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Although many methods have been proposed to estimate attributions of input variables, there still exists a significant theoretical flaw in masking-based attribution methods, i.e., it is hard to examine whether the masking method faithfully represents the absence of input variables. Specifically, for masking-based attributions, setting an input variable to the baseline value is a typical way of representing the absence of the variable. However, there are no studies investigating how to represent the absence of input variables and verify the faithfulness of baseline values. Therefore, we revisit the feature representation of a DNN in terms of causality, and propose to use causal patterns to examine whether the masking method faithfully removes information encoded in input variables. More crucially, it is proven that the causality can be explained as the elementary rationale of the Shapley value. Furthermore, we define the optimal baseline value from the perspective of causality, and we propose a method to learn the optimal baseline value. Experimental results have demonstrated the effectiveness of our method.

In this study, we address the problem of optimizing multi-output black-box functions under uncertain environments. We formulate this problem as the estimation of the uncertain Pareto-frontier (PF) of a multi-output Bayesian surrogate model with two types of variables: design variables and environmental variables. We consider this problem within the context of Bayesian optimization (BO) under uncertain environments, where the design variables are controllable, whereas the environmental variables are assumed to be random and not controllable. The challenge of this problem is to robustly estimate the PF when the distribution of the environmental variables is unknown, that is, to estimate the PF when the environmental variables are generated from the worst possible distribution. We propose a method for solving the BO problem by appropriately incorporating the uncertainties of the environmental variables and their probability distribution. We demonstrate that the proposed method can find an arbitrarily accurate PF with high probability in a finite number of iterations. We also evaluate the performance of the proposed method through numerical experiments.

Federated Learning (FL) is a well-established technique for privacy preserving distributed training. Much attention has been given to various aspects of FL training. A growing number of applications that consume FL-trained models, however, increasingly operate under dynamically and unpredictably variable conditions, rendering a single model insufficient. We argue for training a global family of models cost efficiently in a federated fashion. Training them independently for different tradeoff points incurs $O(k)$ cost for any k architectures of interest, however. Straightforward applications of FL techniques to recent weight-shared training approaches is either infeasible or prohibitively expensive. We propose SuperFed - an architectural framework that incurs $O(1)$ cost to co-train a large family of models in a federated fashion by leveraging weight-shared learning. We achieve an order of magnitude cost savings on both communication and computation by proposing two novel training mechanisms: (a) distribution of weight-shared models to federated clients, (b) central aggregation of arbitrarily overlapping weight-shared model parameters. The combination of these mechanisms is shown to reach an order of magnitude (9.43x) reduction in computation and communication cost for training a $5*10^{18}$-sized family of models, compared to independently training as few as $k = 9$ DNNs without any accuracy loss.

Federated edge learning (FEL) can training a global model from terminal nodes' local dataset, which can make full use of the computing resources of terminal nodes and performs more extensive and efficient machine learning on terminal nodes with protecting user information requirements. Performance of FEL will be suffered from long delay or fault decision as the master collects partial gradients from stragglers which cannot return correct results within a deadline. Inspired by this, in this paper, we propose a novel coded FEL to mitigate stragglers for synchronous gradient with a two-stage dynamic scheme, where we start with part of workers for a duration of before starting the second stage, and on completion of at the first stage, we start remaining workers in the second stage. In particular, the computation latency and transmission latency is essential and should be quantitatively analyzed. Then the dynamically coded coefficients scheme is proposed which is based on historical information including worker completion time. For performance optimization of FEL, a Lyapunov function is designed to maximize admission data balancing fairness and two stage dynamic coding scheme is designed to maximize arrival data among workers. Experimental evidence verifies the derived properties and demonstrates that our proposed solution achieves a better performance for practical network parameters and benchmark datasets in terms of accuracy and resource utilization in the FEL system.

Recently, graph-based models designed for downstream tasks have significantly advanced research on graph neural networks (GNNs). GNN baselines based on neural message-passing mechanisms such as GCN and GAT perform worse as the network deepens. Therefore, numerous GNN variants have been proposed to tackle this performance degradation problem, including many deep GNNs. However, a unified framework is still lacking to connect these existing models and interpret their effectiveness at a high level. In this work, we focus on deep GNNs and propose a novel view for understanding them. We establish a theoretical framework via inference on a probabilistic graphical model. Given the fixed point equation (FPE) derived from the variational inference on the Markov random fields, the deep GNNs, including JKNet, GCNII, DGCN, and the classical GNNs, such as GCN, GAT, and APPNP, can be regarded as different approximations of the FPE. Moreover, given this framework, more accurate approximations of FPE are brought, guiding us to design a more powerful GNN: coupling graph neural network (CoGNet). Extensive experiments are carried out on citation networks and natural language processing downstream tasks. The results demonstrate that the CoGNet outperforms the SOTA models.

Regressing the vector field of a dynamical system from a finite number of observed states is a natural way to learn surrogate models for such systems. A simple and interpretable way to learn a dynamical system from data is to interpolate its vector-field with a data-adapted kernel which can be learned by using Kernel Flows. The method of Kernel Flows is a trainable machine learning method that learns the optimal parameters of a kernel based on the premise that a kernel is good if there is no significant loss in accuracy if half of the data is used. The objective function could be a short-term prediction or some other objective for other variants of Kernel Flows). However, this method is limited by the choice of the base kernel. In this paper, we introduce the method of \emph{Sparse Kernel Flows } in order to learn the ``best'' kernel by starting from a large dictionary of kernels. It is based on sparsifying a kernel that is a linear combination of elemental kernels. We apply this approach to a library of 132 chaotic systems.

Federated learning (FL) has been proposed to protect data privacy and virtually assemble the isolated data silos by cooperatively training models among organizations without breaching privacy and security. However, FL faces heterogeneity from various aspects, including data space, statistical, and system heterogeneity. For example, collaborative organizations without conflict of interest often come from different areas and have heterogeneous data from different feature spaces. Participants may also want to train heterogeneous personalized local models due to non-IID and imbalanced data distribution and various resource-constrained devices. Therefore, heterogeneous FL is proposed to address the problem of heterogeneity in FL. In this survey, we comprehensively investigate the domain of heterogeneous FL in terms of data space, statistical, system, and model heterogeneity. We first give an overview of FL, including its definition and categorization. Then, We propose a precise taxonomy of heterogeneous FL settings for each type of heterogeneity according to the problem setting and learning objective. We also investigate the transfer learning methodologies to tackle the heterogeneity in FL. We further present the applications of heterogeneous FL. Finally, we highlight the challenges and opportunities and envision promising future research directions toward new framework design and trustworthy approaches.

Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify the understanding of diffusion models across both variational and score-based perspectives. We first derive Variational Diffusion Models (VDM) as a special case of a Markovian Hierarchical Variational Autoencoder, where three key assumptions enable tractable computation and scalable optimization of the ELBO. We then prove that optimizing a VDM boils down to learning a neural network to predict one of three potential objectives: the original source input from any arbitrary noisification of it, the original source noise from any arbitrarily noisified input, or the score function of a noisified input at any arbitrary noise level. We then dive deeper into what it means to learn the score function, and connect the variational perspective of a diffusion model explicitly with the Score-based Generative Modeling perspective through Tweedie's Formula. Lastly, we cover how to learn a conditional distribution using diffusion models via guidance.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.