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Parameterized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parameterized quantum circuits in the limit of a large number of qubits and variational parameters. We then find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. We finally validate our analytic results with numerical experiments.

Despite the vast body of literature on Active Learning (AL), there is no comprehensive and open benchmark allowing for efficient and simple comparison of proposed samplers. Additionally, the variability in experimental settings across the literature makes it difficult to choose a sampling strategy, which is critical due to the one-off nature of AL experiments. To address those limitations, we introduce OpenAL, a flexible and open-source framework to easily run and compare sampling AL strategies on a collection of realistic tasks. The proposed benchmark is augmented with interpretability metrics and statistical analysis methods to understand when and why some samplers outperform others. Last but not least, practitioners can easily extend the benchmark by submitting their own AL samplers.

From health to education, income impacts a huge range of life choices. Many papers have leveraged data from online social networks to study precisely this. In this paper, we ask the opposite question: do different levels of income result in different online behaviors? We demonstrate it does. We present the first large-scale study of Nextdoor, a popular location-based social network. We collect 2.6 Million posts from 64,283 neighborhoods in the United States and 3,325 neighborhoods in the United Kingdom, to examine whether online discourse reflects the income and income inequality of a neighborhood. We show that posts from neighborhoods with different income indeed differ, e.g. richer neighborhoods have a more positive sentiment and discuss crimes more, even though their actual crime rates are much lower. We then show that user-generated content can predict both income and inequality. We train multiple machine learning models and predict both income (R-Square=0.841) and inequality (R-Square=0.77).

Family history is considered a risk factor for many diseases because it implicitly captures shared genetic, environmental and lifestyle factors. A nationwide electronic health record (EHR) system spanning multiple generations presents new opportunities for studying a connected network of medical histories for entire families. In this work we present a graph-based deep learning approach for learning explainable, supervised representations of how each family member's longitudinal medical history influences a patient's disease risk. We demonstrate that this approach is beneficial for predicting 10-year disease onset for 5 complex disease phenotypes, compared to clinically-inspired and deep learning baselines for a nationwide EHR system comprising 7 million individuals with up to third-degree relatives. Through the use of graph explainability techniques, we illustrate that a graph-based approach enables more personalized modeling of family information and disease risk by identifying important relatives and features for prediction.

Many early order flow auction designs handle the payment for orders when they execute on the chain rather than when they are won in the auction. Payments in these auctions only take place when the orders are executed, creating a free option for whoever wins the order. Bids in these auctions set the strike price of this option rather than the option premium. This paper develops a simple model of an order flow auction and compares contingent fees with upfront payments as well as mixtures of the two. Results suggest that auctions with a greater share of the payment contingent on execution have lower execution probability, lower revenue, and increased effective spreads in equilibrium. A Reputation system can act as a negative contingent fee, partially mitigating the downsides; however, unless the system is calibrated perfectly, some of the undesirable qualities of the contingent fees remain. Results suggest that designers of order flow auctions should avoid contingent fees whenever possible.

Aiming at the disorder problem (i.e. uncertainty problem) of the utilization of network resources commonly existing in multi-hop transmission networks, the paper proposes the idea and the corresponding supporting theory, i.e. theory of network wave, by constructing volatility information transmission mechanism between the sending nodes and their corresponding receiving nodes of a pair of paths (composed of two primary paths), so as to improve the orderliness of the utilization of network resources. It is proved that the maximum asymptotic throughput of a primary path depends on its intrinsic period, which in itself is equal to the intrinsic interference intensity of a primary path. Based on the proposed theory of network wave, an algorithm for the transmission of information blocks based on the intrinsic period of a primary path is proposed, which can maximize the asymptotic throughput of a primary path. In the cases of traversals with equal opportunities, an algorithm for the cooperative volatility transmission of information blocks in a pair of paths based on the set of maximum supporting elements is proposed. It is proved that the algorithm can maximize the asymptotic joint throughput of a pair of paths. The research results of the paper lay an ideological and theoretical foundation for further exploring more general methods that can improve the orderly utilization of network resources.

Meta-learning has arisen as a successful method for improving training performance by training over many similar tasks, especially with deep neural networks (DNNs). However, the theoretical understanding of when and why overparameterized models such as DNNs can generalize well in meta-learning is still limited. As an initial step towards addressing this challenge, this paper studies the generalization performance of overfitted meta-learning under a linear regression model with Gaussian features. In contrast to a few recent studies along the same line, our framework allows the number of model parameters to be arbitrarily larger than the number of features in the ground truth signal, and hence naturally captures the overparameterized regime in practical deep meta-learning. We show that the overfitted min $\ell_2$-norm solution of model-agnostic meta-learning (MAML) can be beneficial, which is similar to the recent remarkable findings on ``benign overfitting'' and ``double descent'' phenomenon in the classical (single-task) linear regression. However, due to the uniqueness of meta-learning such as task-specific gradient descent inner training and the diversity/fluctuation of the ground-truth signals among training tasks, we find new and interesting properties that do not exist in single-task linear regression. We first provide a high-probability upper bound (under reasonable tightness) on the generalization error, where certain terms decrease when the number of features increases. Our analysis suggests that benign overfitting is more significant and easier to observe when the noise and the diversity/fluctuation of the ground truth of each training task are large. Under this circumstance, we show that the overfitted min $\ell_2$-norm solution can achieve an even lower generalization error than the underparameterized solution.

We employ a toolset -- dubbed Dr. Frankenstein -- to analyse the similarity of representations in deep neural networks. With this toolset, we aim to match the activations on given layers of two trained neural networks by joining them with a stitching layer. We demonstrate that the inner representations emerging in deep convolutional neural networks with the same architecture but different initializations can be matched with a surprisingly high degree of accuracy even with a single, affine stitching layer. We choose the stitching layer from several possible classes of linear transformations and investigate their performance and properties. The task of matching representations is closely related to notions of similarity. Using this toolset, we also provide a novel viewpoint on the current line of research regarding similarity indices of neural network representations: the perspective of the performance on a task.

In many important graph data processing applications the acquired information includes both node features and observations of the graph topology. Graph neural networks (GNNs) are designed to exploit both sources of evidence but they do not optimally trade-off their utility and integrate them in a manner that is also universal. Here, universality refers to independence on homophily or heterophily graph assumptions. We address these issues by introducing a new Generalized PageRank (GPR) GNN architecture that adaptively learns the GPR weights so as to jointly optimize node feature and topological information extraction, regardless of the extent to which the node labels are homophilic or heterophilic. Learned GPR weights automatically adjust to the node label pattern, irrelevant on the type of initialization, and thereby guarantee excellent learning performance for label patterns that are usually hard to handle. Furthermore, they allow one to avoid feature over-smoothing, a process which renders feature information nondiscriminative, without requiring the network to be shallow. Our accompanying theoretical analysis of the GPR-GNN method is facilitated by novel synthetic benchmark datasets generated by the so-called contextual stochastic block model. We also compare the performance of our GNN architecture with that of several state-of-the-art GNNs on the problem of node-classification, using well-known benchmark homophilic and heterophilic datasets. The results demonstrate that GPR-GNN offers significant performance improvement compared to existing techniques on both synthetic and benchmark data.

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.