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Variable selection methods are widely used in molecular biology to detect biomarkers or to infer gene regulatory networks from transcriptomic data. Methods are mainly based on the high-dimensional Gaussian linear regression model and we focus on this framework for this review. We propose a comparison study of variable selection procedures from regularization paths by considering three simulation settings. In the first one, the variables are independent allowing the evaluation of the methods in the theoretical framework used to develop them. In the second setting, two structures of the correlation between variables are considered to evaluate how biological dependencies usually observed affect the estimation. Finally, the third setting mimics the biological complexity of transcription factor regulations, it is the farthest setting from the Gaussian framework. In all the settings, the capacity of prediction and the identification of the explaining variables are evaluated for each method. Our results show that variable selection procedures rely on statistical assumptions that should be carefully checked. The Gaussian assumption and the number of explaining variables are the two key points. As soon as correlation exists, the regularization function Elastic-net provides better results than Lasso. LinSelect, a non-asymptotic model selection method, should be preferred to the eBIC criterion commonly used. Bolasso is a judicious strategy to limit the selection of non explaining variables.

A sentinel network, Ob\'epine, has been designed to monitor SARS-CoV-2 viral load in wastewaters arriving at several tens of wastewater treatment plants in France as an indirect macro-epidemiological parameter. The sources of uncertainty in such monitoring system are numerous and the concentration measurements it provides are left-censored and contain numerous outliers, which biases the results of usual smoothing methods. Hence the need for an adapted pre-processing in order to evaluate the real daily amount of virus arriving to each WWTP. We propose a method based on an auto-regressive model adapted to censored data with outliers. Inference and prediction are produced via a discretised smoother which makes it a very flexible tool. This method is both validated on simulations and on real data from Ob\'epine. The resulting smoothed signal shows a good correlation with other epidemiological indicators and currently contributes to the construction of the wastewater indicators provided each week by Ob\'epine.

In this paper, we consider the multi-armed bandit problem with high-dimensional features. First, we prove a minimax lower bound, $\mathcal{O}\big((\log d)^{\frac{\alpha+1}{2}}T^{\frac{1-\alpha}{2}}+\log T\big)$, for the cumulative regret, in terms of horizon $T$, dimension $d$ and a margin parameter $\alpha\in[0,1]$, which controls the separation between the optimal and the sub-optimal arms. This new lower bound unifies existing regret bound results that have different dependencies on T due to the use of different values of margin parameter $\alpha$ explicitly implied by their assumptions. Second, we propose a simple and computationally efficient algorithm inspired by the general Upper Confidence Bound (UCB) strategy that achieves a regret upper bound matching the lower bound. The proposed algorithm uses a properly centered $\ell_1$-ball as the confidence set in contrast to the commonly used ellipsoid confidence set. In addition, the algorithm does not require any forced sampling step and is thereby adaptive to the practically unknown margin parameter. Simulations and a real data analysis are conducted to compare the proposed method with existing ones in the literature.

Stochastic gradient methods have enabled variational inference for high-dimensional models and large data sets. However, the direction of steepest ascent in the parameter space of a statistical model is given not by the commonly used Euclidean gradient, but the natural gradient which premultiplies the Euclidean gradient by the inverse of the Fisher information matrix. Use of natural gradients in optimization can improve convergence significantly, but inverting the Fisher information matrix is daunting in high-dimensions. The contribution of this article is twofold. First, we derive the natural gradient updates of a Gaussian variational approximation in terms of the mean and Cholesky factor of the covariance matrix, and show that these updates depend only on the first derivative of the variational objective function. Second, we derive complete natural gradient updates for structured variational approximations with a minimal conditional exponential family representation, which include highly flexible mixture of exponential family distributions that can fit skewed or multimodal posteriors. These updates, albeit more complex than those presented priorly, account fully for the dependence between the mixing distribution and the distributions of the components. Further experiments will be carried out to evaluate the performance of proposed methods.

In this paper we consider the problem of quickly detecting changes in hidden Markov models (HMMs) in a Bayesian setting, as well as several structured generalisations including changes in statistically periodic processes, quickest detection of a Markov process across a sensor array, quickest detection of a moving target in a sensor network and quickest change detection (QCD) in multistream data. Our main result establishes an optimal Bayesian HMM QCD rule with a threshold structure. This framework and proof techniques allow us to elegantly establish optimal rules for the structured generalisations by showing that these problems are special cases of the Bayesian HMM QCD problem. The threshold structure enables us to develop bounds to characterise the performance of our optimal rule and provide an efficient method for computing the test statistic. Finally, we examine the performance of our rule in several simulation examples and propose a technique for calculating the optimal threshold.

A recently proposed SLOPE estimator (arXiv:1407.3824) has been shown to adaptively achieve the minimax $\ell_2$ estimation rate under high-dimensional sparse linear regression models (arXiv:1503.08393). Such minimax optimality holds in the regime where the sparsity level $k$, sample size $n$, and dimension $p$ satisfy $k/p \rightarrow 0$, $k\log p/n \rightarrow 0$. In this paper, we characterize the estimation error of SLOPE under the complementary regime where both $k$ and $n$ scale linearly with $p$, and provide new insights into the performance of SLOPE estimators. We first derive a concentration inequality for the finite sample mean square error (MSE) of SLOPE. The quantity that MSE concentrates around takes a complicated and implicit form. With delicate analysis of the quantity, we prove that among all SLOPE estimators, LASSO is optimal for estimating $k$-sparse parameter vectors that do not have tied non-zero components in the low noise scenario. On the other hand, in the large noise scenario, the family of SLOPE estimators are sub-optimal compared with bridge regression such as the Ridge estimator.

Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space, such as the simplex, the time-discretisation error can dominate when we are near the boundary of the space. We demonstrate that while current SGMCMC methods for the simplex perform well in certain cases, they struggle with sparse simplex spaces; when many of the components are close to zero. However, most popular large-scale applications of Bayesian inference on simplex spaces, such as network or topic models, are sparse. We argue that this poor performance is due to the biases of SGMCMC caused by the discretization error. To get around this, we propose the stochastic CIR process, which removes all discretization error and we prove that samples from the stochastic CIR process are asymptotically unbiased. Use of the stochastic CIR process within a SGMCMC algorithm is shown to give substantially better performance for a topic model and a Dirichlet process mixture model than existing SGMCMC approaches.

We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.

Detecting objects and estimating their pose remains as one of the major challenges of the computer vision research community. There exists a compromise between localizing the objects and estimating their viewpoints. The detector ideally needs to be view-invariant, while the pose estimation process should be able to generalize towards the category-level. This work is an exploration of using deep learning models for solving both problems simultaneously. For doing so, we propose three novel deep learning architectures, which are able to perform a joint detection and pose estimation, where we gradually decouple the two tasks. We also investigate whether the pose estimation problem should be solved as a classification or regression problem, being this still an open question in the computer vision community. We detail a comparative analysis of all our solutions and the methods that currently define the state of the art for this problem. We use PASCAL3D+ and ObjectNet3D datasets to present the thorough experimental evaluation and main results. With the proposed models we achieve the state-of-the-art performance in both datasets.

This study considers the 3D human pose estimation problem in a single RGB image by proposing a conditional random field (CRF) model over 2D poses, in which the 3D pose is obtained as a byproduct of the inference process. The unary term of the proposed CRF model is defined based on a powerful heat-map regression network, which has been proposed for 2D human pose estimation. This study also presents a regression network for lifting the 2D pose to 3D pose and proposes the prior term based on the consistency between the estimated 3D pose and the 2D pose. To obtain the approximate solution of the proposed CRF model, the N-best strategy is adopted. The proposed inference algorithm can be viewed as sequential processes of bottom-up generation of 2D and 3D pose proposals from the input 2D image based on deep networks and top-down verification of such proposals by checking their consistencies. To evaluate the proposed method, we use two large-scale datasets: Human3.6M and HumanEva. Experimental results show that the proposed method achieves the state-of-the-art 3D human pose estimation performance.