Data augmentation is known to contribute significantly to the robustness of machine learning models. In most instances, data augmentation is utilized during the training phase. Test-Time Augmentation (TTA) is a technique that instead leverages these data augmentations during the testing phase to achieve robust predictions. More precisely, TTA averages the predictions of multiple data augmentations of an instance to produce a final prediction. Although the effectiveness of TTA has been empirically reported, it can be expected that the predictive performance achieved will depend on the set of data augmentation methods used during testing. In particular, the data augmentation methods applied should make different contributions to performance. That is, it is anticipated that there may be differing degrees of contribution in the set of data augmentation methods used for TTA, and these could have a negative impact on prediction performance. In this study, we consider a weighted version of the TTA based on the contribution of each data augmentation. Some variants of TTA can be regarded as considering the problem of determining the appropriate weighting. We demonstrate that the determination of the coefficients of this weighted TTA can be formalized in a variational Bayesian framework. We also show that optimizing the weights to maximize the marginal log-likelihood suppresses candidates of unwanted data augmentations at the test phase.

Robust policies enable reinforcement learning agents to effectively adapt to and operate in unpredictable, dynamic, and ever-changing real-world environments. Factored representations, which break down complex state and action spaces into distinct components, can improve generalization and sample efficiency in policy learning. In this paper, we explore how the curriculum of an agent using a factored state representation affects the robustness of the learned policy. We experimentally demonstrate three simple curricula, such as varying only the variable of highest regret between episodes, that can significantly enhance policy robustness, offering practical insights for reinforcement learning in complex environments.

Background: Advanced methods for causal inference, such as targeted maximum likelihood estimation (TMLE), require certain conditions for statistical inference. However, in situations where there is not differentiability due to data sparsity or near-positivity violations, the Donsker class condition is violated. In such situations, TMLE variance can suffer from inflation of the type I error and poor coverage, leading to conservative confidence intervals. Cross-validation of the TMLE algorithm (CVTMLE) has been suggested to improve on performance compared to TMLE in settings of positivity or Donsker class violations. We aim to investigate the performance of CVTMLE compared to TMLE in various settings. Methods: We utilised the data-generating mechanism as described in Leger et al. (2022) to run a Monte Carlo experiment under different Donsker class violations. Then, we evaluated the respective statistical performances of TMLE and CVTMLE with different super learner libraries, with and without regression tree methods. Results: We found that CVTMLE vastly improves confidence interval coverage without adversely affecting bias, particularly in settings with small sample sizes and near-positivity violations. Furthermore, incorporating regression trees using standard TMLE with ensemble super learner-based initial estimates increases bias and variance leading to invalid statistical inference. Conclusions: It has been shown that when using CVTMLE the Donsker class condition is no longer necessary to obtain valid statistical inference when using regression trees and under either data sparsity or near-positivity violations. We show through simulations that CVTMLE is much less sensitive to the choice of the super learner library and thereby provides better estimation and inference in cases where the super learner library uses more flexible candidates and is prone to overfitting.

Gaussian processes (GPs) are Bayesian nonparametric models for function approximation with principled predictive uncertainty estimates. Deep Gaussian processes (DGPs) are multilayer generalizations of GPs that can represent complex marginal densities as well as complex mappings. As exact inference is either computationally prohibitive or analytically intractable in GPs and extensions thereof, some existing methods resort to variational inference (VI) techniques for tractable approximations. However, the expressivity of conventional approximate GP models critically relies on independent inducing variables that might not be informative enough for some problems. In this work we introduce amortized variational inference for DGPs, which learns an inference function that maps each observation to variational parameters. The resulting method enjoys a more expressive prior conditioned on fewer input dependent inducing variables and a flexible amortized marginal posterior that is able to model more complicated functions. We show with theoretical reasoning and experimental results that our method performs similarly or better than previous approaches at less computational cost.

Road traffic accidents (RTA) pose a significant public health threat worldwide, leading to considerable loss of life and economic burdens. This is particularly acute in developing countries like Bangladesh. Building reliable models to forecast crash outcomes is crucial for implementing effective preventive measures. To aid in developing targeted safety interventions, this study presents a machine learning-based approach for classifying fatal and non-fatal road accident outcomes using data from the Dhaka metropolitan traffic crash database from 2017 to 2022. Our framework utilizes a range of machine learning classification algorithms, comprising Logistic Regression, Support Vector Machines, Naive Bayes, Random Forest, Decision Tree, Gradient Boosting, LightGBM, and Artificial Neural Network. We prioritize model interpretability by employing the SHAP (SHapley Additive exPlanations) method, which elucidates the key factors influencing accident fatality. Our results demonstrate that LightGBM outperforms other models, achieving a ROC-AUC score of 0.72. The global, local, and feature dependency analyses are conducted to acquire deeper insights into the behavior of the model. SHAP analysis reveals that casualty class, time of accident, location, vehicle type, and road type play pivotal roles in determining fatality risk. These findings offer valuable insights for policymakers and road safety practitioners in developing countries, enabling the implementation of evidence-based strategies to reduce traffic crash fatalities.

Denoising, the process of reducing random fluctuations in a signal to emphasize essential patterns, has been a fundamental problem of interest since the dawn of modern scientific inquiry. Recent denoising techniques, particularly in imaging, have achieved remarkable success, nearing theoretical limits by some measures. Yet, despite tens of thousands of research papers, the wide-ranging applications of denoising beyond noise removal have not been fully recognized. This is partly due to the vast and diverse literature, making a clear overview challenging. This paper aims to address this gap. We present a clarifying perspective on denoisers, their structure, and desired properties. We emphasize the increasing importance of denoising and showcase its evolution into an essential building block for complex tasks in imaging, inverse problems, and machine learning. Despite its long history, the community continues to uncover unexpected and groundbreaking uses for denoising, further solidifying its place as a cornerstone of scientific and engineering practice.

This paper studies the problem of learning Bayesian networks from continuous observational data, generated according to a linear Gaussian structural equation model. We consider an $\ell_0$-penalized maximum likelihood estimator for this problem which is known to have favorable statistical properties but is computationally challenging to solve, especially for medium-sized Bayesian networks. We propose a new coordinate descent algorithm to approximate this estimator and prove several remarkable properties of our procedure: the algorithm converges to a coordinate-wise minimum, and despite the non-convexity of the loss function, as the sample size tends to infinity, the objective value of the coordinate descent solution converges to the optimal objective value of the $\ell_0$-penalized maximum likelihood estimator. Finite-sample statistical consistency guarantees are also established. To the best of our knowledge, our proposal is the first coordinate descent procedure endowed with optimality and statistical guarantees in the context of learning Bayesian networks. Numerical experiments on synthetic and real data demonstrate that our coordinate descent method can obtain near-optimal solutions while being scalable.

If two agents disagree in their decisions, we may suspect they are not both correct. This intuition is formalized for evaluating agents that have carried out a binary classification task. Their agreements and disagreements on a joint test allow us to establish the only group evaluations logically consistent with their responses. This is done by establishing a set of axioms (algebraic relations) that must be universally obeyed by all evaluations of binary responders. A complete set of such axioms are possible for each ensemble of size N. The axioms for $N = 1, 2$ are used to construct a fully logical alarm - one that can prove that at least one ensemble member is malfunctioning using only unlabeled data. The similarities of this approach to formal software verification and its utility for recent agendas of safe guaranteed AI are discussed.

In this tutorial, we present a compact and holistic discussion of Deep Learning with a focus on Convolutional Neural Networks (CNNs) and supervised regression. While there are numerous books and articles on the individual topics we cover, comprehensive and detailed tutorials that address Deep Learning from a foundational yet rigorous and accessible perspective are rare. Most resources on CNNs are either too advanced, focusing on cutting-edge architectures, or too narrow, addressing only specific applications like image classification.This tutorial not only summarizes the most relevant concepts but also provides an in-depth exploration of each, offering a complete yet agile set of ideas. Moreover, we highlight the powerful synergy between learning theory, statistic, and machine learning, which together underpin the Deep Learning and CNN frameworks. We aim for this tutorial to serve as an optimal resource for students, professors, and anyone interested in understanding the foundations of Deep Learning. Upon acceptance we will provide an accompanying repository under \href{https://github.com/neoglez/deep-learning-tutorial}{https://github.com/neoglez/deep-learning-tutorial} Keywords: Tutorial, Deep Learning, Convolutional Neural Networks, Machine Learning.

We study supervised classification for datasets with a very large number of input variables. The na\"ive Bayes classifier is attractive for its simplicity, scalability and effectiveness in many real data applications. When the strong na\"ive Bayes assumption of conditional independence of the input variables given the target variable is not valid, variable selection and model averaging are two common ways to improve the performance. In the case of the na\"ive Bayes classifier, the resulting weighting scheme on the models reduces to a weighting scheme on the variables. Here we focus on direct estimation of variable weights in such a weighted na\"ive Bayes classifier. We propose a sparse regularization of the model log-likelihood, which takes into account prior penalization costs related to each input variable. Compared to averaging based classifiers used up until now, our main goal is to obtain parsimonious robust models with less variables and equivalent performance. The direct estimation of the variable weights amounts to a non-convex optimization problem for which we propose and compare several two-stage algorithms. First, the criterion obtained by convex relaxation is minimized using several variants of standard gradient methods. Then, the initial non-convex optimization problem is solved using local optimization methods initialized with the result of the first stage. The various proposed algorithms result in optimization-based weighted na\"ive Bayes classifiers, that are evaluated on benchmark datasets and positioned w.r.t. to a reference averaging-based classifier.