We prove a semiparametric Bernstein-von Mises theorem for a partially linear regression model with independent priors for the low-dimensional parameter of interest and the infinite-dimensional nuisance parameters. Our result mitigates a prior invariance condition that arises from a loss of information in not knowing the nuisance parameter. The key device is a reparametrization of the regression function that is in the spirit of profile likelihood, and, as a result, the prior invariance condition is automatically satisfied because there is no loss of information in the transformed model. As these prior stability conditions can impose strong restrictions on the underlying data-generating process, our results provide a more robust posterior asymptotic normality theorem than the original parametrization of the partially linear model.
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We study the question of whether submodular functions of random variables satisfying various notions of negative dependence satisfy Chernoff-like concentration inequalities. We prove such a concentration inequality for the lower tail when the random variables satisfy negative association or negative regression, resolving an open problem raised in (\citet{approx/QiuS22}). Previous work showed such concentration results for random variables that come from specific dependent-rounding algorithms (\citet{focs/ChekuriVZ10,soda/HarveyO14}). We discuss some applications of our results to combinatorial optimization and beyond.
Distributed stochastic gradient descent (SGD) with gradient compression has become a popular communication-efficient solution for accelerating distributed learning. One commonly used method for gradient compression is Top-K sparsification, which sparsifies the gradients by a fixed degree during model training. However, there has been a lack of an adaptive approach to adjust the sparsification degree to maximize the potential of the model's performance or training speed. This paper proposes a novel adaptive Top-K in SGD framework that enables an adaptive degree of sparsification for each gradient descent step to optimize the convergence performance by balancing the trade-off between communication cost and convergence error. Firstly, an upper bound of convergence error is derived for the adaptive sparsification scheme and the loss function. Secondly, an algorithm is designed to minimize the convergence error under the communication cost constraints. Finally, numerical results on the MNIST and CIFAR-10 datasets demonstrate that the proposed adaptive Top-K algorithm in SGD achieves a significantly better convergence rate compared to state-of-the-art methods, even after considering error compensation.
We propose a local model-checking proof system for a fragment of CTL. The rules of the proof system are motivated by the well-known fixed-point characterisation of CTL based on unfolding of the temporal operators. To guarantee termination of proofs, we tag the sequents of our proof system with the set of states that have already been explored for the respective temporal formula. We define the semantics of tagged sequents, and then state and prove soundness and completeness of the proof system, as well as termination of proof search for finite-state models.
The renowned proverb, Numbers do not lie, underscores the reliability and insight that lie beneath numbers, a concept of undisputed importance, especially in economics and finance etc. Despite the prosperity of Benford's Law in the first digit analysis, its scope fails to remain comprehensiveness when it comes to deciphering the laws of number. This paper delves into number laws by taking the financial statements of China real estate as a representative, quantitatively study not only the first digit, but also depict the other two dimensions of numbers: frequency and length. The research outcomes transcend mere reservations about data manipulation and open the door to discussions surrounding number diversity and the delineation of the usage insights. This study wields both economic significance and the capacity to foster a deeper comprehension of numerical phenomena.
In this letter, the average mutual information (AMI) of generalized quadrature spatial modulation (GQSM) is first derived for continuous-input continuous-output channels. Our mathematical analysis shows that the calculation error induced by Monte Carlo integration increases exponentially with the signal-to-noise ratio. This nature of GQSM is resolved by deriving a closed-form expression. The derived AMI is compared with other related SM schemes and evaluated for different antenna activation patterns. Our results show that an equiprobable antenna selection method slightly decreases AMI of symbols, while the method significantly improves AMI in total.
We consider relational semantics (R-models) for the Lambek calculus extended with intersection and explicit constants for zero and unit. For its variant without constants and a restriction which disallows empty antecedents, Andreka and Mikulas (1994) prove strong completeness. We show that it fails without this restriction, but, on the other hand, prove weak completeness for non-standard interpretation of constants. For the standard interpretation, even weak completeness fails. The weak completeness result extends to an infinitary setting, for so-called iterative divisions (Kleene star under division). We also prove strong completeness results for product-free fragments.
In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the problem, then we state and prove some convergence results, for which we provide the corresponding mechanical interpretation. Next, we turn to the numerical approximation of the problem based on a finite element scheme. We use a relaxation method to solve the discrete problems that we implement on the computer. Using this method, we provide numerical simulations which validate our convergence results.
The far-field channel model has historically been used in wireless communications due to the simplicity of mathematical modeling and convenience for algorithm design, and its validity for relatively small array apertures. With the need for high data rates, low latency, and ubiquitous connectivity in the sixth generation (6G) of communication systems, new technology enablers such as extremely large antenna arrays (ELAA), reconfigurable intelligent surfaces (RISs), and distributed multiple-input-multiple-output (D-MIMO) systems will be adopted. These enablers not only aim to improve communication services but also have an impact on localization and sensing (L\&S), which are expected to be integrated into future wireless systems. Despite appearing in different scenarios and supporting different frequency bands, these enablers share the so-called near-field (NF) features, which will provide extra geometric information. In this work, starting from a brief description of NF channel features, we highlight the opportunities and challenges for 6G NF L\&S.
We propose personalized Tucker decomposition (perTucker) to address the limitations of traditional tensor decomposition methods in capturing heterogeneity across different datasets. perTucker decomposes tensor data into shared global components and personalized local components. We introduce a mode orthogonality assumption and develop a proximal gradient regularized block coordinate descent algorithm that is guaranteed to converge to a stationary point. By learning unique and common representations across datasets, we demonstrate perTucker's effectiveness in anomaly detection, client classification, and clustering through a simulation study and two case studies on solar flare detection and tonnage signal classification.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
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