Causal discovery identifies causal relationships in data, but the task is more complex for multivariate time series due to the computational demands of methods like VarLiNGAM, which combines a Vector Autoregressive Model with a Linear Non-Gaussian Acyclic Model. This study optimizes causal discovery specifically for time series data, which are common in practical applications. Time series causal discovery is particularly challenging because of temporal dependencies and potential time lag effects. By developing a specialized dataset generator and reducing the computational complexity of the VarLiNGAM model from \( O(m^3 \cdot n) \) to \( O(m^3 + m^2 \cdot n) \), this study enhances the feasibility of processing large datasets. The proposed methods were validated on advanced computational platforms and tested on simulated, real-world, and large-scale datasets, demonstrating improved efficiency and performance. The optimized algorithm achieved 7 to 13 times speedup compared to the original and about 4.5 times speedup compared to the GPU-accelerated version on large-scale datasets with feature sizes from 200 to 400. Our methods extend current causal discovery capabilities, making them more robust, scalable, and applicable to real-world scenarios, facilitating advancements in fields like healthcare and finance.

This paper illustrates the central role of loss functions in data-driven decision making, providing a comprehensive survey on their influence in cost-sensitive classification (CSC) and reinforcement learning (RL). We demonstrate how different regression loss functions affect the sample efficiency and adaptivity of value-based decision making algorithms. Across multiple settings, we prove that algorithms using the binary cross-entropy loss achieve first-order bounds scaling with the optimal policy's cost and are much more efficient than the commonly used squared loss. Moreover, we prove that distributional algorithms using the maximum likelihood loss achieve second-order bounds scaling with the policy variance and are even sharper than first-order bounds. This in particular proves the benefits of distributional RL. We hope that this paper serves as a guide analyzing decision making algorithms with varying loss functions, and can inspire the reader to seek out better loss functions to improve any decision making algorithm.

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.