Furthermore, we illustrate various cases (e.g.,

Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Mat ern kernel temporal Gaussian processes with respect to the kernel covariance function's hyperparameters. It is based on casting the optimization problem as a recursive Bayesian estimation procedure for the parameters of an autoregressive model. We demonstrate that the proposed procedure outperforms maximizing the marginal likelihood as well as Hamiltonian Monte Carlo sampling, both in terms of runtime and ultimate root mean square error in Gaussian process regression.

--Cardinality estimation is a fundamental task in database management systems, aiming to predict query results accurately without executing the queries. However, existing techniques either achieve low estimation accuracy or take high inference latency. Simultaneously achieving high speed and accuracy becomes critical for the cardinality estimation problem. In this paper, we propose a novel data-driven approach called CoDe (Covering with Decompositions) to address this problem. CoDe employs the concept of covering design, which divides the table into multiple smaller, overlapping segments. For each segment, CoDe utilizes tensor decomposition to accurately model its data distribution. Moreover, CoDe introduces innovative algorithms to select the best-fitting distributions for each query, combining them to estimate the final result. Notably, experimental results show that our method represents a significant advancement in cardinality estimation, achieving state-of-the-art levels of both estimation accuracy and inference efficiency. Across various datasets, CoDe achieves absolute accuracy in estimating more than half of the queries. Cardinality estimation poses a critical challenge in database management systems (DBMS) as it aims to predict query results accurately without executing the queries. This task is crucial for query optimization, as it allows the optimizer to devise the most efficient query plans. Despite numerous proposed solutions, cardinality estimation remains an unsolved problem. Two primary approaches have been explored to tackle this issue: workload-driven methods [17], [32] and data-driven methods [27], [47], [49]. Motivation. Figure 1 illustrates the comparison between our work and the limitations of existing methods. Workload-driven methods focus on learning patterns from historical workloads and their corresponding results. While these methods are generally fast, their accuracy can degrade when workloads change or are randomly generated. This limitation stems from their lack of direct access to the underlying data and their heavy reliance on the distribution of past workloads. As a result, they are positioned in the bottom-right corner of the graph. On the other hand, recent advancements in data-driven methods directly learn the data distribution, significantly improving estimation accuracy. The authors are with the Department of Computer Science and Technology, Tsinghua University, Beijing, China. Data-driven methods are often orders of magnitude slower than workload-driven methods, placing them in the top-left corner of the graph. Achieving both high speed and accuracy simultaneously is a critical challenge in cardinality estimation, which our work aims to address. Recent research, such as UAE [45], has explored hybrid approaches that combine data and workload information, using workload patterns to enhance data learning.

Road traffic congestion is a persistent problem. Focusing resources on the causes of congestion is a potentially efficient strategy for reducing slowdowns. We present NEXICA, an algorithm to discover which parts of the highway system tend to cause slowdowns on other parts of the highway. We use time series of road speeds as inputs to our causal discovery algorithm. Finding other algorithms inadequate, we develop a new approach that is novel in three ways. First, it concentrates on just the presence or absence of events in the time series, where an event indicates the temporal beginning of a traffic slowdown. Second, we develop a probabilistic model using maximum likelihood estimation to compute the probabilities of spontaneous and caused slowdowns between two locations on the highway. Third, we train a binary classifier to identify pairs of cause/effect locations trained on pairs of road locations where we are reasonably certain a priori of their causal connections, both positive and negative. We test our approach on six months of road speed data from 195 different highway speed sensors in the Los Angeles area, showing that our approach is superior to state-of-the-art baselines in both accuracy and computation speed.

With the growing complexity of cyberattacks targeting critical infrastructures such as water treatment networks, there is a pressing need for robust anomaly detection strategies that account for both system vulnerabilities and evolving attack patterns. Traditional methods -- statistical, density-based, and graph-based models struggle with distribution shifts and class imbalance in multivariate time series, often leading to high false positive rates. To address these challenges, we propose CGAD, a Causal Graph-based Anomaly Detection framework designed for reliable cyberattack detection in public infrastructure systems. CGAD follows a two-phase supervised framework -- causal profiling and anomaly scoring. First, it learns causal invariant graph structures representing the system's behavior under "Normal" and "Attack" states using Dynamic Bayesian Networks. Second, it employs structural divergence to detect anomalies via causal graph comparison by evaluating topological deviations in causal graphs over time. By leveraging causal structures, CGAD achieves superior adaptability and accuracy in non-stationary and imbalanced time series environments compared to conventional machine learning approaches. By uncovering causal structures beneath volatile sensor data, our framework not only detects cyberattacks with markedly higher precision but also redefines robustness in anomaly detection, proving resilience where traditional models falter under imbalance and drift. Our framework achieves substantial gains in F1 and ROC-AUC scores over best-performing baselines across four industrial datasets, demonstrating robust detection of delayed and structurally complex anomalies.

Convergence rate analysis for general state-space Markov chains is fundamentally important in operations research (stochastic systems) and machine learning (stochastic optimization). This problem, however, is notoriously difficult because traditional analytical methods often do not generate practically useful convergence bounds for realistic Markov chains. We propose the Deep Contractive Drift Calculator (DCDC), the first general-purpose sample-based algorithm for bounding the convergence of Markov chains to stationarity in Wasserstein distance. The DCDC has two components. First, inspired by the new convergence analysis framework in (Qu et.al, 2023), we introduce the Contractive Drift Equation (CDE), the solution of which leads to an explicit convergence bound.

The scientific process is a means for turning the results of experiments into knowledge about the world in which we live. Much research effort has been directed toward automating this process. To do this, one needs to formulate the scientific process in a precise mathematical language. This paper outlines one such language. What is presented here is hardly new. The material leans much on great thinkers of times past as well as more modern contributions. The novel contributions of this paper are: A new, general data processing inequality, a bias variance decomposition for canonical losses, Streamlined proofs of the Blackwell-Sherman-Stein and Randomization Theorems, and Means to calculate deficiency via linear programming.

Causal machine learning has the potential to revolutionize decision-making by combining the predictive power of machine learning algorithms with the theory of causal inference. However, these methods remain underutilized by the broader machine learning community, in part because current empirical evaluations do not permit assessment of their reliability and robustness, undermining their practical utility. Specifically, one of the principal criticisms made by the community is the extensive use of synthetic experiments. We argue, on the contrary, that synthetic experiments are essential and necessary to precisely assess and understand the capabilities of causal machine learning methods. To substantiate our position, we critically review the current evaluation practices, spotlight their shortcomings, and propose a set of principles for conducting rigorous empirical analyses with synthetic data. Adopting the proposed principles will enable comprehensive evaluations that build trust in causal machine learning methods, driving their broader adoption and impactful real-world use.

Understanding causal relationships between variables is fundamental across scientific disciplines. Most causal discovery algorithms rely on two key assumptions: (i) all variables are observed, and (ii) the underlying causal graph is acyclic. While these assumptions simplify theoretical analysis, they are often violated in real-world systems, such as biological networks. Existing methods that account for confounders either assume linearity or struggle with scalability. To address these limitations, we propose DCCD-CONF, a novel framework for differentiable learning of nonlinear cyclic causal graphs in the presence of unmeasured confounders using interventional data. Our approach alternates between optimizing the graph structure and estimating the confounder distribution by maximizing the log-likelihood of the data. Through experiments on synthetic data and real-world gene perturbation datasets, we show that DCCD-CONF outperforms state-of-the-art methods in both causal graph recovery and confounder identification. Additionally, we also provide consistency guarantees for our framework, reinforcing its theoretical soundness.

In multi-agent environments, effective interaction hinges on understanding the beliefs and intentions of other agents. While prior work on goal recognition has largely treated the observer as a passive reasoner, Active Goal Recognition (AGR) focuses on strategically gathering information to reduce uncertainty. We adopt a probabilistic framework for Active Goal Recognition and propose an integrated solution that combines a joint belief update mechanism with a Monte Carlo Tree Search (MCTS) algorithm, allowing the observer to plan efficiently and infer the actor's hidden goal without requiring domain-specific knowledge. Through comprehensive empirical evaluation in a grid-based domain, we show that our joint belief update significantly outperforms passive goal recognition, and that our domain-independent MCTS performs comparably to our strong domain-specific greedy baseline. These results establish our solution as a practical and robust framework for goal inference, advancing the field toward more interactive and adaptive multi-agent systems.