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

Implementations in R of classical general-purpose algorithms for local optimization generally have two major limitations which cause difficulties in applications to complex problems: too loose convergence criteria and too long calculation time. By relying on a Marquardt-Levenberg algorithm (MLA), a Newton-like method particularly robust for solving local optimization problems, we provide with marqLevAlg package an efficient and general-purpose local optimizer which (i) prevents convergence to saddle points by using a stringent convergence criterion based on the relative distance to minimum/maximum in addition to the stability of the parameters and of the objective function; and (ii) reduces the computation time in complex settings by allowing parallel calculations at each iteration. We demonstrate through a variety of cases from the literature that our implementation reliably and consistently reaches the optimum (even when other optimizers fail), and also largely reduces computational time in complex settings through the example of maximum likelihood estimation of different sophisticated statistical models.

The past decade has witnessed a surge of endeavors in statistical inference for high-dimensional sparse regression, particularly via de-biasing or relaxed orthogonalization. Nevertheless, these techniques typically require a more stringent sparsity condition than needed for estimation consistency, which seriously limits their practical applicability. To alleviate such constraint, we propose to exploit the identifiable features to residualize the design matrix before performing debiasing-based inference over the parameters of interest. This leads to a hybrid orthogonalization (HOT) technique that performs strict orthogonalization against the identifiable features but relaxed orthogonalization against the others. Under an approximately sparse model with a mixture of identifiable and unidentifiable signals, we establish the asymptotic normality of the HOT test statistic while accommodating as many identifiable signals as consistent estimation allows. The efficacy of the proposed test is also demonstrated through simulation and analysis of a stock market dataset.

We develop a rapid and accurate contour method for the solution of time-fractional PDEs. The method inverts the Laplace transform via an optimised stable quadrature rule, suitable for infinite-dimensional operators, whose error decreases like $\exp(-cN/\log(N))$ for $N$ quadrature points. The method is parallisable, avoids having to resolve singularities of the solution as $t\downarrow 0$, and avoids the large memory consumption that can be a challenge for time-stepping methods applied to time-fractional PDEs. The ODEs resulting from quadrature are solved using adaptive sparse spectral methods that converge exponentially with optimal linear complexity. These solutions of ODEs are reused for different times. We provide a complete analysis of our approach for fractional beam equations used to model small-amplitude vibration of viscoelastic materials with a fractional Kelvin-Voigt stress-strain relationship. We calculate the system's energy evolution over time and the surface deformation in cases of both constant and non-constant viscoelastic parameters. An infinite-dimensional ``solve-then-discretise'' approach considerably simplifies the analysis, which studies the generalisation of the numerical range of a quasi-linearisation of a suitable operator pencil. This allows us to build an efficient algorithm with explicit error control. The approach can be readily adapted to other time-fractional PDEs and is not constrained to fractional parameters in the range $0<\nu<1$.

This thesis is mainly concerned with state-space approaches for solving deep (temporal) Gaussian process (DGP) regression problems. More specifically, we represent DGPs as hierarchically composed systems of stochastic differential equations (SDEs), and we consequently solve the DGP regression problem by using state-space filtering and smoothing methods. The resulting state-space DGP (SS-DGP) models generate a rich class of priors compatible with modelling a number of irregular signals/functions. Moreover, due to their Markovian structure, SS-DGPs regression problems can be solved efficiently by using Bayesian filtering and smoothing methods. The second contribution of this thesis is that we solve continuous-discrete Gaussian filtering and smoothing problems by using the Taylor moment expansion (TME) method. This induces a class of filters and smoothers that can be asymptotically exact in predicting the mean and covariance of stochastic differential equations (SDEs) solutions. Moreover, the TME method and TME filters and smoothers are compatible with simulating SS-DGPs and solving their regression problems. Lastly, this thesis features a number of applications of state-space (deep) GPs. These applications mainly include, (i) estimation of unknown drift functions of SDEs from partially observed trajectories and (ii) estimation of spectro-temporal features of signals.

In the context of solving inverse problems for physics applications within a Bayesian framework, we present a new approach, Markov Chain Generative Adversarial Neural Networks (MCGANs), to alleviate the computational costs associated with solving the Bayesian inference problem. GANs pose a very suitable framework to aid in the solution of Bayesian inference problems, as they are designed to generate samples from complicated high-dimensional distributions. By training a GAN to sample from a low-dimensional latent space and then embedding it in a Markov Chain Monte Carlo method, we can highly efficiently sample from the posterior, by replacing both the high-dimensional prior and the expensive forward map. We prove that the proposed methodology converges to the true posterior in the Wasserstein-1 distance and that sampling from the latent space is equivalent to sampling in the high-dimensional space in a weak sense. The method is showcased on three test cases where we perform both state and parameter estimation simultaneously. The approach is shown to be up to two orders of magnitude more accurate than alternative approaches while also being up to an order of magnitude computationally faster, in several test cases, including the important engineering setting of detecting leaks in pipelines.

Estimating nested expectations is an important task in computational mathematics and statistics. In this paper we propose a new Monte Carlo method using post-stratification to estimate nested expectations efficiently without taking samples of the inner random variable from the conditional distribution given the outer random variable. This property provides the advantage over many existing methods that it enables us to estimate nested expectations only with a dataset on the pair of the inner and outer variables drawn from the joint distribution. We show an upper bound on the mean squared error of the proposed method under some assumptions. Numerical experiments are conducted to compare our proposed method with several existing methods (nested Monte Carlo method, multilevel Monte Carlo method, and regression-based method), and we see that our proposed method is superior to the compared methods in terms of efficiency and applicability.

Computational design problems arise in a number of settings, from synthetic biology to computer architectures. In this paper, we aim to solve data-driven model-based optimization (MBO) problems, where the goal is to find a design input that maximizes an unknown objective function provided access to only a static dataset of prior experiments. Such data-driven optimization procedures are the only practical methods in many real-world domains where active data collection is expensive (e.g., when optimizing over proteins) or dangerous (e.g., when optimizing over aircraft designs). Typical methods for MBO that optimize the design against a learned model suffer from distributional shift: it is easy to find a design that "fools" the model into predicting a high value. To overcome this, we propose conservative objective models (COMs), a method that learns a model of the objective function that lower bounds the actual value of the ground-truth objective on out-of-distribution inputs, and uses it for optimization. Structurally, COMs resemble adversarial training methods used to overcome adversarial examples. COMs are simple to implement and outperform a number of existing methods on a wide range of MBO problems, including optimizing protein sequences, robot morphologies, neural network weights, and superconducting materials.

Importance sampling is one of the most widely used variance reduction strategies in Monte Carlo rendering. In this paper, we propose a novel importance sampling technique that uses a neural network to learn how to sample from a desired density represented by a set of samples. Our approach considers an existing Monte Carlo rendering algorithm as a black box. During a scene-dependent training phase, we learn to generate samples with a desired density in the primary sample space of the rendering algorithm using maximum likelihood estimation. We leverage a recent neural network architecture that was designed to represent real-valued non-volume preserving ('Real NVP') transformations in high dimensional spaces. We use Real NVP to non-linearly warp primary sample space and obtain desired densities. In addition, Real NVP efficiently computes the determinant of the Jacobian of the warp, which is required to implement the change of integration variables implied by the warp. A main advantage of our approach is that it is agnostic of underlying light transport effects, and can be combined with many existing rendering techniques by treating them as a black box. We show that our approach leads to effective variance reduction in several practical scenarios.

The emerging technique of deep learning has been widely applied in many different areas. However, when adopted in a certain specific domain, this technique should be combined with domain knowledge to improve efficiency and accuracy. In particular, when analyzing the applications of deep learning in sentiment analysis, we found that the current approaches are suffering from the following drawbacks: (i) the existing works have not paid much attention to the importance of different types of sentiment terms, which is an important concept in this area; and (ii) the loss function currently employed does not well reflect the degree of error of sentiment misclassification. To overcome such problem, we propose to combine domain knowledge with deep learning. Our proposal includes using sentiment scores, learnt by regression, to augment training data; and introducing penalty matrix for enhancing the loss function of cross entropy. When experimented, we achieved a significant improvement in classification results.

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in theoretical computer science has shown that, in appropriate distributional models, it is possible to robustly estimate the mean and covariance with polynomial time algorithms that can tolerate a constant fraction of corruptions, independent of the dimension. However, the sample and time complexity of these algorithms is prohibitively large for high-dimensional applications. In this work, we address both of these issues by establishing sample complexity bounds that are optimal, up to logarithmic factors, as well as giving various refinements that allow the algorithms to tolerate a much larger fraction of corruptions. Finally, we show on both synthetic and real data that our algorithms have state-of-the-art performance and suddenly make high-dimensional robust estimation a realistic possibility.