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

This article develops a new algorithm named TTRISK to solve high-dimensional risk-averse optimization problems governed by differential equations (ODEs and/or PDEs) under uncertainty. As an example, we focus on the so-called Conditional Value at Risk (CVaR), but the approach is equally applicable to other coherent risk measures. Both the full and reduced space formulations are considered. The algorithm is based on low rank tensor approximations of random fields discretized using stochastic collocation. To avoid non-smoothness of the objective function underpinning the CVaR, we propose an adaptive strategy to select the width parameter of the smoothed CVaR to balance the smoothing and tensor approximation errors. Moreover, unbiased Monte Carlo CVaR estimate can be computed by using the smoothed CVaR as a control variate. To accelerate the computations, we introduce an efficient preconditioner for the KKT system in the full space formulation.The numerical experiments demonstrate that the proposed method enables accurate CVaR optimization constrained by large-scale discretized systems. In particular, the first example consists of an elliptic PDE with random coefficients as constraints. The second example is motivated by a realistic application to devise a lockdown plan for United Kingdom under COVID-19. The results indicate that the risk-averse framework is feasible with the tensor approximations under tens of random variables.

We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear system which is constructed by imposing appropriate conditions on the moments of the invariant distribution of the mean field limit and on the quadratic variation of the process. Our approach is easy to implement as it only requires the approximation of the moments via the ergodic theorem and the solution of a low-dimensional linear system. Moreover, we prove that our estimator is asymptotically unbiased in the limits of infinite data and infinite number of particles (mean field limit). In addition, we present several numerical experiments that validate the theoretical analysis and show the effectiveness of our methodology to accurately infer parameters in systems of interacting particles.

Predicting neural architecture performance is a challenging task and is crucial to neural architecture design and search. Existing approaches either rely on neural performance predictors which are limited to modeling architectures in a predefined design space involving specific sets of operators and connection rules, and cannot generalize to unseen architectures, or resort to zero-cost proxies which are not always accurate. In this paper, we propose GENNAPE, a Generalized Neural Architecture Performance Estimator, which is pretrained on open neural architecture benchmarks, and aims to generalize to completely unseen architectures through combined innovations in network representation, contrastive pretraining, and fuzzy clustering-based predictor ensemble. Specifically, GENNAPE represents a given neural network as a Computation Graph (CG) of atomic operations which can model an arbitrary architecture. It first learns a graph encoder via Contrastive Learning to encourage network separation by topological features, and then trains multiple predictor heads, which are soft-aggregated according to the fuzzy membership of a neural network. Experiments show that GENNAPE pretrained on NAS-Bench-101 can achieve superior transferability to 5 different public neural network benchmarks, including NAS-Bench-201, NAS-Bench-301, MobileNet and ResNet families under no or minimum fine-tuning. We further introduce 3 challenging newly labelled neural network benchmarks: HiAML, Inception and Two-Path, which can concentrate in narrow accuracy ranges. Extensive experiments show that GENNAPE can correctly discern high-performance architectures in these families. Finally, when paired with a search algorithm, GENNAPE can find architectures that improve accuracy while reducing FLOPs on three families.

In sparse estimation, in which the sum of the loss function and the regularization term is minimized, methods such as the proximal gradient method and the proximal Newton method are applied. The former is slow to converge to a solution, while the latter converges quickly but is inefficient for problems such as group lasso problems. In this paper, we examine how to efficiently find a solution by finding the convergence destination of the proximal gradient method. However, the case in which the Lipschitz constant of the derivative of the loss function is unknown has not been studied theoretically, and only the Newton method has been proposed for the case in which the Lipschitz constant is known. We show that the Newton method converges when the Lipschitz constant is unknown and extend the theory. Furthermore, we propose a new quasi-Newton method that avoids Hessian calculations and improves efficiency, and we prove that it converges quickly, providing a theoretical guarantee. Finally, numerical experiments show that the proposed method can significantly improve the efficiency.

The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical inference and machine learning tasks. However, this information theoretical quantity is not robust against noise in the data, and is computationally prohibitive in large-scale applications. To address these issues, we propose a novel measure of information, termed low-rank matrix-based R\'enyi's entropy, based on low-rank representations of infinitely divisible kernel matrices. The proposed entropy functional inherits the specialty of of the original definition to directly quantify information from data, but enjoys additional advantages including robustness and effective calculation. Specifically, our low-rank variant is more sensitive to informative perturbations induced by changes in underlying distributions, while being insensitive to uninformative ones caused by noises. Moreover, low-rank R\'enyi's entropy can be efficiently approximated by random projection and Lanczos iteration techniques, reducing the overall complexity from $\mathcal{O}(n^3)$ to $\mathcal{O}(n^2 s)$ or even $\mathcal{O}(ns^2)$, where $n$ is the number of data samples and $s \ll n$. We conduct large-scale experiments to evaluate the effectiveness of this new information measure, demonstrating superior results compared to matrix-based R\'enyi's entropy in terms of both performance and computational efficiency.

The time-series forecasting (TSF) problem is a traditional problem in the field of artificial intelligence. Models such as Recurrent Neural Network (RNN), Long Short Term Memory (LSTM), and GRU (Gate Recurrent Units) have contributed to improving the predictive accuracy of TSF. Furthermore, model structures have been proposed to combine time-series decomposition methods, such as seasonal-trend decomposition using Loess (STL) to ensure improved predictive accuracy. However, because this approach is learned in an independent model for each component, it cannot learn the relationships between time-series components. In this study, we propose a new neural architecture called a correlation recurrent unit (CRU) that can perform time series decomposition within a neural cell and learn correlations (autocorrelation and correlation) between each decomposition component. The proposed neural architecture was evaluated through comparative experiments with previous studies using five univariate time-series datasets and four multivariate time-series data. The results showed that long- and short-term predictive performance was improved by more than 10%. The experimental results show that the proposed CRU is an excellent method for TSF problems compared to other neural architectures.

Change point estimation is often formulated as a search for the maximum of a gain function describing improved fits when segmenting the data. Searching through all candidates requires $O(n)$ evaluations of the gain function for an interval with $n$ observations. If each evaluation is computationally demanding (e.g. in high-dimensional models), this can become infeasible. Instead, we propose optimistic search methods with $O(\log n)$ evaluations exploiting specific structure of the gain function. Towards solid understanding of our strategy, we investigate in detail the $p$-dimensional Gaussian changing means setup, including high-dimensional scenarios. For some of our proposals, we prove asymptotic minimax optimality for detecting change points and derive their asymptotic localization rate. These rates (up to a possible log factor) are optimal for the univariate and multivariate scenarios, and are by far the fastest in the literature under the weakest possible detection condition on the signal-to-noise ratio in the high-dimensional scenario. Computationally, our proposed methodology has the worst case complexity of $O(np)$, which can be improved to be sublinear in $n$ if some a-priori knowledge on the length of the shortest segment is available. Our search strategies generalize far beyond the theoretically analyzed setup. We illustrate, as an example, massive computational speedup in change point detection for high-dimensional Gaussian graphical models.

There are existing standard solvers for tackling discrete optimization problems. However, in practice, it is uncommon to apply them directly to the large input space typical of this class of problems. Rather, the input is preprocessed to look for simplifications and to extract the core subset of the problem space, which is called the Kernel. This pre-processing procedure is known in the context of parameterized complexity theory as Kernelization. In this thesis, I implement parallel versions of some Kernelization algorithms and evaluate their performance. The performance of Kernelization algorithms is measured either by the size of the output Kernel or by the time it takes to compute the kernel. Sometimes the Kernel is the same as the original input, so it is desirable to know this, as soon as possible. The problem scope is limited to a particular type of discrete optimisation problem which is a version of the K-clique problem in which nodes of the given graph are pre-coloured legally using k colours. The final evaluation shows that my parallel implementations achieve over 50% improvement in efficiency for at least one of these algorithms. This is attained not just in terms of speed, but it is also able to produce a smaller kernel.

Contact matrices are an important ingredient in age-structured epidemic models to inform the simulated spread of the disease between sub-groups of the population. These matrices are generally derived using resource-intensive diary-based surveys and few exist in the Global South or tailored to vulnerable populations. In particular, no contact matrices exist for refugee settlements - locations under-served by epidemic models in general. In this paper we present a novel, mixed-method approach, for deriving contact matrices in populations which combines a lightweight, rapidly deployable, survey with an agent-based model of the population informed by census and behavioural data. We use this method to derive the first set of contact matrices for the Cox's Bazar refugee settlement in Bangladesh. The matrices from the refugee settlement show strong banding effects due to different age cut-offs in attendance at certain venues, such as distribution centres and religious sites, as well as the important contribution of the demographic profile of the settlement which was encoded in the model. These can have significant implications to the modelled disease dynamics. To validate our approach, we also apply our method to the population of the UK and compare our derived matrices against well-known contact matrices previously collected using traditional approaches. Overall, our findings demonstrate that our mixed-method approach can address some of the challenges of both the traditional and previously proposed agent-based approaches to deriving contact matrices, and has the potential to be rolled-out in other resource-constrained environments. This work therefore contributes to a broader aim of developing new methods and mechanisms of data collection for modelling disease spread in refugee and IDP settlements and better serving these vulnerable communities.

Deep Learning algorithms have achieved the state-of-the-art performance for Image Classification and have been used even in security-critical applications, such as biometric recognition systems and self-driving cars. However, recent works have shown those algorithms, which can even surpass the human capabilities, are vulnerable to adversarial examples. In Computer Vision, adversarial examples are images containing subtle perturbations generated by malicious optimization algorithms in order to fool classifiers. As an attempt to mitigate these vulnerabilities, numerous countermeasures have been constantly proposed in literature. Nevertheless, devising an efficient defense mechanism has proven to be a difficult task, since many approaches have already shown to be ineffective to adaptive attackers. Thus, this self-containing paper aims to provide all readerships with a review of the latest research progress on Adversarial Machine Learning in Image Classification, however with a defender's perspective. Here, novel taxonomies for categorizing adversarial attacks and defenses are introduced and discussions about the existence of adversarial examples are provided. Further, in contrast to exisiting surveys, it is also given relevant guidance that should be taken into consideration by researchers when devising and evaluating defenses. Finally, based on the reviewed literature, it is discussed some promising paths for future research.