This tutorial focuses on efficient methods to predictive monitoring (PM), the problem of detecting at runtime future violations of a given requirement from the current state of a system. While performing model checking at runtime would offer a precise solution to the PM problem, it is generally computationally expensive. To address this scalability issue, several lightweight approaches based on machine learning have recently been proposed. These approaches work by learning an approximate yet efficient surrogate (deep learning) model of the expensive model checker. A key challenge remains to ensure reliable predictions, especially in safety-critical applications. We review our recent work on predictive monitoring, one of the first to propose learning-based approximations for CPS verification of temporal logic specifications and the first in this context to apply conformal prediction (CP) for rigorous uncertainty quantification. These CP-based uncertainty estimators offer statistical guarantees regarding the generalization error of the learning model, and they can be used to determine unreliable predictions that should be rejected. In this tutorial, we present a general and comprehensive framework summarizing our approach to the predictive monitoring of CPSs, examining in detail several variants determined by three main dimensions: system dynamics (deterministic, non-deterministic, stochastic), state observability, and semantics of requirements' satisfaction (Boolean or quantitative).

Dynamic Bayesian Networks (DBNs), renowned for their interpretability, have become increasingly vital in representing complex stochastic processes in various domains such as gene expression analysis, healthcare, and traffic prediction. Structure learning of DBNs from data is challenging, particularly for datasets with thousands of variables. Most current algorithms for DBN structure learning are adaptations from those used in static Bayesian Networks (BNs), and are typically focused on small-scale problems. In order to solve large-scale problems while taking full advantage of existing algorithms, this paper introduces a novel divide-and-conquer strategy, originally developed for static BNs, and adapts it for large-scale DBN structure learning. In this work, we specifically concentrate on 2 Time-sliced Bayesian Networks (2-TBNs), a special class of DBNs. Furthermore, we leverage the prior knowledge of 2-TBNs to enhance the performance of the strategy we introduce. Our approach significantly improves the scalability and accuracy of 2-TBN structure learning. Experimental results demonstrate the effectiveness of our method, showing substantial improvements over existing algorithms in both computational efficiency and structure learning accuracy. On problem instances with more than 1,000 variables, our approach improves two accuracy metrics by 74.45% and 110.94% on average , respectively, while reducing runtime by 93.65% on average.

We assume to be given structural equations over discrete variables inducing a directed acyclic graph, namely, a structural causal model, together with data about its internal nodes. The question we want to answer is how we can compute bounds for partially identifiable counterfactual queries from such an input. We start by giving a map from structural casual models to credal networks. This allows us to compute exact counterfactual bounds via algorithms for credal nets on a subclass of structural causal models. Exact computation is going to be inefficient in general given that, as we show, causal inference is NP-hard even on polytrees. We target then approximate bounds via a causal EM scheme. We evaluate their accuracy by providing credible intervals on the quality of the approximation; we show through a synthetic benchmark that the EM scheme delivers accurate results in a fair number of runs. In the course of the discussion, we also point out what seems to be a neglected limitation to the trending idea that counterfactual bounds can be computed without knowledge of the structural equations. We also present a real case study on palliative care to show how our algorithms can readily be used for practical purposes.

Two linearly uncorrelated binary variables must be also independent because non-linear dependence cannot manifest with only two possible states. This inherent linearity is the atom of dependency constituting any complex form of relationship. Inspired by this observation, we develop a framework called binary expansion linear effect (BELIEF) for understanding arbitrary relationships with a binary outcome. Models from the BELIEF framework are easily interpretable because they describe the association of binary variables in the language of linear models, yielding convenient theoretical insight and striking Gaussian parallels. With BELIEF, one may study generalized linear models (GLM) through transparent linear models, providing insight into how the choice of link affects modeling. For example, setting a GLM interaction coefficient to zero does not necessarily lead to the kind of no-interaction model assumption as understood under their linear model counterparts. Furthermore, for a binary response, maximum likelihood estimation for GLMs paradoxically fails under complete separation, when the data are most discriminative, whereas BELIEF estimation automatically reveals the perfect predictor in the data that is responsible for complete separation. We explore these phenomena and provide related theoretical results. We also provide preliminary empirical demonstration of some theoretical results.

The ice shelves buttressing the Antarctic ice sheet determine the rate of ice-discharge into the surrounding oceans. The geometry of ice shelves, and hence their buttressing strength, is determined by ice flow as well as by the local surface accumulation and basal melt rates, governed by atmospheric and oceanic conditions. Contemporary methods resolve one of these rates, but typically not both. Moreover, there is little information of how they changed in time. We present a new method to simultaneously infer the surface accumulation and basal melt rates averaged over decadal and centennial timescales. We infer the spatial dependence of these rates along flow line transects using internal stratigraphy observed by radars, using a kinematic forward model of internal stratigraphy. We solve the inverse problem using simulation-based inference (SBI). SBI performs Bayesian inference by training neural networks on simulations of the forward model to approximate the posterior distribution, allowing us to also quantify uncertainties over the inferred parameters. We demonstrate the validity of our method on a synthetic example, and apply it to Ekstr\"om Ice Shelf, Antarctica, for which newly acquired radar measurements are available. We obtain posterior distributions of surface accumulation and basal melt averaging over 42, 84, 146, and 188 years before 2022. Our results suggest stable atmospheric and oceanographic conditions over this period in this catchment of Antarctica. Use of observed internal stratigraphy can separate the effects of surface accumulation and basal melt, allowing them to be interpreted in a historical context of the last centuries and beyond.

Decision trees have found widespread application within the machine learning community due to their flexibility and interpretability. This paper is directed towards learning decision trees from data using a Bayesian approach, which is challenging due to the potentially enormous parameter space required to span all tree models. Several approaches have been proposed to combat this challenge, with one of the more successful being Markov chain Monte Carlo (MCMC) methods. The efficacy and efficiency of MCMC methods fundamentally rely on the quality of the so-called proposals, which is the focus of this paper. In particular, this paper investigates using a Hamiltonian Monte Carlo (HMC) approach to explore the posterior of Bayesian decision trees more efficiently by exploiting the geometry of the likelihood within a global update scheme. Two implementations of the novel algorithm are developed and compared to existing methods by testing against standard datasets in the machine learning and Bayesian decision tree literature. HMC-based methods are shown to perform favourably with respect to predictive test accuracy, acceptance rate, and tree complexity.

We explore the idea of aligning an AI assistant by inverting a model of users' (unknown) preferences from observed interactions. To validate our proposal, we run proof-of-concept simulations in the economic ultimatum game, formalizing user preferences as policies that guide the actions of simulated players. We find that the AI assistant accurately aligns its behavior to match standard policies from the economic literature (e.g., selfish, altruistic). However, the assistant's learned policies lack robustness and exhibit limited generalization in an out-of-distribution setting when confronted with a currency (e.g., grams of medicine) that was not included in the assistant's training distribution. Additionally, we find that when there is inconsistency in the relationship between language use and an unknown policy (e.g., an altruistic policy combined with rude language), the assistant's learning of the policy is slowed. Overall, our preliminary results suggest that developing simulation frameworks in which AI assistants need to infer preferences from diverse users can provide a valuable approach for studying practical alignment questions.

The Internet is used by billions of users every day because it offers fast and free communication tools and platforms. Nevertheless, with this significant increase in usage, huge amounts of spam are generated every second, which wastes internet resources and, more importantly, users' time. This study investigates the use of machine learning models to classify URLs as spam or nonspam. We first extract the features from the URL as it has only one feature, and then we compare the performance of several models, including k nearest neighbors, bagging, random forest, logistic regression, and others. Experimental results demonstrate that bagging outperformed other models and achieved the highest accuracy of 98.64%. In addition, bagging outperformed the current state-of-the-art approaches which emphasize its effectiveness in addressing spam-related challenges on the Internet. This suggests that bagging is a promising approach for URL spam classification.

In many fields of scientific research and real-world applications, unbiased estimation of causal effects from non-experimental data is crucial for understanding the mechanism underlying the data and for decision-making on effective responses or interventions. A great deal of research has been conducted to address this challenging problem from different angles. For estimating causal effect in observational data, assumptions such as Markov condition, faithfulness and causal sufficiency are always made. Under the assumptions, full knowledge such as, a set of covariates or an underlying causal graph, is typically required. A practical challenge is that in many applications, no such full knowledge or only some partial knowledge is available. In recent years, research has emerged to use search strategies based on graphical causal modelling to discover useful knowledge from data for causal effect estimation, with some mild assumptions, and has shown promise in tackling the practical challenge. In this survey, we review these data-driven methods on causal effect estimation for a single treatment with a single outcome of interest and focus on the challenges faced by data-driven causal effect estimation. We concisely summarise the basic concepts and theories that are essential for data-driven causal effect estimation using graphical causal modelling but are scattered around the literature. We identify and discuss the challenges faced by data-driven causal effect estimation and characterise the existing methods by their assumptions and the approaches to tackling the challenges. We analyse the strengths and limitations of the different types of methods and present an empirical evaluation to support the discussions. We hope this review will motivate more researchers to design better data-driven methods based on graphical causal modelling for the challenging problem of causal effect estimation.

Multivariate time series are everywhere. Nevertheless, real-world time series data often exhibit numerous missing values, which is the time series imputation task. Although previous deep learning methods have been shown to be effective for time series imputation, they are shown to produce overconfident imputations, which might be a potentially overlooked threat to the reliability of the intelligence system. Score-based diffusion method(i.e., CSDI) is effective for the time series imputation task but computationally expensive due to the nature of the generative diffusion model framework. In this paper, we propose a non-generative time series imputation method that produces accurate imputations with inherent uncertainty and meanwhile is computationally efficient. Specifically, we incorporate deep ensembles into quantile regression with a shared model backbone and a series of quantile discrimination functions.This framework combines the merits of accurate uncertainty estimation of deep ensembles and quantile regression and above all, the shared model backbone tremendously reduces most of the computation overhead of the multiple ensembles. We examine the performance of the proposed method on two real-world datasets: air quality and health-care datasets and conduct extensive experiments to show that our method excels at making deterministic and probabilistic predictions. Compared with the score-based diffusion method: CSDI, we can obtain comparable forecasting results and is better when more data is missing. Furthermore, as a non-generative model compared with CSDI, the proposed method consumes a much smaller computation overhead, yielding much faster training speed and fewer model parameters.