The vast majority of the literature on learning dynamical systems or stochastic processes from time series has focused on stable or ergodic systems, for both Bayesian and frequentist inference procedures. However, most real-world systems are only metastable, that is, the dynamics appear to be stable on some time scale, but are in fact unstable over longer time scales. Consistency of inference for metastable systems may not be possible, but one can ask about metaconsistency: Do inference procedures converge when observations are taken over a large but finite time interval, but diverge on longer time scales? In this paper we introduce, discuss, and quantify metaconsistency in a Bayesian framework. We discuss how metaconsistency can be exploited to efficiently infer a model for a sub-system of a larger system, where inference on the global behavior may require much more data. We also discuss the relation between meta-consistency and the spectral properties of the model dynamical system in the case of uniformly ergodic diffusions.

Artificial intelligence (AI) has revolutionized decision-making processes and systems throughout society and, in particular, has emerged as a significant technology in high-impact scenarios of national interest. Yet, despite AI's impressive predictive capabilities in controlled settings, it still suffers from a range of practical setbacks preventing its widespread use in various critical scenarios. In particular, it is generally unclear if a given AI system's predictions can be trusted by decision-makers in downstream applications. To address the need for more transparent, robust, and trustworthy AI systems, a suite of tools has been developed to quantify the uncertainty of AI predictions and, more generally, enable AI to "self-assess" the reliability of its predictions. In this manuscript, we categorize methods for AI self-assessment along several key dimensions and provide guidelines for selecting and designing the appropriate method for a practitioner's needs. In particular, we focus on uncertainty estimation techniques that consider the impact of self-assessment on the choices made by downstream decision-makers and on the resulting costs and benefits of decision outcomes. To demonstrate the utility of our methodology for self-assessment design, we illustrate its use for two realistic national-interest scenarios. This manuscript is a practical guide for machine learning engineers and AI system users to select the ideal self-assessment techniques for each problem.

In order to deploy deep neural networks (DNNs) in high-stakes scenarios, it is imperative that DNNs provide inference robust to external perturbations - both intentional and unintentional. Although the resilience of DNNs to intentional and unintentional perturbations has been widely investigated, a unified vision of these inherently intertwined problem domains is still missing. In this work, we fill this gap by providing a survey of the state of the art and highlighting the similarities of the proposed approaches.We also analyze the research challenges that need to be addressed to deploy resilient and secure DNNs. As there has not been any such survey connecting the resilience of DNNs to intentional and unintentional perturbations, we believe this work can help advance the frontier in both domains by enabling the exchange of ideas between the two communities.

Machine learning has witnessed remarkable breakthroughs in recent years. As machine learning permeates various aspects of daily life, individuals and organizations increasingly interact with these systems, exhibiting a wide range of social and adversarial behaviors. These behaviors may have a notable impact on the behavior and performance of machine learning systems. Specifically, during these interactions, data may be generated by strategic individuals, collected by self-interested data collectors, possibly poisoned by adversarial attackers, and used to create predictors, models, and policies satisfying multiple objectives. As a result, the machine learning systems' outputs might degrade, such as the susceptibility of deep neural networks to adversarial examples (Shafahi et al., 2018; Szegedy et al., 2013) and the diminished performance of classic algorithms in the presence of strategic individuals (Ahmadi et al., 2021). Addressing these challenges is imperative for the success of machine learning in societal settings.

In modern and personalised education, there is a growing interest in developing learners' competencies and accurately assessing them. In a previous work, we proposed a procedure for deriving a learner model for automatic skill assessment from a task-specific competence rubric, thus simplifying the implementation of automated assessment tools. The previous approach, however, suffered two main limitations: (i) the ordering between competencies defined by the assessment rubric was only indirectly modelled; (ii) supplementary skills, not under assessment but necessary for accomplishing the task, were not included in the model. In this work, we address issue (i) by introducing dummy observed nodes, strictly enforcing the skills ordering without changing the network's structure. In contrast, for point (ii), we design a network with two layers of gates, one performing disjunctive operations by noisy-OR gates and the other conjunctive operations through logical ANDs. Such changes improve the model outcomes' coherence and the modelling tool's flexibility without compromising the model's compact parametrisation, interpretability and simple experts' elicitation. We used this approach to develop a learner model for Computational Thinking (CT) skills assessment. The CT-cube skills assessment framework and the Cross Array Task (CAT) are used to exemplify it and demonstrate its feasibility.

Positive and negative dependence are fundamental concepts that characterize the attractive and repulsive behavior of random subsets. Although some probabilistic models are known to exhibit positive or negative dependence, it is challenging to seamlessly bridge them with a practicable probabilistic model. In this study, we introduce a new family of distributions, named the discrete kernel point process (DKPP), which includes determinantal point processes and parts of Boltzmann machines. We also develop some computational methods for probabilistic operations and inference with DKPPs, such as calculating marginal and conditional probabilities and learning the parameters. Our numerical experiments demonstrate the controllability of positive and negative dependence and the effectiveness of the computational methods for DKPPs.

Estimating treatment effects from observational data is of central interest across numerous application domains. Individual treatment effect offers the most granular measure of treatment effect on an individual level, and is the most useful to facilitate personalized care. However, its estimation and inference remain underdeveloped due to several challenges. In this article, we propose a novel conformal diffusion model-based approach that addresses those intricate challenges. We integrate the highly flexible diffusion modeling, the model-free statistical inference paradigm of conformal inference, along with propensity score and covariate local approximation that tackle distributional shifts. We unbiasedly estimate the distributions of potential outcomes for individual treatment effect, construct an informative confidence interval, and establish rigorous theoretical guarantees. We demonstrate the competitive performance of the proposed method over existing solutions through extensive numerical studies.

We present two new approaches for point prediction with streaming data. One is based on the Count-Min sketch (CMS) and the other is based on Gaussian process priors with a random bias. These methods are intended for the most general predictive problems where no true model can be usefully formulated for the data stream. In statistical contexts, this is often called the $\mathcal{M}$-open problem class. Under the assumption that the data consists of i.i.d samples from a fixed distribution function $F$, we show that the CMS-based estimates of the distribution function are consistent. We compare our new methods with two established predictors in terms of cumulative $L^1$ error. One is based on the Shtarkov solution (often called the normalized maximum likelihood) in the normal experts setting and the other is based on Dirichlet process priors. These comparisons are for two cases. The first is one-pass meaning that the updating of the predictors is done using the fact that the CMS is a sketch. For predictors that are not one-pass, we use streaming $K$-means to give a representative subset of fixed size that can be updated as data accumulate. Preliminary computational work suggests that the one-pass median version of the CMS method is rarely outperformed by the other methods for sufficiently complex data. We also find that predictors based on Gaussian process priors with random biases perform well. The Shtarkov predictors we use here did not perform as well probably because we were only using the simplest example. The other predictors seemed to perform well mainly when the data did not look like they came from an M-open data generator.

Bayesian estimation is a vital tool in robotics as it allows systems to update the belief of the robot state using incomplete information from noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and measurement noise, as well as the state distribution, are all unimodal and Gaussian. However, there are numerous scenarios and systems that do not comply with these assumptions. Existing non-parametric filters that are used to model multimodal distributions have drawbacks that limit their ability to represent a diverse set of distributions. In this paper, we introduce a novel approach to nonparametric Bayesian filtering to cope with multimodal distributions using harmonic exponential distributions. This approach leverages two key insights of harmonic exponential distributions: a) the product of two distributions can be expressed as the element-wise addition of their log-likelihood Fourier coefficients, and b) the convolution of two distributions can be efficiently computed as the tensor product of their Fourier coefficients. These observations enable the development of an efficient and exact solution to the Bayes filter up to the band limit of a Fourier transform. We demonstrate our filter's superior performance compared with established nonparametric filtering methods across a range of simulated and real-world localization tasks.

Recent advancements in machine learning have accelerated its widespread adoption across various real-world applications. However, in safety-critical domains, the deployment of machine learning models is riddled with challenges due to their complexity, lack of interpretability, and absence of formal guarantees regarding their behavior. In this paper, we introduce a verification framework tailored for Bayesian networks, designed to address these drawbacks. Our framework comprises two key components: (1) a two-step compilation and encoding scheme that translates Bayesian networks into Boolean logic literals, and (2) formal verification queries that leverage these literals to verify various properties encoded as constraints. Specifically, we introduce two verification queries: if-then rules (ITR) and feature monotonicity (FMO). We benchmark the efficiency of our verification scheme and demonstrate its practical utility in real-world scenarios.