Designing effective graph neural networks (GNNs) with message passing has two fundamental challenges, i.e., determining optimal message-passing pathways and designing local aggregators. Previous methods of designing optimal pathways are limited with information loss on the input features. On the other hand, existing local aggregators generally fail to extract multi-scale features and approximate diverse operators under limited parameter scales. In contrast to these methods, Euclidean convolution has been proven as an expressive aggregator, making it a perfect candidate for GNN construction. However, the challenges of generalizing Euclidean convolution to graphs arise from the irregular structure of graphs. To bridge the gap between Euclidean space and graph topology, we propose a differentiable method that applies permutations to calibrate input graphs for Euclidean convolution. The permutations constrain all nodes in a row regardless of their input order and therefore enable the flexible generalization of Euclidean convolution to graphs. Based on the graph calibration, we propose the Compressed Convolution Network (CoCN) for hierarchical graph representation learning. CoCN follows local feature-learning and global parameter-sharing mechanisms of convolution neural networks. The whole model can be trained end-to-end, with compressed convolution applied to learn individual node features and their corresponding structure features. CoCN can further borrow successful practices from Euclidean convolution, including residual connection and inception mechanism. We validate CoCN on both node-level and graph-level benchmarks. CoCN achieves superior performance over competitive GNN baselines. Codes are available at https://github.com/sunjss/CoCN.

In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of machine learning, the use of data-driven population-level distributions (encoded, e.g., in a trained deep neural network) as priors is emerging as an appealing alternative to simple parametric priors in a variety of inverse problems. However, in many astrophysical applications, it is often difficult or even impossible to acquire independent and identically distributed samples from the underlying data-generating process of interest to train these models. In these cases, corrupted data or a surrogate, e.g. a simulator, is often used to produce training samples, meaning that there is a risk of obtaining misspecified priors. This, in turn, can bias the inferred posteriors in ways that are difficult to quantify, which limits the potential applicability of these models in real-world scenarios. In this work, we propose addressing this issue by iteratively updating the population-level distributions by retraining the model with posterior samples from different sets of observations and showcase the potential of this method on the problem of background image reconstruction in strong gravitational lensing when score-based models are used as data-driven priors. We show that starting from a misspecified prior distribution, the updated distribution becomes progressively closer to the underlying population-level distribution, and the resulting posterior samples exhibit reduced bias after several updates.

Causal inference plays an important role in explanatory analysis and decision making across various fields like statistics, marketing, health care, and education. Its main task is to estimate treatment effects and make intervention policies. Traditionally, most of the previous works typically focus on the binary treatment setting that there is only one treatment for a unit to adopt or not. However, in practice, the treatment can be much more complex, encompassing multi-valued, continuous, or bundle options. In this paper, we refer to these as complex treatments and systematically and comprehensively review the causal inference methods for addressing them. First, we formally revisit the problem definition, the basic assumptions, and their possible variations under specific conditions. Second, we sequentially review the related methods for multi-valued, continuous, and bundled treatment settings. In each situation, we tentatively divide the methods into two categories: those conforming to the unconfoundedness assumption and those violating it. Subsequently, we discuss the available datasets and open-source codes. Finally, we provide a brief summary of these works and suggest potential directions for future research.

In this paper, we present a new solution to the problem of large-scale multi-building and multi-floor indoor localization based on linked neural networks, where each neural network is dedicated to a sub-problem and trained under a hierarchical stage-wise training framework. When the measured data from sensors have a hierarchical representation as in multi-building and multi-floor indoor localization, it is important to exploit the hierarchical nature in data processing to provide a scalable solution. In this regard, the hierarchical stage-wise training framework extends the original stage-wise training framework to the case of multiple linked networks by training a lower-hierarchy network based on the prior knowledge gained from the training of higher-hierarchy networks. The experimental results with the publicly-available UJIIndoorLoc multi-building and multi-floor Wi-Fi RSSI fingerprint database demonstrate that the linked neural networks trained under the proposed hierarchical stage-wise training framework can achieve a three-dimensional localization error of 8.19 m, which, to the best of the authors' knowledge, is the most accurate result ever obtained for neural network-based models trained and evaluated with the full datasets of the UJIIndoorLoc database, and that, when applied to a model based on hierarchical convolutional neural networks, the proposed training framework can also significantly reduce the three-dimensional localization error from 11.78 m to 8.71 m.

Query embedding approaches answer complex logical queries over incomplete knowledge graphs (KGs) by computing and operating on low-dimensional vector representations of entities, relations, and queries. However, current query embedding models heavily rely on excessively parameterized neural networks and cannot explain the knowledge learned from the graph. We propose a novel query embedding method, AConE, which explains the knowledge learned from the graph in the form of SROI^{-} description logic axioms while being more parameter-efficient than most existing approaches. AConE associates queries to a SROI^{-} description logic concept. Every SROI^{-} concept is embedded as a cone in complex vector space, and each SROI^{-} relation is embedded as a transformation that rotates and scales cones. We show theoretically that AConE can learn SROI^{-} axioms, and defines an algebra whose operations correspond one to one to SROI^{-} description logic concept constructs. Our empirical study on multiple query datasets shows that AConE achieves superior results over previous baselines with fewer parameters. Notably on the WN18RR dataset, AConE achieves significant improvement over baseline models. We provide comprehensive analyses showing that the capability to represent axioms positively impacts the results of query answering.

Consider the model where we can access a parity function through random uniform labeled examples in the presence of random classification noise. In this paper, we show that approximating the number of relevant variables in the parity function is as hard as properly learning parities. More specifically, let $\gamma:{\mathbb R}^+\to {\mathbb R}^+$, where $\gamma(x) \ge x$, be any strictly increasing function. In our first result, we show that from any polynomial-time algorithm that returns a $\gamma$-approximation, $D$ (i.e., $\gamma^{-1}(d(f)) \leq D \leq \gamma(d(f))$), of the number of relevant variables~$d(f)$ for any parity $f$, we can, in polynomial time, construct a solution to the long-standing open problem of polynomial-time learning $k(n)$-sparse parities (parities with $k(n)\le n$ relevant variables), where $k(n) = \omega_n(1)$. In our second result, we show that from any $T(n)$-time algorithm that, for any parity $f$, returns a $\gamma$-approximation of the number of relevant variables $d(f)$ of $f$, we can, in polynomial time, construct a $poly(\Gamma(n))T(\Gamma(n)^2)$-time algorithm that properly learns parities, where $\Gamma(x)=\gamma(\gamma(x))$. If $T(\Gamma(n)^2)=\exp({o(n/\log n)})$, this would resolve another long-standing open problem of properly learning parities in the presence of random classification noise in time $\exp({o(n/\log n)})$.

The concept of robustness is of paramount importance across a variety of fields, particularly those involving practical statistical parameter estimation based on real-world observations. However, robust estimation techniques introduced in various methodologies aim to achieve different objectives, and each technique has been examined within individual frameworks. It is crucial to reexamine the purpose behind robust estimation and provide an integrated perspective across disciplinary boundaries. To facilitate this, this study initially classifies the goals of robust estimation methods into three categories: resistance to (1) outlier contamination (see, e.g., Huber and Ronchetti (1981) and Hampel et al. (1986)), (2) user-specified imaginary dataset-perturbation (see, e.g., Ben-Tal and Nemirovski (2002) and Biggio et al. (2013)), and (3) model misspecification. Notably, (3) can be addressed using expressive models in certain cases; (3) will be discussed later but will not be the main focus. Therefore, this study primarily focuses on the following two categories within the context of linear regression: (1) Outlier-resistance. Outliers are data points that deviate significantly from the overall trend of the other observations in a dataset. Since the presence of outliers can affect statistical parameter estimation, potentially leading to unintended results, outlier-resistant estimation has been a focus for many decades (Huber and Ronchetti, 1981; Hampel et al., 1986; Maronna et al., 2006) mainly in the field of statistics. Originating from the works of Tukey (1960) and Huber (1964), many outlier-resistant estimations are designed by modifying the loss function.

This paper introduces Diffuse-TreeVAE, a deep generative model that integrates hierarchical clustering into the framework of Denoising Diffusion Probabilistic Models (DDPMs). The proposed approach generates new images by sampling from a root embedding of a learned latent tree VAE-based structure, it then propagates through hierarchical paths, and utilizes a second-stage DDPM to refine and generate distinct, high-quality images for each data cluster. The result is a model that not only improves image clarity but also ensures that the generated samples are representative of their respective clusters, addressing the limitations of previous VAE-based methods and advancing the state of clustering-based generative modeling.

Behavioural biometric authentication systems entail an enrolment period that is burdensome for the user. In this work, we explore generating synthetic gestures from a few real user gestures with generative deep learning, with the application of training a simple (i.e. non-deep-learned) authentication model. Specifically, we show that utilising synthetic data alongside real data can reduce the number of real datapoints a user must provide to enrol into a biometric system. To validate our methods, we use the publicly available dataset of WatchAuth, a system proposed in 2022 for authenticating smartwatch payments using the physical gesture of reaching towards a payment terminal. We develop a regularised autoencoder model for generating synthetic user-specific wrist motion data representing these physical gestures, and demonstrate the diversity and fidelity of our synthetic gestures. We show that using synthetic gestures in training can improve classification ability for a real-world system. Through this technique we can reduce the number of gestures required to enrol a user into a WatchAuth-like system by more than 40% without negatively impacting its error rates.

Warning: this paper contains model outputs exhibiting unethical information. Large Language Models (LLMs) have achieved significant breakthroughs, but their generated unethical content poses potential risks. Measuring value alignment of LLMs becomes crucial for their regulation and responsible deployment. Numerous datasets have been constructed to assess social bias, toxicity, and ethics in LLMs, but they suffer from evaluation chronoeffect, that is, as models rapidly evolve, existing data becomes leaked or undemanding, overestimating ever-developing LLMs. To tackle this problem, we propose GETA, a novel generative evolving testing approach that dynamically probes the underlying moral baselines of LLMs. Distinct from previous adaptive testing methods that rely on static datasets with limited difficulty, GETA incorporates an iteratively-updated item generator which infers each LLM's moral boundaries and generates difficulty-tailored testing items, accurately reflecting the true alignment extent. This process theoretically learns a joint distribution of item and model response, with item difficulty and value conformity as latent variables, where the generator co-evolves with the LLM, addressing chronoeffect. We evaluate various popular LLMs with diverse capabilities and demonstrate that GETA can create difficulty-matching testing items and more accurately assess LLMs' values, better consistent with their performance on unseen OOD and i.i.d.