We study interactions between agents in multi-agent systems, in which the agents are misinformed with regards to the game that they play, essentially having a subjective and incorrect understanding of the setting, without being aware of it. For that, we introduce a new game-theoretic concept, called misinformation games, that provides the necessary toolkit to study this situation. Subsequently, we enhance this framework by developing a time-discrete procedure (called the Adaptation Procedure) that captures iterative interactions in the above context. During the Adaptation Procedure, the agents update their information and reassess their behaviour in each step. We demonstrate our ideas through an implementation, which is used to study the efficiency and characteristics of the Adaptation Procedure.

Alzheimer's disease (AD) is a neurodegenerative disorder marked by memory loss and cognitive decline, making early detection vital for timely intervention. However, early diagnosis is challenging due to the heterogeneous presentation of symptoms. Resting-state fMRI (rs-fMRI) captures spontaneous brain activity and functional connectivity, which are known to be disrupted in AD and mild cognitive impairment (MCI). Traditional methods, such as Pearson's correlation, have been used to calculate association matrices, but these approaches often overlook the dynamic and non-stationary nature of brain activity. In this study, we introduce a novel method that integrates discrete wavelet transform (DWT) and graph theory to model the dynamic behavior of brain networks. By decomposing rs-fMRI signals using DWT, our approach captures the time-frequency representation of brain activity, allowing for a more nuanced analysis of the underlying network dynamics. Graph theory provides a robust mathematical framework to analyze these complex networks, while machine learning is employed to automate the discrimination of different stages of AD based on learned patterns from different frequency bands. We applied our method to a dataset of rs-fMRI images from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database, demonstrating its potential as an early diagnostic tool for AD and for monitoring disease progression. Our statistical analysis identifies specific brain regions and connections that are affected in AD and MCI, at different frequency bands, offering deeper insights into the disease's impact on brain function.

In the early stages of drug discovery, decisions regarding which experiments to pursue can be influenced by computational models. These decisions are critical due to the time-consuming and expensive nature of the experiments. Therefore, it is becoming essential to accurately quantify the uncertainty in machine learning predictions, such that resources can be used optimally and trust in the models improves. While computational methods for drug discovery often suffer from limited data and sparse experimental observations, additional information can exist in the form of censored labels that provide thresholds rather than precise values of observations. However, the standard approaches that quantify uncertainty in machine learning cannot fully utilize censored labels. In this work, we adapt ensemble-based, Bayesian, and Gaussian models with tools to learn from censored labels by using the Tobit model from survival analysis. Our results demonstrate that despite the partial information available in censored labels, they are essential to accurately and reliably model the real pharmaceutical setting.

Missing data is commonly encountered in practice, and when the missingness is non-ignorable, effective remediation depends on knowledge of the missingness mechanism. Learning the underlying missingness mechanism from the data is not possible in general, so adversaries can exploit this fact by maliciously engineering non-ignorable missingness mechanisms. Such Adversarial Missingness (AM) attacks have only recently been motivated and introduced, and then successfully tailored to mislead causal structure learning algorithms into hiding specific cause-and-effect relationships. However, existing AM attacks assume the modeler (victim) uses full-information maximum likelihood methods to handle the missing data, and are of limited applicability when the modeler uses different remediation strategies. In this work we focus on associational learning in the context of AM attacks. We consider (i) complete case analysis, (ii) mean imputation, and (iii) regression-based imputation as alternative strategies used by the modeler. Instead of combinatorially searching for missing entries, we propose a novel probabilistic approximation by deriving the asymptotic forms of these methods used for handling the missing entries. We then formulate the learning of the adversarial missingness mechanism as a bi-level optimization problem. Experiments on generalized linear models show that AM attacks can be used to change the p-values of features from significant to insignificant in real datasets, such as the California-housing dataset, while using relatively moderate amounts of missingness (<20%). Additionally, we assess the robustness of our attacks against defense strategies based on data valuation.

Operator learning focuses on approximating mappings $\mathcal{G}^\dagger:\mathcal{U} \rightarrow\mathcal{V}$ between infinite-dimensional spaces of functions, such as $u: \Omega_u\rightarrow\mathbb{R}$ and $v: \Omega_v\rightarrow\mathbb{R}$. This makes it particularly suitable for solving parametric nonlinear partial differential equations (PDEs). While most machine learning methods for operator learning rely on variants of deep neural networks (NNs), recent studies have shown that Gaussian Processes (GPs) are also competitive while offering interpretability and theoretical guarantees. In this paper, we introduce a hybrid GP/NN-based framework for operator learning that leverages the strengths of both methods. Instead of approximating the function-valued operator $\mathcal{G}^\dagger$, we use a GP to approximate its associated real-valued bilinear form $\widetilde{\mathcal{G}}^\dagger: \mathcal{U}\times\mathcal{V}^*\rightarrow\mathbb{R}.$ This bilinear form is defined by $\widetilde{\mathcal{G}}^\dagger(u,\varphi) := [\varphi,\mathcal{G}^\dagger(u)],$ which allows us to recover the operator $\mathcal{G}^\dagger$ through $\mathcal{G}^\dagger(u)(y)=\widetilde{\mathcal{G}}^\dagger(u,\delta_y).$ The GP mean function can be zero or parameterized by a neural operator and for each setting we develop a robust training mechanism based on maximum likelihood estimation (MLE) that can optionally leverage the physics involved. Numerical benchmarks show that (1) it improves the performance of a base neural operator by using it as the mean function of a GP, and (2) it enables zero-shot data-driven models for accurate predictions without prior training. Our framework also handles multi-output operators where $\mathcal{G}^\dagger:\mathcal{U} \rightarrow\prod_{s=1}^S\mathcal{V}^s$, and benefits from computational speed-ups via product kernel structures and Kronecker product matrix representations.

Heart disease is a serious worldwide health issue because it claims the lives of many people who might have been treated if the disease had been identified earlier. The leading cause of death in the world is cardiovascular disease, usually referred to as heart disease. Creating reliable, effective, and precise predictions for these diseases is one of the biggest issues facing the medical world today. Although there are tools for predicting heart diseases, they are either expensive or challenging to apply for determining a patient's risk. The best classifier for foretelling and spotting heart disease was the aim of this research. This experiment examined a range of machine learning approaches, including Logistic Regression, K-Nearest Neighbor, Support Vector Machine, and Artificial Neural Networks, to determine which machine learning algorithm was most effective at predicting heart diseases. One of the most often utilized data sets for this purpose, the UCI heart disease repository provided the data set for this study. The K-Nearest Neighbor technique was shown to be the most effective machine learning algorithm for determining whether a patient has heart disease. It will be beneficial to conduct further studies on the application of additional machine learning algorithms for heart disease prediction.

We introduce a general iterative procedure called risk-based calibration (RC) designed to minimize the empirical risk under the 0-1 loss (empirical error) for probabilistic classifiers. These classifiers are based on modeling probability distributions, including those constructed from the joint distribution (generative) and those based on the class conditional distribution (conditional). RC can be particularized to any probabilistic classifier provided a specific learning algorithm that computes the classifier's parameters in closed form using data statistics. RC reinforces the statistics aligned with the true class while penalizing those associated with other classes, guided by the 0-1 loss. The proposed method has been empirically tested on 30 datasets using na\"ive Bayes, quadratic discriminant analysis, and logistic regression classifiers. RC improves the empirical error of the original closed-form learning algorithms and, more notably, consistently outperforms the gradient descent approach with the three classifiers.

This paper introduces a novel family of deep dynamical models designed to represent continuous-time sequence data. This family of models generates each data point in the time series by a neural emission model, which is a non-linear transformation of a latent state vector. The trajectory of the latent states is implicitly described by a neural ordinary differential equation (ODE), with the initial state following an informative prior distribution parameterized by an energy-based model. Furthermore, we can extend this model to disentangle dynamic states from underlying static factors of variation, represented as time-invariant variables in the latent space. We train the model using maximum likelihood estimation with Markov chain Monte Carlo (MCMC) in an end-to-end manner, without requiring additional assisting components such as an inference network. Our experiments on oscillating systems, videos and real-world state sequences (MuJoCo) illustrate that ODEs with the learnable energy-based prior outperform existing counterparts, and can generalize to new dynamic parameterization, enabling long-horizon predictions.

This book uses the modern theory of artificial intelligence (AI) to understand human suffering or mental pain. Both humans and sophisticated AI agents process information about the world in order to achieve goals and obtain rewards, which is why AI can be used as a model of the human brain and mind. This book intends to make the theory accessible to a relatively general audience, requiring only some relevant scientific background. The book starts with the assumption that suffering is mainly caused by frustration. Frustration means the failure of an agent (whether AI or human) to achieve a goal or a reward it wanted or expected. Frustration is inevitable because of the overwhelming complexity of the world, limited computational resources, and scarcity of good data. In particular, such limitations imply that an agent acting in the real world must cope with uncontrollability, unpredictability, and uncertainty, which all lead to frustration. Fundamental in such modelling is the idea of learning, or adaptation to the environment. While AI uses machine learning, humans and animals adapt by a combination of evolutionary mechanisms and ordinary learning. Even frustration is fundamentally an error signal that the system uses for learning. This book explores various aspects and limitations of learning algorithms and their implications regarding suffering. At the end of the book, the computational theory is used to derive various interventions or training methods that will reduce suffering in humans. The amount of frustration is expressed by a simple equation which indicates how it can be reduced. The ensuing interventions are very similar to those proposed by Buddhist and Stoic philosophy, and include mindfulness meditation. Therefore, this book can be interpreted as an exposition of a computational theory justifying why such philosophies and meditation reduce human suffering.

The identification theory for causal effects in directed acyclic graphs (DAGs) with hidden variables is well-developed, but methods for estimating and inferring functionals beyond the g-formula remain limited. Previous studies have proposed semiparametric estimators for identifiable functionals in a broad class of DAGs with hidden variables. While demonstrating double robustness in some models, existing estimators face challenges, particularly with density estimation and numerical integration for continuous variables, and their estimates may fall outside the parameter space of the target estimand. Their asymptotic properties are also underexplored, especially when using flexible statistical and machine learning models for nuisance estimation. This study addresses these challenges by introducing novel one-step corrected plug-in and targeted minimum loss-based estimators of causal effects for a class of DAGs that extend classical back-door and front-door criteria (known as the treatment primal fixability criterion in prior literature). These estimators leverage machine learning to minimize modeling assumptions while ensuring key statistical properties such as asymptotic linearity, double robustness, efficiency, and staying within the bounds of the target parameter space. We establish conditions for nuisance functional estimates in terms of L2(P)-norms to achieve root-n consistent causal effect estimates. To facilitate practical application, we have developed the flexCausal package in R.