Machine learning models $-$ now commonly developed to screen, diagnose, or predict health conditions $-$ are evaluated with a variety of performance metrics. An important first step in assessing the practical utility of a model is to evaluate its average performance over an entire population of interest. In many settings, it is also critical that the model makes good predictions within predefined subpopulations. For instance, showing that a model is fair or equitable requires evaluating the model's performance in different demographic subgroups. However, subpopulation performance metrics are typically computed using only data from that subgroup, resulting in higher variance estimates for smaller groups. We devise a procedure to measure subpopulation performance that can be more sample-efficient than the typical subsample estimates. We propose using an evaluation model $-$ a model that describes the conditional distribution of the predictive model score $-$ to form model-based metric (MBM) estimates. Our procedure incorporates model checking and validation, and we propose a computationally efficient approximation of the traditional nonparametric bootstrap to form confidence intervals. We evaluate MBMs on two main tasks: a semi-synthetic setting where ground truth metrics are available and a real-world hospital readmission prediction task. We find that MBMs consistently produce more accurate and lower variance estimates of model performance for small subpopulations.

Breiman's classic paper casts data analysis as a choice between two cultures: data modelers and algorithmic modelers. Stated broadly, data modelers use simple, interpretable models with well-understood theoretical properties to analyze data. Algorithmic modelers prioritize predictive accuracy and use more flexible function approximations to analyze data. This dichotomy overlooks a third set of models $-$ mechanistic models derived from scientific theories (e.g., ODE/SDE simulators). Mechanistic models encode application-specific scientific knowledge about the data. And while these categories represent extreme points in model space, modern computational and algorithmic tools enable us to interpolate between these points, producing flexible, interpretable, and scientifically-informed hybrids that can enjoy accurate and robust predictions, and resolve issues with data analysis that Breiman describes, such as the Rashomon effect and Occam's dilemma. Challenges still remain in finding an appropriate point in model space, with many choices on how to compose model components and the degree to which each component informs inferences.

Game-theoretic attribution techniques based on Shapley values are used extensively to interpret black-box machine learning models, but their exact calculation is generally NP-hard, requiring approximation methods for non-trivial models. As the computation of Shapley values can be expressed as a summation over a set of permutations, a common approach is to sample a subset of these permutations for approximation. Unfortunately, standard Monte Carlo sampling methods can exhibit slow convergence, and more sophisticated quasi Monte Carlo methods are not well defined on the space of permutations. To address this, we investigate new approaches based on two classes of approximation methods and compare them empirically. First, we demonstrate quadrature techniques in a RKHS containing functions of permutations, using the Mallows kernel to obtain explicit convergence rates of $O(1/n)$, improving on $O(1/\sqrt{n})$ for plain Monte Carlo. The RKHS perspective also leads to quasi Monte Carlo type error bounds, with a tractable discrepancy measure defined on permutations. Second, we exploit connections between the hypersphere $\mathbb{S}^{d-2}$ and permutations to create practical algorithms for generating permutation samples with good properties. Experiments show the above techniques provide significant improvements for Shapley value estimates over existing methods, converging to a smaller RMSE in the same number of model evaluations.

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimating the parameters of a system along with its unknown noise processes. In particular, we propose a Bayesian nonparametric approach for system identification in discrete time nonlinear random dynamical systems assuming only the order of the Markov process is known. The proposed method replaces the assumption of Gaussian distributed error components with a highly flexible family of probability density functions based on Bayesian nonparametric priors. Additionally, the functional form of the system is estimated by leveraging Bayesian neural networks which also leads to flexible uncertainty quantification. Asymptotically on the number of hidden neurons, the proposed model converges to full nonparametric Bayesian regression model. A Gibbs sampler for posterior inference is proposed and its effectiveness is illustrated in simulated and real time series.

Quantum causality is an emerging field of study which has the potential to greatly advance our understanding of quantum systems. One of the most important problems in quantum causality is linked to this prominent aphorism that states correlation does not mean causation. A direct generalization of the existing causal inference techniques to the quantum domain is not possible due to superposition and entanglement. We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. For this purpose, we leverage the concept of conditional density matrices to develop a scalable algorithmic approach for inferring causality in the presence of latent confounders (common causes) in quantum systems. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links, where it is validated that the input before noise as a latent confounder is the cause of the noisy outputs. We also demonstrate that the proposed approach outperforms the results of classical causal inference even when the variables are classical by exploiting quantum dependence between variables through density matrices rather than joint probability distributions. Thus, the proposed approach unifies classical and quantum causal inference in a principled way. This successful inference on a synthetic quantum dataset can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks.

Probabilistic graphical modeling (PGM) provides a framework for formulating an interpretable generative process of data and expressing uncertainty about unknowns, but it lacks flexibility. Deep learning (DL) is an alternative framework for learning from data that has achieved great empirical success in recent years. DL offers great flexibility, but it lacks the interpretability and calibration of PGM. This thesis develops deep probabilistic graphical modeling (DPGM.) DPGM consists in leveraging DL to make PGM more flexible. DPGM brings about new methods for learning from data that exhibit the advantages of both PGM and DL. We use DL within PGM to build flexible models endowed with an interpretable latent structure. One model class we develop extends exponential family PCA using neural networks to improve predictive performance while enforcing the interpretability of the latent factors. Another model class we introduce enables accounting for long-term dependencies when modeling sequential data, which is a challenge when using purely DL or PGM approaches. Finally, DPGM successfully solves several outstanding problems of probabilistic topic models, a widely used family of models in PGM. DPGM also brings about new algorithms for learning with complex data. We develop reweighted expectation maximization, an algorithm that unifies several existing maximum likelihood-based algorithms for learning models parameterized by neural networks. This unifying view is made possible using expectation maximization, a canonical inference algorithm in PGM. We also develop entropy-regularized adversarial learning, a learning paradigm that deviates from the traditional maximum likelihood approach used in PGM. From the DL perspective, entropy-regularized adversarial learning provides a solution to the long-standing mode collapse problem of generative adversarial networks, a widely used DL approach.

The Expectation-Maximization (EM) algorithm is one of the main algorithms in machine learning for estimation of model parameters [2][3][4]. For example, it is used to estimate mixing coefficients, means, and covariances in mixture models as shown in Figure 1. Its objective is to maximize the likelihood p(X θ) where X is a matrix of observed data and θ is a vector of model parameters. This is maximum likelihood estimation and in practice the log-likelihood ln p(X θ) is maximized. The model parameters that maximize this function are deemed to be the correct model parameters.

The Elo rating system has been used world wide for individual sports and team sports, as exemplified by the European Go Federation (EGF), International Chess Federation (FIDE), International Federation of Association Football (FIFA), and many others. To evaluate the performance of artificial intelligence agents, it is natural to evaluate them on the same Elo scale as humans, such as the rating of 5185 attributed to AlphaGo Zero. There are several fundamental differences between humans and AI that suggest modifications to the system, which in turn require revisiting Elo's fundamental rationale. AI is typically trained on many more games than humans play, and we have little a-priori information on newly created AI agents. Further, AI is being extended into games which are asymmetric between the players, and which could even have large complex boards with different setup in every game, such as commercial paper strategy games. We present a revised rating system, and guidelines for tournaments, to reflect these differences.

We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of (conditional) random variables and non-stochastic variables, (extended) stochastic conditional independence and some form of functional conditional independence. Transitional conditional independence is asymmetric in general and it will be shown that it satisfies all desired relevance relations in terms of left and right versions of the separoid rules, except symmetry, on standard, analytic and universal measurable spaces. As a preparation we prove a disintegration theorem for transition probabilities, i.e. the existence and essential uniqueness of (regular) conditional Markov kernels, on those spaces. Transitional conditional independence will be able to express classical statistical concepts like sufficiency, adequacy and ancillarity. As an application, we will then show how transitional conditional independence can be used to prove a directed global Markov property for causal graphical models that allow for non-stochastic input variables in strong generality. This will then also allow us to show the main rules of causal do-calculus, relating observational and interventional distributions, in such measure theoretic generality.

The emergence of Artificial Intelligence of Things (AIoT) has provided novel insights for many social computing applications such as group recommender systems. As distance among people has been greatly shortened, it has been a more general demand to provide personalized services to groups instead of individuals. In order to capture group-level preference features from individuals, existing methods were mostly established via aggregation and face two aspects of challenges: secure data management workflow is absent, and implicit preference feedbacks is ignored. To tackle current difficulties, this paper proposes secure Artificial Intelligence of Things for implicit Group Recommendations (SAIoT-GR). As for hardware module, a secure IoT structure is developed as the bottom support platform. As for software module, collaborative Bayesian network model and non-cooperative game are can be introduced as algorithms. Such a secure AIoT architecture is able to maximize the advantages of the two modules. In addition, a large number of experiments are carried out to evaluate the performance of the SAIoT-GR in terms of efficiency and robustness.