Survival Analysis (SA) constitutes the default method for time-to-event modeling due to its ability to estimate event probabilities of sparsely occurring events over time. In this work, we show how to improve the training and inference of SA models by decoupling their full expression into (1) an aggregated baseline hazard, which captures the overall behavior of a given population, and (2) independently distributed survival scores, which model idiosyncratic probabilistic dynamics of its given members, in a fully parametric setting. The proposed inference method is shown to dynamically handle right-censored observation horizons, and to achieve competitive performance when compared to other state-of-the-art methods in a variety of real-world datasets, including computationally inefficient Deep Learning-based SA methods and models that require MCMC for inference. Nevertheless, our method achieves robust results from the outset, while not being subjected to fine-tuning or hyperparameter optimization.

Inferring causal structure from data is a challenging task of fundamental importance in science. Often, observational data alone is not enough to uniquely identify a system's causal structure. The use of interventional data can address this issue, however, acquiring these samples typically demands a considerable investment of time and physical or financial resources. In this work, we are concerned with the acquisition of interventional data in a targeted manner to minimize the number of required experiments. We propose a novel Gradient-based Intervention Targeting method, abbreviated GIT, that'trusts' the gradient estimator of a gradient-based causal discovery framework to provide signals for the intervention targeting function. We provide extensive experiments in simulated and real-world datasets and demonstrate that GIT performs on par with competitive baselines, surpassing them in the low-data regime.

Sharpness-aware minimization (SAM) and related adversarial deep-learning methods can drastically improve generalization, but their underlying mechanisms are not yet fully understood. Here, we establish SAM as a relaxation of the Bayes objective where the expected negative-loss is replaced by the optimal convex lower bound, obtained by using the so-called Fenchel biconjugate. The connection enables a new Adam-like extension of SAM to automatically obtain reasonable uncertainty estimates, while sometimes also improving its accuracy. By connecting adversarial and Bayesian methods, our work opens a new path to robustness.

Maize, a crucial crop globally cultivated across vast regions, especially in sub-Saharan Africa, Asia, and Latin America, occupies 197 million hectares as of 2021. Various statistical and machine learning models, including mixed-effect models, random coefficients models, random forests, and deep learning architectures, have been devised to predict maize yield. These models consider factors such as genotype, environment, genotype-environment interaction, and field management. However, the existing models often fall short of fully exploiting the complex network of causal relationships among these factors and the hierarchical structure inherent in agronomic data. This study introduces an innovative approach integrating random effects into Bayesian networks (BNs), leveraging their capacity to model causal and probabilistic relationships through directed acyclic graphs. Rooted in the linear mixed-effects models framework and tailored for hierarchical data, this novel approach demonstrates enhanced BN learning. Application to a real-world agronomic trial produces a model with improved interpretability, unveiling new causal connections. Notably, the proposed method significantly reduces the error rate in maize yield prediction from 28% to 17%. These results advocate for the preference of BNs in constructing practical decision support tools for hierarchical agronomic data, facilitating causal inference.

The probability of an event is in the range of [0, 1]. In a sample space S, the value of probability determines whether an outcome is true or false. The probability of an event Pr(A) that will never occur = 0. The probability of the event Pr(B) that will certainly occur = 1. This makes both events A and B thus a certainty. Furthermore, the sum of probabilities Pr(E1) + Pr(E2) + ... + Pr(En) of a finite set of events in a given sample space S = 1. Conversely, the difference of the sum of two probabilities that will certainly occur is 0. Firstly, this paper discusses Bayes' theorem, then complement of probability and the difference of probability for occurrences of learning-events, before applying these in the prediction of learning objects in student learning. Given the sum total of 1; to make recommendation for student learning, this paper submits that the difference of argMaxPr(S) and probability of student-performance quantifies the weight of learning objects for students. Using a dataset of skill-set, the computational procedure demonstrates: i) the probability of skill-set events that has occurred that would lead to higher level learning; ii) the probability of the events that has not occurred that requires subject-matter relearning; iii) accuracy of decision tree in the prediction of student performance into class labels; and iv) information entropy about skill-set data and its implication on student cognitive performance and recommendation of learning [1].

The theory of Bayesian learning incorporates the use of Student-t Processes to model heavy-tailed distributions and datasets with outliers. However, despite Student-t Processes having a similar computational complexity as Gaussian Processes, there has been limited emphasis on the sparse representation of this model. This is mainly due to the increased difficulty in modeling and computation compared to previous sparse Gaussian Processes. Our motivation is to address the need for a sparse representation framework that reduces computational complexity, allowing Student-t Processes to be more flexible for real-world datasets. To achieve this, we leverage the conditional distribution of Student-t Processes to introduce sparse inducing points. Bayesian methods and variational inference are then utilized to derive a well-defined lower bound, facilitating more efficient optimization of our model through stochastic gradient descent. We propose two methods for computing the variational lower bound, one utilizing Monte Carlo sampling and the other employing Jensen's inequality to compute the KL regularization term in the loss function. We propose adopting these approaches as viable alternatives to Gaussian processes when the data might contain outliers or exhibit heavy-tailed behavior, and we provide specific recommendations for their applicability. We evaluate the two proposed approaches on various synthetic and real-world datasets from UCI and Kaggle, demonstrating their effectiveness compared to baseline methods in terms of computational complexity and accuracy, as well as their robustness to outliers.

The blooming diffusion probabilistic models (DPMs) have garnered significant interest due to their impressive performance and the elegant inspiration they draw from physics. While earlier DPMs relied upon the Markovian assumption, recent methods based on differential equations have been rapidly applied to enhance the efficiency and capabilities of these models. However, a theoretical interpretation encapsulating these diverse algorithms is insufficient yet pressingly required to guide further development of DPMs. In response to this need, we present FreeFlow, a framework that provides a thorough explanation of the diffusion formula as time-dependent optimal transport, where the evolutionary pattern of probability density is given by the gradient flows of a functional defined in Wasserstein space. Crucially, our framework necessitates a unified description that not only clarifies the subtle mechanism of DPMs but also indicates the roots of some defects through creative involvement of Lagrangian and Eulerian views to understand the evolution of probability flow. We particularly demonstrate that the core equation of FreeFlow condenses all stochastic and deterministic DPMs into a single case, showcasing the expansibility of our method. Furthermore, the Riemannian geometry employed in our work has the potential to bridge broader subjects in mathematics, which enable the involvement of more profound tools for the establishment of more outstanding and generalized models in the future.

Leveraging neural networks as surrogate models for turbulence simulation is a topic of growing interest. At the same time, embodying the inherent uncertainty of simulations in the predictions of surrogate models remains very challenging. The present study makes a first attempt to use denoising diffusion probabilistic models (DDPMs) to train an uncertainty-aware surrogate model for turbulence simulations. Due to its prevalence, the simulation of flows around airfoils with various shapes, Reynolds numbers, and angles of attack is chosen as the learning objective. Our results show that DDPMs can successfully capture the whole distribution of solutions and, as a consequence, accurately estimate the uncertainty of the simulations. The performance of DDPMs is also compared with varying baselines in the form of Bayesian neural networks and heteroscedastic models. Experiments demonstrate that DDPMs outperform the other methods regarding a variety of accuracy metrics. Besides, it offers the advantage of providing access to the complete distributions of uncertainties rather than providing a set of parameters. As such, it can yield realistic and detailed samples from the distribution of solutions. All source codes and datasets utilized in this study are publicly available.

In his "ship of state" allegory (\textit{Republic}, Book VI, 488) Plato poses a question -- how can a crew of sailors presumed to know little about the art of navigation recognize the true pilot among them? The allegory argues that a simple majority voting procedure cannot safely determine who is most qualified to pilot a ship when the voting members are ignorant or biased. We formalize Plato's concerns by considering the problem in AI safety of monitoring noisy AI agents in unsupervised settings. An algorithm evaluating AI agents using unlabeled data would be subject to the evaluation dilemma - how would we know the evaluation algorithm was correct itself? This endless validation chain can be avoided by considering purely algebraic functions of the observed responses. We can construct complete postulates than can prove or disprove the logical consistency of any grading algorithm. A complete set of postulates exists whenever we are evaluating $N$ experts that took $T$ tests with $Q$ questions with $R$ responses each. We discuss evaluating binary classifiers that have taken a single test - the $(N,T=1,Q,R=2)$ tests. We show how some of the postulates have been previously identified in the ML literature but not recognized as such - the \textbf{agreement equations} of Platanios. The complete postulates for pair correlated binary classifiers are considered and we show how it allows for error correlations to be quickly calculated. An algebraic evaluator based on the assumption that the ensemble is error independent is compared with grading by majority voting on evaluations using the \uciadult and and \texttt{two-norm} datasets. Throughout, we demonstrate how the formalism of logical consistency via algebraic postulates of evaluation can help increase the safety of machines using AI algorithms.

We consider two-player zero-sum stochastic games and propose a two-timescale $Q$-learning algorithm with function approximation that is payoff-based, convergent, rational, and symmetric between the two players. In two-timescale $Q$-learning, the fast-timescale iterates are updated in spirit to the stochastic gradient descent and the slow-timescale iterates (which we use to compute the policies) are updated by taking a convex combination between its previous iterate and the latest fast-timescale iterate. Introducing the slow timescale as well as its update equation marks as our main algorithmic novelty. In the special case of linear function approximation, we establish, to the best of our knowledge, the first last-iterate finite-sample bound for payoff-based independent learning dynamics of these types. The result implies a polynomial sample complexity to find a Nash equilibrium in such stochastic games. To establish the results, we model our proposed algorithm as a two-timescale stochastic approximation and derive the finite-sample bound through a Lyapunov-based approach. The key novelty lies in constructing a valid Lyapunov function to capture the evolution of the slow-timescale iterates. Specifically, through a change of variable, we show that the update equation of the slow-timescale iterates resembles the classical smoothed best-response dynamics, where the regularized Nash gap serves as a valid Lyapunov function. This insight enables us to construct a valid Lyapunov function via a generalized variant of the Moreau envelope of the regularized Nash gap. The construction of our Lyapunov function might be of broad independent interest in studying the behavior of stochastic approximation algorithms.