In many research fields in artificial intelligence, it has been shown that deep neural networks are useful to estimate unknown functions on high dimensional input spaces. However, their generalization performance is not yet completely clarified from the theoretical point of view because they are nonidentifiable and singular learning machines. Moreover, a ReLU function is not differentiable, to which algebraic or analytic methods in singular learning theory cannot be applied. In this paper, we study a deep ReLU neural network in overparametrized cases and prove that the Bayesian free energy, which is equal to the minus log marginal likelihoodor the Bayesian stochastic complexity, is bounded even if the number of layers are larger than necessary to estimate an unknown data-generating function. Since the Bayesian generalization error is equal to the increase of the free energy as a function of a sample size, our result also shows that the Bayesian generalization error does not increase even if a deep ReLU neural network is designed to be sufficiently large or in an opeverparametrized state.

Data-driven approaches coupled with physical knowledge are powerful techniques to model systems. The goal of such models is to efficiently solve for the underlying field by combining measurements with known physical laws. As many systems contain unknown elements, such as missing parameters, noisy data, or incomplete physical laws, this is widely approached as an uncertainty quantification problem. The common techniques to handle all the variables typically depend on the numerical scheme used to approximate the posterior, and it is desirable to have a method which is independent of any such discretization. Information field theory (IFT) provides the tools necessary to perform statistics over fields that are not necessarily Gaussian. We extend IFT to physics-informed IFT (PIFT) by encoding the functional priors with information about the physical laws which describe the field. The posteriors derived from this PIFT remain independent of any numerical scheme and can capture multiple modes, allowing for the solution of problems which are ill-posed. We demonstrate our approach through an analytical example involving the Klein-Gordon equation. We then develop a variant of stochastic gradient Langevin dynamics to draw samples from the joint posterior over the field and model parameters. We apply our method to numerical examples with various degrees of model-form error and to inverse problems involving nonlinear differential equations. As an addendum, the method is equipped with a metric which allows the posterior to automatically quantify model-form uncertainty. Because of this, our numerical experiments show that the method remains robust to even an incorrect representation of the physics given sufficient data. We numerically demonstrate that the method correctly identifies when the physics cannot be trusted, in which case it automatically treats learning the field as a regression problem.

Several algorithms for learning the structure of dynamic Bayesian networks (DBNs) require an a priori ordering of variables, which influences the determined graph topology. However, it is often unclear how to determine this order if feature importance is unknown, especially as an exhaustive search is usually impractical. In this paper, we introduce Ranking Approaches for Unknown Structures (RAUS), an automated framework to systematically inform variable ordering and learn networks end-to-end. RAUS leverages existing statistical methods (Cramers V, chi-squared test, and information gain) to compare variable ordering, resultant generated network topologies, and DBN performance. RAUS enables end-users with limited DBN expertise to implement models via command line interface. We evaluate RAUS on the task of predicting impending acute kidney injury (AKI) from inpatient clinical laboratory data. Longitudinal observations from 67,460 patients were collected from our electronic health record (EHR) and Kidney Disease Improving Global Outcomes (KDIGO) criteria were then applied to define AKI events. RAUS learns multiple DBNs simultaneously to predict a future AKI event at different time points (i.e., 24-, 48-, 72-hours in advance of AKI). We also compared the results of the learned AKI prediction models and variable orderings to baseline techniques (logistic regression, random forests, and extreme gradient boosting). The DBNs generated by RAUS achieved 73-83% area under the receiver operating characteristic curve (AUCROC) within 24-hours before AKI; and 71-79% AUCROC within 48-hours before AKI of any stage in a 7-day observation window. Insights from this automated framework can help efficiently implement and interpret DBNs for clinical decision support. The source code for RAUS is available in GitHub at https://github.com/dgrdn08/RAUS .

Maximum likelihood (ML) learning for energy-based models (EBMs) is challenging, partly due to non-convergence of Markov chain Monte Carlo.Several variations of ML learning have been proposed, but existing methods all fail to achieve both post-training image generation and proper density estimation. We propose to introduce diffusion data and learn a joint EBM, called diffusion assisted-EBMs, through persistent training (i.e., using persistent contrastive divergence) with an enhanced sampling algorithm to properly sample from complex, multimodal distributions. We present results from a 2D illustrative experiment and image experiments and demonstrate that, for the first time for image data, persistently trained EBMs can {\it simultaneously} achieve long-run stability, post-training image generation, and superior out-of-distribution detection.

The societal impact of pre-trained language models has prompted researchers to probe them for strong associations between protected attributes and value-loaded terms, from slur to prestigious job titles. Such work is said to probe models for bias or fairness-or such probes 'into representational biases' are said to be 'motivated by fairness'-suggesting an intimate connection between bias and fairness. We provide conceptual clarity by distinguishing between association biases (Caliskan et al., 2022) and empirical fairness (Shen et al., 2022) and show the two can be independent. Our main contribution, however, is showing why this should not come as a surprise. To this end, we first provide a thought experiment, showing how association bias and empirical fairness can be completely orthogonal. Next, we provide empirical evidence that there is no correlation between bias metrics and fairness metrics across the most widely used language models. Finally, we survey the sociological and psychological literature and show how this literature provides ample support for expecting these metrics to be uncorrelated.

Reliably estimating the uncertainty of a prediction throughout the model lifecycle is crucial in many safety-critical applications. The most common way to measure this uncertainty is via the predicted confidence. While this tends to work well for in-domain samples, these estimates are unreliable under domain drift and restricted to classification. Alternatively, proper scores can be used for most predictive tasks but a bias-variance decomposition for model uncertainty does not exist in the current literature. In this work we introduce a general bias-variance decomposition for proper scores, giving rise to the Bregman Information as the variance term. We discover how exponential families and the classification log-likelihood are special cases and provide novel formulations. Surprisingly, we can express the classification case purely in the logit space. We showcase the practical relevance of this decomposition on several downstream tasks, including model ensembles and confidence regions. Further, we demonstrate how different approximations of the instance-level Bregman Information allow reliable out-of-distribution detection for all degrees of domain drift.

The rapid and accurate detection of COVID-19 cases is critical for timely treatment and preventing the spread of the disease. In this study, a two-stage feature extraction framework using eight state-of-the-art pre-trained deep Convolutional Neural Networks (CNNs) and an autoencoder is proposed to determine the health conditions of patients (COVID-19, Normal, Viral Pneumonia) based on chest X-rays. The X-ray scans are divided into four equally sized sections and analyzed by deep pre-trained CNNs. Subsequently, an autoencoder with three hidden layers is trained to extract reproductive features from the concatenated ouput of CNNs. To evaluate the performance of the proposed framework, three different classifiers, which are single-layer perceptron (SLP), multi-layer perceptron (MLP), and support vector machine (SVM) are used. Furthermore, the deep CNN architectures are used to create benchmark models and trained on the same dataset for comparision. The proposed framework outperforms other frameworks wih pre-trained feature extractors in binary classification and shows competitive results in three-class classification. The proposed methodology is task-independent and suitable for addressing various problems. The results show that the discriminative features are a subset of the reproductive features, suggesting that extracting task-independent features is superior to the extraction only task-based features. The flexibility and task-independence of the reproductive features make the conceptive information approach more favorable. The proposed methodology is novel and shows promising results for analyzing medical image data.

A key challenge in sequential decision making is optimizing systems safely under partial information. While much of the literature has focused on the cases of either partially known states or partially known dynamics, it is further exacerbated in cases where both states and dynamics are partially known. Computing heparin doses for patients fits this paradigm since the concentration of heparin in the patient cannot be measured directly and the rates at which patients metabolize heparin vary greatly between individuals. While many proposed solutions are model free, they require complex models and have difficulty ensuring safety. However, if some of the structure of the dynamics is known, a model based approach can be leveraged to provide safe policies. In this paper we propose such a framework to address the challenge of optimizing personalized heparin doses. We use a predictive model parameterized individually by patient to predict future therapeutic effects. We then leverage this model using a scenario generation based approach that is capable of ensuring patient safety. We validate our models with numerical experiments by comparing the predictive capabilities of our model against existing machine learning techniques and demonstrating how our dosing algorithm can treat patients in a simulated ICU environment.

Globally, the external Internet is increasingly being connected to the contemporary industrial control system. As a result, there is an immediate need to protect the network from several threats. The key infrastructure of industrial activity may be protected from harm by using an intrusion detection system (IDS), a preventive measure mechanism, to recognize new kinds of dangerous threats and hostile activities. The most recent artificial intelligence (AI) techniques used to create IDS in many kinds of industrial control networks are examined in this study, with a particular emphasis on IDS-based deep transfer learning (DTL). This latter can be seen as a type of information fusion that merge, and/or adapt knowledge from multiple domains to enhance the performance of the target task, particularly when the labeled data in the target domain is scarce. Publications issued after 2015 were taken into account. These selected publications were divided into three categories: DTL-only and IDS-only are involved in the introduction and background, and DTL-based IDS papers are involved in the core papers of this review. Researchers will be able to have a better grasp of the current state of DTL approaches used in IDS in many different types of networks by reading this review paper. Other useful information, such as the datasets used, the sort of DTL employed, the pre-trained network, IDS techniques, the evaluation metrics including accuracy/F-score and false alarm rate (FAR), and the improvement gained, were also covered. The algorithms, and methods used in several studies, or illustrate deeply and clearly the principle in any DTL-based IDS subcategory are presented to the reader.

In the literature on deep neural networks, there is considerable interest in developing activation functions that can enhance neural network performance. In recent years, there has been renewed scientific interest in proposing activation functions that can be trained throughout the learning process, as they appear to improve network performance, especially by reducing overfitting. In this paper, we propose a trainable activation function whose parameters need to be estimated. A fully Bayesian model is developed to automatically estimate from the learning data both the model weights and activation function parameters. An MCMC-based optimization scheme is developed to build the inference. The proposed method aims to solve the aforementioned problems and improve convergence time by using an efficient sampling scheme that guarantees convergence to the global maximum. The proposed scheme is tested on three datasets with three different CNNs. Promising results demonstrate the usefulness of our proposed approach in improving model accuracy due to the proposed activation function and Bayesian estimation of the parameters.