The classical notion of causal effect identifiability is defined in terms of treatment and outcome variables. In this note, we consider the identifiability of state-based causal effects: how an intervention on a particular state of treatment variables affects a particular state of outcome variables. We demonstrate that state-based causal effects may be identifiable even when variable-based causal effects may not. Moreover, we show that this separation occurs only when additional knowledge -- such as context-specific independencies and conditional functional dependencies -- is available. We further examine knowledge that constrains the states of variables, and show that such knowledge does not improve identifiability on its own but can improve both variable-based and state-based identifiability when combined with other knowledge such as context-specific independencies. Our findings highlight situations where causal effects of interest may be estimable from observational data and this identifiability may be missed by existing variable-based frameworks.

In modern times, people have numerous online accounts, but they rarely read the Terms of Service or Privacy Policy of those sites, despite claiming otherwise, due to the practical difficulty in comprehending them. The mist of data privacy practices forms a major barrier for user-centred Web approaches, and for data sharing and reusing in an agentic world. Existing research proposed methods for using formal languages and reasoning for verifying the compliance of a specified policy, as a potential cure for ignoring privacy policies. However, a critical gap remains in the creation or acquisition of such formal policies at scale. We present a semantic-centric approach for using state-of-the-art large language models (LLM), to automatically identify key information about privacy practices from privacy policies, and construct $\mathit{Pr}^2\mathit{Graph}$, knowledge graph with grounding from Data Privacy Vocabulary (DPV) for privacy practices, to support downstream tasks. Along with the pipeline, the $\mathit{Pr}^2\mathit{Graph}$ for the top-100 popular websites is also released as a public resource, by using the pipeline for analysis. We also demonstrate how the $\mathit{Pr}^2\mathit{Graph}$ can be used to support downstream tasks by constructing formal policy representations such as Open Digital Right Language (ODRL) or perennial semantic Data Terms of Use (psDToU). To evaluate the technology capability, we enriched the Policy-IE dataset by employing legal experts to create custom annotations. We benchmarked the performance of different large language models for our pipeline and verified their capabilities. Overall, they shed light on the possibility of large-scale analysis of online services' privacy practices, as a promising direction to audit the Web and the Internet. We release all datasets and source code as public resources to facilitate reuse and improvement.

There has been a growing interest in translating C code to Rust due to Rust's robust memory and thread safety guarantees. Tools such as C2RUST enable syntax-guided transpilation from C to semantically equivalent Rust code. However, the resulting Rust programs often rely heavily on unsafe constructs--particularly raw pointers--which undermines Rust's safety guarantees. This paper aims to improve the memory safety of Rust programs generated by C2RUST by eliminating raw pointers. Specifically, we propose a peephole raw pointer rewriting technique that lifts raw pointers in individual functions to appropriate Rust data structures. Technically, PR2 employs decision-tree-based prompting to guide the pointer lifting process. Additionally, it leverages code change analysis to guide the repair of errors introduced during rewriting, effectively addressing errors encountered during compilation and test case execution. We implement PR2 as a prototype and evaluate it using gpt-4o-mini on 28 real-world C projects. The results show that PR2 successfully eliminates 13.22% of local raw pointers across these projects, significantly enhancing the safety of the translated Rust code. On average, PR2 completes the transformation of a project in 5.44 hours, at an average cost of $1.46.

Among other uses, neural networks are a powerful tool for solving deterministic and Bayesian inverse problems in real-time. In the Bayesian framework, variational autoencoders, a specialized type of neural network, enable the estimation of model parameters and their distribution based on observational data allowing to perform real-time inverse uncertainty quantification. In this work, we build upon existing research [Goh, H. et al., Proceedings of Machine Learning Research, 2022] by proposing a novel loss function to train variational autoencoders for Bayesian inverse problems. When the forward map is affine, we provide a theoretical proof of the convergence of the latent states of variational autoencoders to the posterior distribution of the model parameters. We validate this theoretical result through numerical tests and we compare the proposed variational autoencoder with the existing one in the literature. Finally, we test the proposed variational autoencoder on the Laplace equation.

We study the identification of causal effects, motivated by two improvements to identifiability which can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable causal effect may become identifiable when certain variables are functional. Second, certain functional variables can be excluded from being observed without affecting the identifiability of a causal effect, which may significantly reduce the number of needed variables in observational data. Our results are largely based on an elimination procedure which removes functional variables from a causal graph while preserving key properties in the resulting causal graph, including the identifiability of causal effects.

Linear classifiers and leaky ReLU networks trained by gradient flow on the logistic loss have an implicit bias towards solutions which satisfy the Karush--Kuhn--Tucker (KKT) conditions for margin maximization. In this work we establish a number of settings where the satisfaction of these KKT conditions implies benign overfitting in linear classifiers and in two-layer leaky ReLU networks: the estimators interpolate noisy training data and simultaneously generalize well to test data. The settings include variants of the noisy class-conditional Gaussians considered in previous work as well as new distributional settings where benign overfitting has not been previously observed. The key ingredient to our proof is the observation that when the training data is nearly-orthogonal, both linear classifiers and leaky ReLU networks satisfying the KKT conditions for their respective margin maximization problems behave like a nearly uniform average of the training examples.

How to measure the degree of uncertainty of a given frame of discernment has been a hot topic for years. A lot of meaningful works have provided some effective methods to measure the degree properly. However, a crucial factor, sequence of propositions, is missing in the definition of traditional frame of discernment. In this paper, a detailed definition of ordinal frame of discernment has been provided. Besides, an innovative method utilizing a concept of computer vision to combine the order of propositions and the mass of them is proposed to better manifest relationships between the two important element of the frame of discernment. More than that, a specially designed method covering some powerful tools in indicating the degree of uncertainty of a traditional frame of discernment is also offered to give an indicator of level of uncertainty of an ordinal frame of discernment on the level of vector.

We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous theoretical analysis. We show that the proposed algorithms enjoy linear convergence and that their sample complexity is independent of the condition number of the unknown true low-rank matrix. By leveraging recent advances in low-rank matrix approximation techniques, we show that our algorithms achieve computational speed-ups over existing methods. Finally, we complement our theory with some numerical experiments.