We consider the problem of transferring knowledge from a source, or proxy, domain to a new target domain for learning a high-dimensional regression model with possibly different features. Recently, the statistical properties of homogeneous transfer learning have been investigated. However, most homogeneous transfer and multi-task learning methods assume that the target and proxy domains have the same feature space, limiting their practical applicability. In applications, target and proxy feature spaces are frequently inherently different, for example, due to the inability to measure some variables in the target data-poor environments. Conversely, existing heterogeneous transfer learning methods do not provide statistical error guarantees, limiting their utility for scientific discovery. We propose a two-stage method that involves learning the relationship between the missing and observed features through a projection step in the proxy data and then solving a joint penalized regression optimization problem in the target data. We develop an upper bound on the method's parameter estimation risk and prediction risk, assuming that the proxy and the target domain parameters are sparsely different. Our results elucidate how estimation and prediction error depend on the complexity of the model, sample size, the extent of overlap, and correlation between matched and mismatched features.

We introduce the neural tangent kernel (NTK) regime for two-layer neural operators and analyze their generalization properties. For early-stopped gradient descent (GD), we derive fast convergence rates that are known to be minimax optimal within the framework of non-parametric regression in reproducing kernel Hilbert spaces (RKHS). We provide bounds on the number of hidden neurons and the number of second-stage samples necessary for generalization. To justify our NTK regime, we additionally show that any operator approximable by a neural operator can also be approximated by an operator from the RKHS. A key application of neural operators is learning surrogate maps for the solution operators of partial differential equations (PDEs). We consider the standard Poisson equation to illustrate our theoretical findings with simulations.

The correctness of computations remains a significant challenge in computer science, with traditional approaches relying on automated testing or formal verification. Self-testing/correcting programs introduce an alternative paradigm, allowing a program to verify and correct its own outputs via randomized reductions, a concept that previously required manual derivation. In this paper, we present Bitween, a method and tool for automated learning of randomized (self)-reductions and program properties in numerical programs. Bitween combines symbolic analysis and machine learning, with a surprising finding: polynomial-time linear regression, a basic optimization method, is not only sufficient but also highly effective for deriving complex randomized self-reductions and program invariants, often outperforming sophisticated mixed-integer linear programming solvers. We establish a theoretical framework for learning these reductions and introduce RSR-Bench, a benchmark suite for evaluating Bitween's capabilities on scientific and machine learning functions. Our empirical results show that Bitween surpasses state-of-the-art tools in scalability, stability, and sample efficiency when evaluated on nonlinear invariant benchmarks like NLA-DigBench. Bitween is open-source as a Python package and accessible via a web interface that supports C language programs.

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.

Models based on human-understandable concepts have received extensive attention to improve model interpretability for trustworthy artificial intelligence in the field of medical image analysis. These methods can provide convincing explanations for model decisions but heavily rely on the detailed annotation of pre-defined concepts. Consequently, they may not be effective in cases where concepts or annotations are incomplete or low-quality. Although some methods automatically discover effective and new visual concepts rather than using pre-defined concepts or could find some human-understandable concepts via large Language models, they are prone to veering away from medical diagnostic evidence and are challenging to understand. In this paper, we propose a concept complement bottleneck model for interpretable medical image diagnosis with the aim of complementing the existing concept set and finding new concepts bridging the gap between explainable models. Specifically, we propose to use concept adapters for specific concepts to mine the concept differences and score concepts in their own attention channels to support almost fairly concept learning. Then, we devise a concept complement strategy to learn new concepts while jointly using known concepts to improve model performance. Comprehensive experiments on medical datasets demonstrate that our model outperforms the state-of-the-art competitors in concept detection and disease diagnosis tasks while providing diverse explanations to ensure model interpretability effectively.

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit from this development. Difficulties still arise when we can only access summarized data consisting of representative features, summary statistics, and data point counts. Such situations frequently occur primarily due to concerns about confidentiality and management costs associated with spatial data. This study tackles learning and inference using only summarized data within the framework of Gaussian process regression. To address this challenge, we analyze the approximation errors in the marginal likelihood and posterior distribution that arise from utilizing representative features. We also introduce the concept of sample quasi-likelihood, which facilitates learning and inference using only summarized data. Non-Gaussian likelihoods satisfying certain assumptions can be captured by specifying a variance function that characterizes a sample quasi-likelihood function. Theoretical and experimental results demonstrate that the approximation performance is influenced by the granularity of summarized data relative to the length scale of covariance functions. Experiments on a real-world dataset highlight the practicality of our method for spatial modeling.

Long-form document matching aims to judge the relevance between two documents and has been applied to various scenarios. Most existing works utilize hierarchical or long context models to process documents, which achieve coarse understanding but may ignore details. Some researchers construct a document view with similar sentences about aligned document subtopics to focus on detailed matching signals. However, a long document generally contains multiple subtopics. The matching signals are heterogeneous from multiple topics. Considering only the homologous aligned subtopics may not be representative enough and may cause biased modeling. In this paper, we introduce a new framework to model representative matching signals. First, we propose to capture various matching signals through subtopics of document pairs. Next, We construct multiple document views based on subtopics to cover heterogeneous and valuable details. However, existing spatial aggregation methods like attention, which integrate all these views simultaneously, are hard to integrate heterogeneous information. Instead, we propose temporal aggregation, which effectively integrates different views gradually as the training progresses. Experimental results show that our learning framework is effective on several document-matching tasks, including news duplication and legal case retrieval.

In this paper, we study a system in which a sensor forwards status updates to a receiver through an error-prone channel, while the receiver sends the transmission results back to the sensor via a reliable channel. Both channels are subject to random delays. To evaluate the timeliness of the status information at the receiver, we use the Age of Information (AoI) metric. The objective is to design a sampling policy that minimizes the expected time-average AoI, even when the channel statistics (e.g., delay distributions) are unknown. We first review the threshold structure of the optimal offline policy under known channel statistics and then reformulate the design of the online algorithm as a stochastic approximation problem. We propose a Robbins-Monro algorithm to solve this problem and demonstrate that the optimal threshold can be approximated almost surely. Moreover, we prove that the cumulative AoI regret of the online algorithm increases with rate $\mathcal{O}(\ln K)$, where $K$ is the number of successful transmissions. In addition, our algorithm is shown to be minimax order optimal, in the sense that for any online learning algorithm, the cumulative AoI regret up to the $K$-th successful transmissions grows with the rate at least $\Omega(\ln K)$ in the worst case delay distribution. Finally, we improve the stability of the proposed online learning algorithm through a momentum-based stochastic gradient descent algorithm. Simulation results validate the performance of our proposed algorithm.

Full-packet encryption is a technique used by modern evasive Virtual Private Networks (VPNs) to avoid protocol-based flagging from censorship models by disguising their traffic as random noise on the network. Traditional methods for censoring full-packet-encryption based VPN protocols requires assuming a substantial amount of collateral damage, as other non-VPN network traffic that appears random will be blocked. I tested several machine learning-based classification models against the Aggressive Circumvention of Censorship (ACC) protocol, a fully-encrypted evasive VPN protocol which merges strategies from a wide variety of currently in-use evasive VPN protocols. My testing found that while ACC was able to survive our models when compared to random noise, it was easily detectable with minimal collateral damage using several different machine learning models when within a stream of regular network traffic. While resistant to the current techniques deployed by nation-state censors, the ACC protocol and other evasive protocols are potentially subject to packet-based protocol identification utilizing similar classification models.

With the widespread application of machine learning in financial risk management, conventional wisdom suggests that longer training periods and more feature variables contribute to improved model performance. This paper, focusing on mortgage default prediction, empirically discovers a phenomenon that contradicts traditional knowledge: in time series prediction, increased training data timespan and additional non-critical features actually lead to significant deterioration in prediction effectiveness. Using Fannie Mae's mortgage data, the study compares predictive performance across different time window lengths (2012-2022) and feature combinations, revealing that shorter time windows (such as single-year periods) paired with carefully selected key features yield superior prediction results. The experimental results indicate that extended time spans may introduce noise from historical data and outdated market patterns, while excessive non-critical features interfere with the model's learning of core default factors. This research not only challenges the traditional "more is better" approach in data modeling but also provides new insights and practical guidance for feature selection and time window optimization in financial risk prediction.