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The ever-growing size of modern space-time data sets, such as those collected by remote sensing, requires new techniques for their efficient and automated processing, including gap-filling of missing values. CUDA-based parallelization on GPU has become a popular way to dramatically increase computational efficiency of various approaches. Recently, we have proposed a computationally efficient and competitive, yet simple spatial prediction approach inspired from statistical physics models, called modified planar rotator (MPR) method. Its GPU implementation allowed additional impressive computational acceleration exceeding two orders of magnitude in comparison with CPU calculations. In the current study we propose a rather general approach to modelling spatial heterogeneity in GPU-implemented spatial prediction methods for two-dimensional gridded data by introducing spatial variability to model parameters. Predictions of unknown values are obtained from non-equilibrium conditional simulations, assuming ``local'' equilibrium conditions. We demonstrate that the proposed method leads to significant improvements in both prediction performance and computational efficiency.

The compute-intensive nature of neural networks (NNs) limits their deployment in resource-constrained environments such as cell phones, drones, autonomous robots, etc. Hence, developing robust sparse models fit for safety-critical applications has been an issue of longstanding interest. Though adversarial training with model sparsification has been combined to attain the goal, conventional adversarial training approaches provide no formal guarantee that the models would be robust against any rogue samples in a restricted space around a benign sample. Recently proposed verified local robustness techniques provide such a guarantee. This is the first paper that combines the ideas from verified local robustness and dynamic sparse training to develop `SparseVLR'-- a novel framework to search verified locally robust sparse networks. Obtained sparse models exhibit accuracy and robustness comparable to their dense counterparts at sparsity as high as 99%. Furthermore, unlike most conventional sparsification techniques, SparseVLR does not require a pre-trained dense model, reducing the training time by 50%. We exhaustively investigated SparseVLR's efficacy and generalizability by evaluating various benchmark and application-specific datasets across several models.

With the goal of increasing the speed and efficiency in robotic dual-arm manipulation, a novel control approach is presented that utilizes intentional simultaneous impacts to rapidly grasp objects. This approach uses the time-invariant reference spreading framework, in which partly-overlapping ante- and post-impact reference vector fields are used. These vector fields are coupled via the impact dynamics in proximity of the expected impact area, minimizing the otherwise large velocity errors after the impact and the corresponding large control efforts. A purely spatial task is introduced to strongly encourage the synchronization of impact times of the two arms. An interim-impact control phase provides robustness in the execution against the inevitable lack of exact impact simultaneity and the corresponding unreliable velocity error. In this interim phase, a position feedback signal is derived from the ante-impact velocity reference, which is used to enforce sustained contact in all contact points without using velocity error feedback. With an eye towards real-life implementation, the approach is formulated using a QP control framework, and is validated using numerical simulations on a realistic robot model with flexible joints and low-level torque control.

In this article, we consider the problem of estimating fractional processes based on noisy high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we exhibit a sequence of consistent estimators for the unknown parameters of interest by proving a law of large numbers for associated variation functionals. In contrast to the semimartingale setting, the optimal window size for pre-averaging depends on the unknown roughness parameter of the underlying process. We evaluate the performance of our estimators in a simulation study and use them to empirically verify Kolmogorov's 2/3-law in turbulence data contaminated by instrument noise.

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.

Marketing is an important mechanism to increase user engagement and improve platform revenue, and heterogeneous causal learning can help develop more effective strategies. Most decision-making problems in marketing can be formulated as resource allocation problems and have been studied for decades. Existing works usually divide the solution procedure into two fully decoupled stages, i.e., machine learning (ML) and operation research (OR) -- the first stage predicts the model parameters and they are fed to the optimization in the second stage. However, the error of the predicted parameters in ML cannot be respected and a series of complex mathematical operations in OR lead to the increased accumulative errors. Essentially, the improved precision on the prediction parameters may not have a positive correlation on the final solution due to the side-effect from the decoupled design. In this paper, we propose a novel approach for solving resource allocation problems to mitigate the side-effects. Our key intuition is that we introduce the decision factor to establish a bridge between ML and OR such that the solution can be directly obtained in OR by only performing the sorting or comparison operations on the decision factor. Furthermore, we design a customized loss function that can conduct direct heterogeneous causal learning on the decision factor, an unbiased estimation of which can be guaranteed when the loss converges. As a case study, we apply our approach to two crucial problems in marketing: the binary treatment assignment problem and the budget allocation problem with multiple treatments. Both large-scale simulations and online A/B Tests demonstrate that our approach achieves significant improvement compared with state-of-the-art.

The main challenge for fine-grained few-shot image classification is to learn feature representations with higher inter-class and lower intra-class variations, with a mere few labelled samples. Conventional few-shot learning methods however cannot be naively adopted for this fine-grained setting -- a quick pilot study reveals that they in fact push for the opposite (i.e., lower inter-class variations and higher intra-class variations). To alleviate this problem, prior works predominately use a support set to reconstruct the query image and then utilize metric learning to determine its category. Upon careful inspection, we further reveal that such unidirectional reconstruction methods only help to increase inter-class variations and are not effective in tackling intra-class variations. In this paper, we for the first time introduce a bi-reconstruction mechanism that can simultaneously accommodate for inter-class and intra-class variations. In addition to using the support set to reconstruct the query set for increasing inter-class variations, we further use the query set to reconstruct the support set for reducing intra-class variations. This design effectively helps the model to explore more subtle and discriminative features which is key for the fine-grained problem in hand. Furthermore, we also construct a self-reconstruction module to work alongside the bi-directional module to make the features even more discriminative. Experimental results on three widely used fine-grained image classification datasets consistently show considerable improvements compared with other methods. Codes are available at: //github.com/PRIS-CV/Bi-FRN.

We study the fundamental question of how to define and measure the distance from calibration for probabilistic predictors. While the notion of perfect calibration is well-understood, there is no consensus on how to quantify the distance from perfect calibration. Numerous calibration measures have been proposed in the literature, but it is unclear how they compare to each other, and many popular measures such as Expected Calibration Error (ECE) fail to satisfy basic properties like continuity. We present a rigorous framework for analyzing calibration measures, inspired by the literature on property testing. We propose a ground-truth notion of distance from calibration: the $\ell_1$ distance to the nearest perfectly calibrated predictor. We define a consistent calibration measure as one that is a polynomial factor approximation to the this distance. Applying our framework, we identify three calibration measures that are consistent and can be estimated efficiently: smooth calibration, interval calibration, and Laplace kernel calibration. The former two give quadratic approximations to the ground truth distance, which we show is information-theoretically optimal. Our work thus establishes fundamental lower and upper bounds on measuring distance to calibration, and also provides theoretical justification for preferring certain metrics (like Laplace kernel calibration) in practice.

Adversarial Imitation Learning (AIL) is a class of popular state-of-the-art Imitation Learning algorithms commonly used in robotics. In AIL, an artificial adversary's misclassification is used as a reward signal that is optimized by any standard Reinforcement Learning (RL) algorithm. Unlike most RL settings, the reward in AIL is $differentiable$ but current model-free RL algorithms do not make use of this property to train a policy. The reward is AIL is also shaped since it comes from an adversary. We leverage the differentiability property of the shaped AIL reward function and formulate a class of Actor Residual Critic (ARC) RL algorithms. ARC algorithms draw a parallel to the standard Actor-Critic (AC) algorithms in RL literature and uses a residual critic, $C$ function (instead of the standard $Q$ function) to approximate only the discounted future return (excluding the immediate reward). ARC algorithms have similar convergence properties as the standard AC algorithms with the additional advantage that the gradient through the immediate reward is exact. For the discrete (tabular) case with finite states, actions, and known dynamics, we prove that policy iteration with $C$ function converges to an optimal policy. In the continuous case with function approximation and unknown dynamics, we experimentally show that ARC aided AIL outperforms standard AIL in simulated continuous-control and real robotic manipulation tasks. ARC algorithms are simple to implement and can be incorporated into any existing AIL implementation with an AC algorithm. Video and link to code are available at: //sites.google.com/view/actor-residual-critic.

Process mining is a methodology for the derivation and analysis of process models based on the event log. When process mining is employed to analyze business processes, the process discovery step, the conformance checking step, and the enhancements step are repeated. If a user wants to analyze a process from multiple perspectives (such as activity perspectives, originator perspectives, and time perspectives), the above procedure, inconveniently, has to be repeated over and over again. Although past studies involving process mining have applied detailed stepwise methodologies, no attempt has been made to incorporate and optimize multi-perspective process mining procedures. This paper contributes to developing a solution approach to this problem. First, we propose an automatic discovery framework of a multi-perspective process model based on deep Q-Learning. Our Dual Experience Replay with Experience Distribution (DERED) approach can automatically perform process model discovery steps, conformance check steps, and enhancements steps. Second, we propose a new method that further optimizes the experience replay (ER) method, one of the key algorithms of deep Q-learning, to improve the learning performance of reinforcement learning agents. Finally, we validate our approach using six real-world event datasets collected in port logistics, steel manufacturing, finance, IT, and government administration. We show that our DERED approach can provide users with multi-perspective, high-quality process models that can be employed more conveniently for multi-perspective process mining.