Selecting the step size for the Metropolis-adjusted Langevin algorithm (MALA) is necessary in order to obtain satisfactory performance. However, finding an adequate step size for an arbitrary target distribution can be a difficult task and even the best step size can perform poorly in specific regions of the space when the target distribution is sufficiently complex. To resolve this issue we introduce autoMALA, a new Markov chain Monte Carlo algorithm based on MALA that automatically sets its step size at each iteration based on the local geometry of the target distribution. We prove that autoMALA has the correct invariant distribution, despite continual automatic adjustments of the step size. Our experiments demonstrate that autoMALA is competitive with related state-of-the-art MCMC methods, in terms of the number of log density evaluations per effective sample, and it outperforms state-of-the-art samplers on targets with varying geometries. Furthermore, we find that autoMALA tends to find step sizes comparable to optimally-tuned MALA when a fixed step size suffices for the whole domain.
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Click-through rate (CTR) Prediction is a crucial task in personalized information retrievals, such as industrial recommender systems, online advertising, and web search. Most existing CTR Prediction models utilize explicit feature interactions to overcome the performance bottleneck of implicit feature interactions. Hence, deep CTR models based on parallel structures (e.g., DCN, FinalMLP, xDeepFM) have been proposed to obtain joint information from different semantic spaces. However, these parallel subcomponents lack effective supervisory signals, making it challenging to efficiently capture valuable multi-views feature interaction information in different semantic spaces. To address this issue, we propose a simple yet effective novel CTR model: Contrast-enhanced Through Network for CTR (CETN), so as to ensure the diversity and homogeneity of feature interaction information. Specifically, CETN employs product-based feature interactions and the augmentation (perturbation) concept from contrastive learning to segment different semantic spaces, each with distinct activation functions. This improves diversity in the feature interaction information captured by the model. Additionally, we introduce self-supervised signals and through connection within each semantic space to ensure the homogeneity of the captured feature interaction information. The experiments and research conducted on four real datasets demonstrate that our model consistently outperforms twenty baseline models in terms of AUC and Logloss.
The field of adversarial textual attack has significantly grown over the last few years, where the commonly considered objective is to craft adversarial examples (AEs) that can successfully fool the target model. However, the imperceptibility of attacks, which is also essential for practical attackers, is often left out by previous studies. In consequence, the crafted AEs tend to have obvious structural and semantic differences from the original human-written text, making them easily perceptible. In this work, we advocate leveraging multi-objectivization to address such issue. Specifically, we reformulate the problem of crafting AEs as a multi-objective optimization problem, where the attack imperceptibility is considered as an auxiliary objective. Then, we propose a simple yet effective evolutionary algorithm, dubbed HydraText, to solve this problem. To the best of our knowledge, HydraText is currently the only approach that can be effectively applied to both score-based and decision-based attack settings. Exhaustive experiments involving 44237 instances demonstrate that HydraText consistently achieves competitive attack success rates and better attack imperceptibility than the recently proposed attack approaches. A human evaluation study also shows that the AEs crafted by HydraText are more indistinguishable from human-written text. Finally, these AEs exhibit good transferability and can bring notable robustness improvement to the target model by adversarial training.
The classical two-sample test of Kolmogorov-Smirnov (KS) is widely used to test whether empirical samples come from the same distribution. Even though most statistical packages provide an implementation, carrying out the test in big data settings can be challenging because it requires a full sort of the data. The popular Apache Spark system for big data processing provides a 1-sample KS test, but not the 2-sample version. Moreover, recent Spark versions provide the approxQuantile method for querying $\epsilon$-approximate quantiles. We build on approxQuantile to propose a variation of the classical Kolmogorov-Smirnov two-sample test that constructs approximate cumulative distribution functions (CDF) from $\epsilon$-approximate quantiles. We derive error bounds of the approximate CDF and show how to use this information to carry out KS tests. Psuedocode for the approach requires 15 executable lines. A Python implementation appears in the appendix.
Leveraging the potential of Virtualised Network Functions (VNFs) requires a clear understanding of the link between resource consumption and performance. The current state of the art tries to do that by utilising Machine Learning (ML) and specifically Supervised Learning (SL) models for given network environments and VNF types assuming single-objective optimisation targets. Taking a different approach poses a novel VNF profiler optimising multi-resource type allocation and performance objectives using adapted Reinforcement Learning (RL). Our approach can meet Key Performance Indicator (KPI) targets while minimising multi-resource type consumption and optimising the VNF output rate compared to existing single-objective solutions. Our experimental evaluation with three real-world VNF types over a total of 39 study scenarios (13 per VNF), for three resource types (virtual CPU, memory, and network link capacity), verifies the accuracy of resource allocation predictions and corresponding successful profiling decisions via a benchmark comparison between our RL model and SL models. We also conduct a complementary exhaustive search-space study revealing that different resources impact performance in varying ways per VNF type, implying the necessity of multi-objective optimisation, individualised examination per VNF type, and adaptable online profile learning, such as with the autonomous online learning approach of iOn-Profiler.
Compressed Sensing (CS) encompasses a broad array of theoretical and applied techniques for recovering signals, given partial knowledge of their coefficients. Its applications span various fields, including mathematics, physics, engineering, and several medical sciences. Motivated by our interest in the mathematics behind Magnetic Resonance Imaging (MRI) and CS, we employ convex analysis techniques to analytically determine equivalents of Lagrange multipliers for optimization problems with inequality constraints, specifically a weighted LASSO with voxel-wise weighting. We investigate this problem under assumptions on the fidelity term $\Vert{Ax-b}\Vert_2^2$, either concerning the sign of its gradient or orthogonality-like conditions of its matrix. To be more precise, we either require the sign of each coordinate of $2(Ax-b)^TA$ to be fixed within a rectangular neighborhood of the origin, with the side lengths of the rectangle dependent on the constraints, or we assume $A^TA$ to be diagonal. The objective of this work is to explore the relationship between Lagrange multipliers and the constraints of a weighted variant of LASSO, specifically in the mentioned cases where this relationship can be computed explicitly. As they scale the regularization terms of the weighted LASSO, Lagrange multipliers serve as tuning parameters for the weighted LASSO, prompting the question of their potential effective use as tuning parameters in applications like MR image reconstruction and denoising. This work represents an initial step in this direction.
The Spatial Pattern Matching (SPM) query allows for the retrieval of Points of Interest (POIs) based on spatial patterns defined by keywords and distance criteria. However, it does not consider the connectivity between POIs. In this study, we introduce the Qualitative and Quantitative Spatial Pattern Matching (QQ-SPM) query, an extension of the SPM query that incorporates qualitative connectivity constraints. To answer the proposed query type, we propose the QQESPM algorithm, which adapts the state-of-the-art ESPM algorithm to handle connectivity constraints. Performance tests comparing QQESPM to a baseline approach demonstrate QQESPM's superiority in addressing the proposed query type.
We propose a new method called the Metropolis-adjusted Mirror Langevin algorithm for approximate sampling from distributions whose support is a compact and convex set. This algorithm adds an accept-reject filter to the Markov chain induced by a single step of the mirror Langevin algorithm (Zhang et al., 2020), which is a basic discretisation of the mirror Langevin dynamics. Due to the inclusion of this filter, our method is unbiased relative to the target, while known discretisations of the mirror Langevin dynamics including the mirror Langevin algorithm have an asymptotic bias. We give upper bounds for the mixing time of the proposed algorithm when the potential is relatively smooth, convex, and Lipschitz with respect to a self-concordant mirror function. As a consequence of the reversibility of the Markov chain induced by the algorithm, we obtain an exponentially better dependence on the error tolerance for approximate sampling. We also present numerical experiments that corroborate our theoretical findings.
Quantum computing devices are believed to be powerful in solving the prime factorization problem, which is at the heart of widely deployed public-key cryptographic tools. However, the implementation of Shor's quantum factorization algorithm requires significant resources scaling linearly with the number size; taking into account an overhead that is required for quantum error correction the estimation is that 20 millions of (noisy) physical qubits are required for factoring 2048-bit RSA key in 8 hours. Recent proposal by Yan et al. claims a possibility of solving the factorization problem with sublinear quantum resources. As we demonstrate in our work, this proposal lacks systematic analysis of the computational complexity of the classical part of the algorithm, which exploits the Schnorr's lattice-based approach. We provide several examples illustrating the need in additional resource analysis for the proposed quantum factorization algorithm.
This manuscript is devoted to investigating the conservation laws of incompressible Navier-Stokes equations(NSEs), written in the energy-momentum-angular momentum conserving(EMAC) formulation, after being linearized by the two-level methods. With appropriate correction steps(e.g., Stoke/Newton corrections), we show that the two-level methods, discretized from EMAC NSEs, could preserve momentum, angular momentum, and asymptotically preserve energy. Error estimates and (asymptotic) conservative properties are analyzed and obtained, and numerical experiments are conducted to validate the theoretical results, mainly confirming that the two-level linearized methods indeed possess the property of (almost) retainability on conservation laws. Moreover, experimental error estimates and optimal convergence rates of two newly defined types of pressure approximation in EMAC NSEs are also obtained.
While question answering over knowledge bases (KBQA) has shown progress in addressing factoid questions, KBQA with numerical reasoning remains relatively unexplored. In this paper, we focus on the complex numerical reasoning in KBQA and propose a new task, NR-KBQA, which necessitates the ability to perform both multi-hop reasoning and numerical reasoning. We design a logic form in Python format called PyQL to represent the reasoning process of numerical reasoning questions. To facilitate the development of NR-KBQA, we present a large dataset called MarkQA, which is automatically constructed from a small set of seeds. Each question in MarkQA is equipped with its corresponding SPARQL query, alongside the step-by-step reasoning process in the QDMR format and PyQL program. Experimental results of some state-of-the-art QA methods on the MarkQA show that complex numerical reasoning in KBQA faces great challenges.
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