The effectiveness of graphical recommender system depends on the quantity and quality of negative sampling. This paper selects some typical recommender system models, as well as some latest negative sampling strategies on the models as baseline. Based on typical graphical recommender model, we divide sample region into assigned-n areas and use AdaSim to give different weight to these areas to form positive set and negative set. Because of the volume and significance of negative items, we also proposed a subset selection model to narrow the core negative samples.
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This paper introduces a formulation of the variable density incompressible Navier-Stokes equations by modifying the nonlinear terms in a consistent way. For Galerkin discretizations, the formulation leads to full discrete conservation of mass, squared density, momentum, angular momentum and kinetic energy without the divergence-free constraint being strongly enforced. In addition to favorable conservation properties, the formulation is shown to make the density field invariant to global shifts. The effect of viscous regularizations on conservation properties is also investigated. Numerical tests validate the theory developed in this work. The new formulation shows superior performance compared to other formulations from the literature, both in terms of accuracy for smooth problems and in terms of robustness.
We prove a discrete analogue for the composition of the fractional integral and Caputo derivative. This result is relevant in numerical analysis of fractional PDEs when one discretizes the Caputo derivative with the so-called L1 scheme. The proof is based on asymptotic evaluation of the discrete sums with the use of the Euler-Maclaurin summation formula.
Model-based sequential approaches to discrete "black-box" optimization, including Bayesian optimization techniques, often access the same points multiple times for a given objective function in interest, resulting in many steps to find the global optimum. Here, we numerically study the effect of a postprocessing method on Bayesian optimization that strictly prohibits duplicated samples in the dataset. We find the postprocessing method significantly reduces the number of sequential steps to find the global optimum, especially when the acquisition function is of maximum a posterior estimation. Our results provide a simple but general strategy to solve the slow convergence of Bayesian optimization for high-dimensional problems.
This paper studies the computational and statistical aspects of quantile and pseudo-Huber tensor decomposition. The integrated investigation of computational and statistical issues of robust tensor decomposition poses challenges due to the non-smooth loss functions. We propose a projected sub-gradient descent algorithm for tensor decomposition, equipped with either the pseudo-Huber loss or the quantile loss. In the presence of both heavy-tailed noise and Huber's contamination error, we demonstrate that our algorithm exhibits a so-called phenomenon of two-phase convergence with a carefully chosen step size schedule. The algorithm converges linearly and delivers an estimator that is statistically optimal with respect to both the heavy-tailed noise and arbitrary corruptions. Interestingly, our results achieve the first minimax optimal rates under Huber's contamination model for noisy tensor decomposition. Compared with existing literature, quantile tensor decomposition removes the requirement of specifying a sparsity level in advance, making it more flexible for practical use. We also demonstrate the effectiveness of our algorithms in the presence of missing values. Our methods are subsequently applied to the food balance dataset and the international trade flow dataset, both of which yield intriguing findings.
Accurate predictive models of the visual cortex neural response to natural visual stimuli remain a challenge in computational neuroscience. In this work, we introduce V1T, a novel Vision Transformer based architecture that learns a shared visual and behavioral representation across animals. We evaluate our model on two large datasets recorded from mouse primary visual cortex and outperform previous convolution-based models by more than 12.7% in prediction performance. Moreover, we show that the self-attention weights learned by the Transformer correlate with the population receptive fields. Our model thus sets a new benchmark for neural response prediction and can be used jointly with behavioral and neural recordings to reveal meaningful characteristic features of the visual cortex.
This work considers Bayesian experimental design for the inverse boundary value problem of linear elasticity in a two-dimensional setting. The aim is to optimize the positions of compactly supported pressure activations on the boundary of the examined body in order to maximize the value of the resulting boundary deformations as data for the inverse problem of reconstructing the Lam\'e parameters inside the object. We resort to a linearized measurement model and adopt the framework of Bayesian experimental design, under the assumption that the prior and measurement noise distributions are mutually independent Gaussians. This enables the use of the standard Bayesian A-optimality criterion for deducing optimal positions for the pressure activations. The (second) derivatives of the boundary measurements with respect to the Lam\'e parameters and the positions of the boundary pressure activations are deduced to allow minimizing the corresponding objective function, i.e., the trace of the covariance matrix of the posterior distribution, by a gradient-based optimization algorithm. Two-dimensional numerical experiments are performed to demonstrate the functionality of our approach.
Binary responses arise in a multitude of statistical problems, including binary classification, bioassay, current status data problems and sensitivity estimation. There has been an interest in such problems in the Bayesian nonparametrics community since the early 1970s, but inference given binary data is intractable for a wide range of modern simulation-based models, even when employing MCMC methods. Recently, Christensen (2023) introduced a novel simulation technique based on counting permutations, which can estimate both posterior distributions and marginal likelihoods for any model from which a random sample can be generated. However, the accompanying implementation of this technique struggles when the sample size is too large (n > 250). Here we present perms, a new implementation of said technique which is substantially faster and able to handle larger data problems than the original implementation. It is available both as an R package and a Python library. The basic usage of perms is illustrated via two simple examples: a tractable toy problem and a bioassay problem. A more complex example involving changepoint analysis is also considered. We also cover the details of the implementation and illustrate the computational speed gain of perms via a simple simulation study.
Benefiting from the development of deep learning, text-to-speech (TTS) techniques using clean speech have achieved significant performance improvements. The data collected from real scenes often contains noise and generally needs to be denoised by speech enhancement models. Noise-robust TTS models are often trained using the enhanced speech, which thus suffer from speech distortion and background noise that affect the quality of the synthesized speech. Meanwhile, it was shown that self-supervised pre-trained models exhibit excellent noise robustness on many speech tasks, implying that the learned representation has a better tolerance for noise perturbations. In this work, we therefore explore pre-trained models to improve the noise robustness of TTS models. Based on HiFi-GAN, we first propose a representation-to-waveform vocoder, which aims to learn to map the representation of pre-trained models to the waveform. We then propose a text-to-representation FastSpeech2 model, which aims to learn to map text to pre-trained model representations. Experimental results on the LJSpeech and LibriTTS datasets show that our method outperforms those using speech enhancement methods in both subjective and objective metrics. Audio samples are available at: //zqs01.github.io/rep2wav.
This paper studies the cosine as basis function for the approximation of univariate and continuous functions without memory. This work studies a supervised learning to obtain the approximation coefficients, instead of using the Discrete Cosine Transform (DCT). Due to the finite dynamics and orthogonality of the cosine basis functions, simple gradient algorithms, such as the Normalized Least Mean Squares (NLMS), can benefit from it and present a controlled and predictable convergence time and error misadjustment. Due to its simplicity, the proposed technique ranks as the best in terms of learning quality versus complexity, and it is presented as an attractive technique to be used in more complex supervised learning systems. Simulations illustrate the performance of the approach. This paper celebrates the 50th anniversary of the publication of the DCT by Nasir Ahmed in 1973.
We provide a new sequent calculus that enjoys syntactic cut-elimination and strongly terminating backward proof search for the intuitionistic Strong L\"ob logic $\sf{iSL}$, an intuitionistic modal logic with a provability interpretation. A novel measure on sequents is used to prove both the termination of the naive backward proof search strategy, and the admissibility of cut in a syntactic and direct way, leading to a straightforward cut-elimination procedure. All proofs have been formalised in the interactive theorem prover Coq.
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