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

Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the coefficients of the polynomial. However, in many applications, the input may be partially known or not known at all, rendering conventional regression approaches not applicable. In this paper, we formally state the (potentially partial) blind regression problem, illustrate some of its theoretical properties, and propose algorithmic approaches to solve it. As a case-study, we apply our methods to a jitter-correction problem and corroborate its performance.

We propose the Terminating-Random Experiments (T-Rex) selector, a fast variable selection method for high-dimensional data. The T-Rex selector controls a user-defined target false discovery rate (FDR) while maximizing the number of selected variables. This is achieved by fusing the solutions of multiple early terminated random experiments. The experiments are conducted on a combination of the original predictors and multiple sets of randomly generated dummy predictors. A finite sample proof based on martingale theory for the FDR control property is provided. Numerical simulations confirm that the FDR is controlled at the target level while allowing for a high power. We prove under mild conditions that the dummies can be sampled from any univariate probability distribution with finite expectation and variance. The computational complexity of the proposed method is linear in the number of variables. The T-Rex selector outperforms state-of-the-art methods for FDR control on a simulated genome-wide association study (GWAS), while its sequential computation time is more than two orders of magnitude lower than that of the strongest benchmark methods. The open source R package TRexSelector containing the implementation of the T-Rex selector is available on CRAN.

We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression coefficient tensor. Traditional tensor regression methods making use of the Tucker decomposition either assume the dimension of the core tensor to be known or estimate it via cross-validation or some model selection criteria. However, no existing method can simultaneously estimate the model dimension (the dimension of the core tensor) and other model parameters. To fill this gap, we develop an efficient Markov Chain Monte Carlo (MCMC) algorithm to estimate both the model dimension and parameters for posterior inference. Besides the MCMC sampler, we also develop an ultra-fast optimization-based computing algorithm wherein the maximum a posteriori estimators for parameters are computed, and the model dimension is optimized via a simulated annealing algorithm. The proposed Bayesian framework provides a natural way for uncertainty quantification. Through extensive simulation studies, we evaluate the proposed Bayesian tensor-on-tensor regression model and show its superior performance compared to alternative methods. We also demonstrate its practical effectiveness by applying it to two real-world datasets, including facial imaging data and 3D motion data.

Variational Bayes methods are a scalable estimation approach for many complex state space models. However, existing methods exhibit a trade-off between accurate estimation and computational efficiency. This paper proposes a variational approximation that mitigates this trade-off. This approximation is based on importance densities that have been proposed in the context of efficient importance sampling. By directly conditioning on the observed data, the proposed method produces an accurate approximation to the exact posterior distribution. Because the steps required for its calibration are computationally efficient, the approach is faster than existing variational Bayes methods. The proposed method can be applied to any state space model that has a closed-form measurement density function and a state transition distribution that belongs to the exponential family of distributions. We illustrate the method in numerical experiments with stochastic volatility models and a macroeconomic empirical application using a high-dimensional state space model.

Variable selection is crucial for sparse modeling in this age of big data. Missing values are common in data, and make variable selection more complicated. The approach of multiple imputation (MI) results in multiply imputed datasets for missing values, and has been widely applied in various variable selection procedures. However, directly performing variable selection on the whole MI data or bootstrapped MI data may not be worthy in terms of computation cost. To fast identify the active variables in the linear regression model, we propose the adaptive grafting procedure with three pooling rules on MI data. The proposed methods proceed iteratively, which starts from finding the active variables based on the complete case subset and then expand the working data matrix with both the number of active variables and available observations. A comprehensive simulation study shows the selection accuracy in different aspects and computational efficiency of the proposed methods. Two real-life examples illustrate the strength of the proposed methods.

Deep Learning-based image synthesis techniques have been applied in healthcare research for generating medical images to support open research and augment medical datasets. Training generative adversarial neural networks (GANs) usually require large amounts of training data. Federated learning (FL) provides a way of training a central model using distributed data while keeping raw data locally. However, given that the FL server cannot access the raw data, it is vulnerable to backdoor attacks, an adversarial by poisoning training data. Most backdoor attack strategies focus on classification models and centralized domains. It is still an open question if the existing backdoor attacks can affect GAN training and, if so, how to defend against the attack in the FL setting. In this work, we investigate the overlooked issue of backdoor attacks in federated GANs (FedGANs). The success of this attack is subsequently determined to be the result of some local discriminators overfitting the poisoned data and corrupting the local GAN equilibrium, which then further contaminates other clients when averaging the generator's parameters and yields high generator loss. Therefore, we proposed FedDetect, an efficient and effective way of defending against the backdoor attack in the FL setting, which allows the server to detect the client's adversarial behavior based on their losses and block the malicious clients. Our extensive experiments on two medical datasets with different modalities demonstrate the backdoor attack on FedGANs can result in synthetic images with low fidelity. After detecting and suppressing the detected malicious clients using the proposed defense strategy, we show that FedGANs can synthesize high-quality medical datasets (with labels) for data augmentation to improve classification models' performance.

High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix structure and temporal dynamics in such data, Wang et al. (2017) proposed a matrix factor model that is shown to provide effective analysis. In this paper, we establish a general framework for incorporating domain or prior knowledge in the matrix factor model through linear constraints. The proposed framework is shown to be useful in achieving parsimonious parameterization, facilitating interpretation of the latent matrix factor, and identifying specific factors of interest. Fully utilizing the prior-knowledge-induced constraints results in more efficient and accurate modeling, inference, dimension reduction as well as a clear and better interpretation of the results. In this paper, constrained, multi-term, and partially constrained factor models for matrix-variate time series are developed, with efficient estimation procedures and their asymptotic properties. We show that the convergence rates of the constrained factor loading matrices are much faster than those of the conventional matrix factor analysis under many situations. Simulation studies are carried out to demonstrate the finite-sample performance of the proposed method and its associated asymptotic properties. We illustrate the proposed model with three applications, where the constrained matrix-factor models outperform their unconstrained counterparts in the power of variance explanation under the out-of-sample 10-fold cross-validation setting.

Deep learning shows excellent potential in generation tasks thanks to deep latent representation. Generative models are classes of models that can generate observations randomly concerning certain implied parameters. Recently, the diffusion Model has become a rising class of generative models by its power-generating ability. Nowadays, great achievements have been reached. More applications except for computer vision, speech generation, bioinformatics, and natural language processing are to be explored in this field. However, the diffusion model has its genuine drawback of a slow generation process, single data types, low likelihood, and the inability for dimension reduction. They are leading to many enhanced works. This survey makes a summary of the field of the diffusion model. We first state the main problem with two landmark works -- DDPM and DSM, and a unified landmark work -- Score SDE. Then, we present improved techniques for existing problems in the diffusion-based model field, including speed-up improvement For model speed-up improvement, data structure diversification, likelihood optimization, and dimension reduction. Regarding existing models, we also provide a benchmark of FID score, IS, and NLL according to specific NFE. Moreover, applications with diffusion models are introduced including computer vision, sequence modeling, audio, and AI for science. Finally, there is a summarization of this field together with limitations \& further directions. The summation of existing well-classified methods is in our Github://github.com/chq1155/A-Survey-on-Generative-Diffusion-Model.

Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the data, which are common features in many real-world statistics and machine learning applications. In this work, we propose a Bayesian nonparametric approach to linear regression that performs variable selection while accounting for outliers and heteroskedasticity. Our proposed model is an instance of a Dirichlet process scale mixture model with the advantage that we can derive the full conditional distributions of all parameters in closed form, hence producing an efficient Gibbs sampler for posterior inference. Moreover, we present how to extend the model to account for heavy-tailed response variables. The performance of the model is tested against competing algorithms on synthetic and real-world datasets.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.