亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Current quantum hardware prohibits any direct use of large classical datasets. Coresets allow for a succinct description of these large datasets and their solution in a computational task is competitive with the solution on the original dataset. The method of combining coresets with small quantum computers to solve a given task that requires a large number of data points was first introduced by Harrow [arXiv:2004.00026]. In this paper, we apply the coreset method in three different well-studied classical machine learning problems, namely Divisive Clustering, 3-means Clustering, and Gaussian Mixture Model Clustering. We provide a Hamiltonian formulation of the aforementioned problems for which the number of qubits scales linearly with the size of the coreset. Then, we evaluate how the variational quantum eigensolver (VQE) performs on these problems and demonstrate the practical efficiency of coresets when used along with a small quantum computer. We perform noiseless simulations on instances of sizes up to 25 qubits on CUDA Quantum and show that our approach provides comparable performance to classical solvers.

Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other deep learning methods. However, the spatial domain of its input function needs to be identical to its output, which limits its applicability. For instance, the widely used Fourier neural operator (FNO) fails to approximate the operator that maps the boundary condition to the PDE solution. To address this issue, we propose a novel framework called resolution-invariant deep operator (RDO) that decouples the spatial domain of the input and output. RDO is motivated by the Deep operator network (DeepONet) and it does not require retraining the network when the input/output is changed compared with DeepONet. RDO takes functional input and its output is also functional so that it keeps the resolution invariant property of NO. It can also resolve PDEs with complex geometries whereas NO fail. Various numerical experiments demonstrate the advantage of our method over DeepONet and FNO.

Deep generative models are key-enabling technology to computer vision, text generation and large language models. Denoising diffusion probabilistic models (DDPMs) have recently gained much attention due to their ability to generate diverse and high-quality samples in many computer vision tasks, as well as to incorporate flexible model architectures and relatively simple training scheme. Quantum generative models, empowered by entanglement and superposition, have brought new insight to learning classical and quantum data. Inspired by the classical counterpart, we propose the \emph{quantum denoising diffusion probabilistic model} (QuDDPM) to enable efficiently trainable generative learning of quantum data. QuDDPM adopts sufficient layers of circuits to guarantee expressivity, while introduces multiple intermediate training tasks as interpolation between the target distribution and noise to avoid barren plateau and guarantee efficient training. We provide bounds on the learning error and demonstrate QuDDPM's capability in learning correlated quantum noise model, quantum many-body phases and topological structure of quantum data. The results provide a paradigm for versatile and efficient quantum generative learning.

This paper develops a flexible and computationally efficient multivariate volatility model, which allows for dynamic conditional correlations and volatility spillover effects among financial assets. The new model has desirable properties such as identifiability and computational tractability for many assets. A sufficient condition of the strict stationarity is derived for the new process. Two quasi-maximum likelihood estimation methods are proposed for the new model with and without low-rank constraints on the coefficient matrices respectively, and the asymptotic properties for both estimators are established. Moreover, a Bayesian information criterion with selection consistency is developed for order selection, and the testing for volatility spillover effects is carefully discussed. The finite sample performance of the proposed methods is evaluated in simulation studies for small and moderate dimensions. The usefulness of the new model and its inference tools is illustrated by two empirical examples for 5 stock markets and 17 industry portfolios, respectively.

Granular flow problems characterized by large deformations are widespread in various applications, including coastal and geotechnical engineering. The paper deals with the application of a rigid-perfectly plastic two-phase model extended by the Drucker-Prager yield criterion to simulate granular media with a finite volume flow solver (FV). The model refers to the combination of a Bingham fluid and an Eulerian strain measure to assess the failure region of granular dam slides. A monolithic volume-of-fluid (VoF) method is used to distinguish between the air and granular phases, both governed by the incompressible Navier-Stokes equations. The numerical framework enables modeling of large displacements and arbitrary shapes for large-scale applications. The displayed validation and verification focuses on the rigid-perfectly plastic material model for non-cohesive and cohesive materials with varying angles of repose. Results indicate a good agreement of the predicted soil surface and strain results with experimental and numerical data.

This paper investigates the effect of the design matrix on the ability (or inability) to estimate a sparse parameter in linear regression. More specifically, we characterize the optimal rate of estimation when the smallest singular value of the design matrix is bounded away from zero. In addition to this information-theoretic result, we provide and analyze a procedure which is simultaneously statistically optimal and computationally efficient, based on soft thresholding the ordinary least squares estimator. Most surprisingly, we show that the Lasso estimator -- despite its widespread adoption for sparse linear regression -- is provably minimax rate-suboptimal when the minimum singular value is small. We present a family of design matrices and sparse parameters for which we can guarantee that the Lasso with any choice of regularization parameter -- including those which are data-dependent and randomized -- would fail in the sense that its estimation rate is suboptimal by polynomial factors in the sample size. Our lower bound is strong enough to preclude the statistical optimality of all forms of the Lasso, including its highly popular penalized, norm-constrained, and cross-validated variants.

The extensive use of HPC infrastructures and frameworks for running dataintensive applications has led to a growing interest in data partitioning techniques and strategies. In fact, application performance can be heavily affected by how data are partitioned, which in turn depends on the selected size for data blocks, i.e. the block size. Therefore, finding an effective partitioning, i.e. a suitable block size, is a key strategy to speed-up parallel data-intensive applications and increase scalability. This paper describes a methodology, namely BLEST-ML (BLock size ESTimation through Machine Learning), for block size estimation that relies on supervised machine learning techniques. The proposed methodology was evaluated by designing an implementation tailored to dislib, a distributed computing library highly focused on machine learning algorithms built on top of the PyCOMPSs framework. We assessed the effectiveness of the provided implementation through an extensive experimental evaluation considering different algorithms from dislib, datasets, and infrastructures, including the MareNostrum 4 supercomputer. The results we obtained show the ability of BLEST-ML to efficiently determine a suitable way to split a given dataset, thus providing a proof of its applicability to enable the efficient execution of data-parallel applications in high performance environments.

With the development and popularity of sensors installed in manufacturing systems, complex data are collected during manufacturing processes, which brings challenges for traditional process control methods. This paper proposes a novel process control and monitoring method for the complex structure of high-dimensional image-based overlay errors (modeled in tensor form), which are collected in semiconductor manufacturing processes. The proposed method aims to reduce overlay errors using limited control recipes. We first build a high-dimensional process model and propose different tensor-on-vector regression algorithms to estimate parameters in the model to alleviate the curse of dimensionality. Then, based on the estimate of tensor parameters, the exponentially weighted moving average (EWMA) controller for tensor data is designed whose stability is theoretically guaranteed. Considering the fact that low-dimensional control recipes cannot compensate for all high-dimensional disturbances on the image, control residuals are monitored to prevent significant drifts of uncontrollable high-dimensional disturbances. Through extensive simulations and real case studies, the performances of parameter estimation algorithms and the EWMA controller in tensor space are evaluated. Compared with existing image-based feedback controllers, the superiority of our method is verified especially when disturbances are not stable.

It is well-known that decision-making problems from stochastic control can be formulated by means of forward-backward stochastic differential equation (FBSDE). Recently, the authors of Ji et al. 2022 proposed an efficient deep learning-based algorithm which was based on the stochastic maximum principle (SMP). In this paper, we provide a convergence result for this deep SMP-BSDE algorithm and compare its performance with other existing methods. In particular, by adopting a similar strategy as in Han and Long 2020, we derive a posteriori error estimate, and show that the total approximation error can be bounded by the value of the loss functional and the discretization error. We present numerical examples for high-dimensional stochastic control problems, both in case of drift- and diffusion control, which showcase superior performance compared to existing algorithms.

We consider a general multivariate model where univariate marginal distributions are known up to a parameter vector and we are interested in estimating that parameter vector without specifying the joint distribution, except for the marginals. If we assume independence between the marginals and maximize the resulting quasi-likelihood, we obtain a consistent but inefficient QMLE estimator. If we assume a parametric copula (other than independence) we obtain a full MLE, which is efficient but only under a correct copula specification and may be biased if the copula is misspecified. Instead we propose a sieve MLE estimator (SMLE) which improves over QMLE but does not have the drawbacks of full MLE. We model the unknown part of the joint distribution using the Bernstein-Kantorovich polynomial copula and assess the resulting improvement over QMLE and over misspecified FMLE in terms of relative efficiency and robustness. We derive the asymptotic distribution of the new estimator and show that it reaches the relevant semiparametric efficiency bound. Simulations suggest that the sieve MLE can be almost as efficient as FMLE relative to QMLE provided there is enough dependence between the marginals. We demonstrate practical value of the new estimator with several applications. First, we apply SMLE in an insurance context where we build a flexible semi-parametric claim loss model for a scenario where one of the variables is censored. As in simulations, the use of SMLE leads to tighter parameter estimates. Next, we consider financial risk management examples and show how the use of SMLE leads to superior Value-at-Risk predictions. The paper comes with an online archive which contains all codes and datasets.