Score-based causal discovery methods can effectively identify causal relationships by evaluating candidate graphs and selecting the one with the highest score. One popular class of scores is kernel-based generalized score functions, which can adapt to a wide range of scenarios and work well in practice because they circumvent assumptions about causal mechanisms and data distributions. Despite these advantages, kernel-based generalized score functions pose serious computational challenges in time and space, with a time complexity of $\mathcal{O}(n^3)$ and a memory complexity of $\mathcal{O}(n^2)$, where $n$ is the sample size. In this paper, we propose an approximate kernel-based generalized score function with $\mathcal{O}(n)$ time and space complexities by using low-rank technique and designing a set of rules to handle the complex composite matrix operations required to calculate the score, as well as developing sampling algorithms for different data types to benefit the handling of diverse data types efficiently. Our extensive causal discovery experiments on both synthetic and real-world data demonstrate that compared to the state-of-the-art method, our method can not only significantly reduce computational costs, but also achieve comparable accuracy, especially for large datasets.

We propose a greedy search-and-score algorithm for ancestral graphs, which include directed as well as bidirected edges, originating from unobserved latent variables. The normalized likelihood score of ancestral graphs is estimated in terms of multivariate information over relevant ``ac-connected subsets'' of vertices, C, that are connected through collider paths confined to the ancestor set of C. For computational efficiency, the proposed two-step algorithm relies on local information scores limited to the close surrounding vertices of each node (step 1) and edge (step 2). This computational strategy, although restricted to information contributions from ac-connected subsets containing up to two-collider paths, is shown to outperform state-of-the-art causal discovery methods on challenging benchmark datasets.

Diffusion models have emerged as powerful tools for generative modeling, demonstrating exceptional capability in capturing target data distributions from large datasets. However, fine-tuning these massive models for specific downstream tasks, constraints, and human preferences remains a critical challenge. While recent advances have leveraged reinforcement learning algorithms to tackle this problem, much of the progress has been empirical, with limited theoretical understanding. To bridge this gap, we propose a stochastic control framework for fine-tuning diffusion models. Building on denoising diffusion probabilistic models as the pre-trained reference dynamics, our approach integrates linear dynamics control with Kullback-Leibler regularization. We establish the well-posedness and regularity of the stochastic control problem and develop a policy iteration algorithm (PI-FT) for numerical solution. We show that PI-FT achieves global convergence at a linear rate. Unlike existing work that assumes regularities throughout training, we prove that the control and value sequences generated by the algorithm maintain the regularity. Additionally, we explore extensions of our framework to parametric settings and continuous-time formulations.

Simulation is critical for safety evaluation in autonomous driving, particularly in capturing complex interactive behaviors. However, generating realistic and controllable traffic scenarios in long-tail situations remains a significant challenge. Existing generative models suffer from the conflicting objective between user-defined controllability and realism constraints, which is amplified in safety-critical contexts. In this work, we introduce the Causal Compositional Diffusion Model (CCDiff), a structure-guided diffusion framework to address these challenges. We first formulate the learning of controllable and realistic closed-loop simulation as a constrained optimization problem. Then, CCDiff maximizes controllability while adhering to realism by automatically identifying and injecting causal structures directly into the diffusion process, providing structured guidance to enhance both realism and controllability. Through rigorous evaluations on benchmark datasets and in a closed-loop simulator, CCDiff demonstrates substantial gains over state-of-the-art approaches in generating realistic and user-preferred trajectories. Our results show CCDiff's effectiveness in extracting and leveraging causal structures, showing improved closed-loop performance based on key metrics such as collision rate, off-road rate, FDE, and comfort.

Whole-body hemodynamics simulators, which model blood flow and pressure waveforms as functions of physiological parameters, are now essential tools for studying cardiovascular systems. However, solving the corresponding inverse problem of mapping observations (e.g., arterial pressure waveforms at specific locations in the arterial network) back to plausible physiological parameters remains challenging. Leveraging recent advances in simulation-based inference, we cast this problem as statistical inference by training an amortized neural posterior estimator on a newly built large dataset of cardiac simulations that we publicly release. To better align simulated data with real-world measurements, we incorporate stochastic elements modeling exogenous effects. The proposed framework can further integrate in-vivo data sources to refine its predictive capabilities on real-world data. In silico, we demonstrate that the proposed framework enables finely quantifying uncertainty associated with individual measurements, allowing trustworthy prediction of four biomarkers of clinical interest--namely Heart Rate, Cardiac Output, Systemic Vascular Resistance, and Left Ventricular Ejection Time--from arterial pressure waveforms and photoplethysmograms. Furthermore, we validate the framework in vivo, where our method accurately captures temporal trends in CO and SVR monitoring on the VitalDB dataset. Finally, the predictive error made by the model monotonically increases with the predicted uncertainty, thereby directly supporting the automatic rejection of unusable measurements.

This study investigates the performance of three popular tokenization tools: MeCab, Sudachi, and SentencePiece, when applied as a preprocessing step for sentiment-based text classification of Japanese texts. Using Term Frequency-Inverse Document Frequency (TF-IDF) vectorization, we evaluate two traditional machine learning classifiers: Multinomial Naive Bayes and Logistic Regression. The results reveal that Sudachi produces tokens closely aligned with dictionary definitions, while MeCab and SentencePiece demonstrate faster processing speeds. The combination of SentencePiece, TF-IDF, and Logistic Regression outperforms the other alternatives in terms of classification performance.

Cross-Project Defect Prediction (CPDP) poses a non-trivial challenge to construct a reliable defect predictor by leveraging data from other projects, particularly when data owners are concerned about data privacy. In recent years, Federated Learning (FL) has become an emerging paradigm to guarantee privacy information by collaborative training a global model among multiple parties without sharing raw data. While the direct application of FL to the CPDP task offers a promising solution to address privacy concerns, the data heterogeneity arising from proprietary projects across different companies or organizations will bring troubles for model training. In this paper, we study the privacy-preserving cross-project defect prediction with data heterogeneity under the federated learning framework. To address this problem, we propose a novel knowledge enhancement approach named FedDP with two simple but effective solutions: 1. Local Heterogeneity Awareness and 2. Global Knowledge Distillation. Specifically, we employ open-source project data as the distillation dataset and optimize the global model with the heterogeneity-aware local model ensemble via knowledge distillation. Experimental results on 19 projects from two datasets demonstrate that our method significantly outperforms baselines.

We live in a world full of complex systems which we need to improve our understanding of. To accomplish this, purely probabilistic investigations are often not enough. They are only the first step and must be followed by learning the system's underlying mechanisms. This is what the discipline of causality is concerned with. Many of those complex systems contain feedback loops which means that our methods have to allow for cyclic causal relations. Furthermore, systems are rarely sufficiently isolated, which means that there are usually hidden confounders, i.e., unmeasured variables that each causally affects more than one measured variable. Finally, data is often distorted by contaminating processes, and we need to apply methods that are robust against such distortions. That's why we consider the robustness of LLC, see \cite{llc}, one of the few causal analysis methods that can deal with cyclic models with hidden confounders. Following a theoretical analysis of LLC's robustness properties, we also provide robust extensions of LLC. To facilitate reproducibility and further research in this field, we make the source code publicly available.

Recent advances in MCMC use normalizing flows to precondition target distributions and enable jumps to distant regions. However, there is currently no systematic comparison of different normalizing flow architectures for MCMC. As such, many works choose simple flow architectures that are readily available and do not consider other models. Guidelines for choosing an appropriate architecture would reduce analysis time for practitioners and motivate researchers to take the recommended models as foundations to be improved. We provide the first such guideline by extensively evaluating many normalizing flow architectures on various flow-based MCMC methods and target distributions. When the target density gradient is available, we show that flow-based MCMC outperforms classic MCMC for suitable NF architecture choices with minor hyperparameter tuning. When the gradient is unavailable, flow-based MCMC wins with off-the-shelf architectures. We find contractive residual flows to be the best general-purpose models with relatively low sensitivity to hyperparameter choice. We also provide various insights into normalizing flow behavior within MCMC when varying their hyperparameters, properties of target distributions, and the overall computational budget.

We Training neural architectures is a resource-intensive endeavor, utilize a seq2seq variational autoencoder framework to analyze often demanding considerable computational power the initial stages of a learning curve and predict its future and time. Researchers have developed various methodologies progression. This predictive capability is further enhanced to predict the performance of neural networks early in by an architecture-aware component that produces a graphlevel the training process using learning curve data. Some methods embedding from the architecture's topology, employing Domhan et al. (2015); Gargiani et al. (2019); Adriaensen techniques like Graph Convolutional Networks (GCN) Kipf et al. (2023) apply Bayesian inference to project these and Welling (2016) and Differentiable Pooling Ying et al. curves forward, while others employ time-series prediction (2018). This integration not only improves the accuracy of techniques, such as LSTM networks. Despite their effectiveness, learning curve extrapolations compared to existing methods these approaches (Swersky et al., 2014; Baker et al., but also significantly facilitates model ranking, potentially 2017) typically overlook the architectural features of networks, leading to more efficient use of computational resources, missing out on crucial insights that could be derived from the accelerated experimentation cycles, and faster progress in the models' topology.