbation, and model updates. In addition, commonly used metrics and datasets are also presented. The paper also highlights the challenges that need to be addressed, including attack sophistication, standardization, transferability, interpretability, training data, and resource constraints. The contributions of this paper include discussions about the potential benefits of MU and its future directions. Additionally, the paper emphasizes the need for researchers and practitioners to continue exploring and refining unlearning techniques to ensure that ML models can adapt to changing circumstances while maintaining user trust. The importance of unlearning is further highlighted in making Artificial Intelligence (AI) more trustworthy and transparent, especially with the increasing importance of AI in various domains that involve large amounts of personal user data.

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.