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

In this paper, we investigate the optimal statistical performance and the impact of computational constraints for independent component analysis (ICA). Our goal is twofold. On the one hand, we characterize the precise role of dimensionality on sample complexity and statistical accuracy, and how computational consideration may affect them. In particular, we show that the optimal sample complexity is linear in dimensionality, and interestingly, the commonly used sample kurtosis-based approaches are necessarily suboptimal. However, the optimal sample complexity becomes quadratic, up to a logarithmic factor, in the dimension if we restrict ourselves to estimates that can be computed with low-degree polynomial algorithms. On the other hand, we develop computationally tractable estimates that attain both the optimal sample complexity and minimax optimal rates of convergence. We study the asymptotic properties of the proposed estimates and establish their asymptotic normality that can be readily used for statistical inferences. Our method is fairly easy to implement and numerical experiments are presented to further demonstrate its practical merits.

Without writing a single line of code by a human, an example Monte Carlo simulation based application for stochastic dependence modeling with copulas is developed using a state-of-the-art large language model (LLM) fine-tuned for conversations. This includes interaction with ChatGPT in natural language and using mathematical formalism, which, under careful supervision by a human-expert, led to producing a working code in MATLAB, Python and R for sampling from a given copula model, evaluation of the model's density, performing maximum likelihood estimation, optimizing the code for parallel computing for CPUs as well as for GPUs, and visualization of the computed results. In contrast to other emerging studies that assess the accuracy of LLMs like ChatGPT on tasks from a selected area, this work rather investigates ways how to achieve a successful solution of a standard statistical task in a collaboration of a human-expert and artificial intelligence (AI). Particularly, through careful prompt engineering, we separate successful solutions generated by ChatGPT from unsuccessful ones, resulting in a comprehensive list of related pros and cons. It is demonstrated that if the typical pitfalls are avoided, we can substantially benefit from collaborating with an AI partner. For example, we show that if ChatGPT is not able to provide a correct solution due to a lack of or incorrect knowledge, the human-expert can feed it with the correct knowledge, e.g., in the form of mathematical theorems and formulas, and make it to apply the gained knowledge in order to provide a solution that is correct. Such ability presents an attractive opportunity to achieve a programmed solution even for users with rather limited knowledge of programming techniques.

The information bottleneck (IB) method offers an attractive framework for understanding representation learning, however its applications are often limited by its computational intractability. Analytical characterization of the IB method is not only of practical interest, but it can also lead to new insights into learning phenomena. Here we consider a generalized IB problem, in which the mutual information in the original IB method is replaced by correlation measures based on Renyi and Jeffreys divergences. We derive an exact analytical IB solution for the case of Gaussian correlated variables. Our analysis reveals a series of structural transitions, similar to those previously observed in the original IB case. We find further that although solving the original, Renyi and Jeffreys IB problems yields different representations in general, the structural transitions occur at the same critical tradeoff parameters, and the Renyi and Jeffreys IB solutions perform well under the original IB objective. Our results suggest that formulating the IB method with alternative correlation measures could offer a strategy for obtaining an approximate solution to the original IB problem.

We describe a fast method for solving elliptic partial differential equations (PDEs) with uncertain coefficients using kernel interpolation at a lattice point set. By representing the input random field of the system using the model proposed by Kaarnioja, Kuo, and Sloan (SIAM J.~Numer.~Anal.~2020), in which a countable number of independent random variables enter the random field as periodic functions, it was shown by Kaarnioja, Kazashi, Kuo, Nobile, and Sloan (Numer.~Math.~2022) that the lattice-based kernel interpolant can be constructed for the PDE solution as a function of the stochastic variables in a highly efficient manner using fast Fourier transform (FFT). In this work, we discuss the connection between our model and the popular ``affine and uniform model'' studied widely in the literature of uncertainty quantification for PDEs with uncertain coefficients. We also propose a new class of weights entering the construction of the kernel interpolant -- \emph{serendipitous weights} -- which dramatically improve the computational performance of the kernel interpolant for PDE problems with uncertain coefficients, and allow us to tackle function approximation problems up to very high dimensionalities. Numerical experiments are presented to showcase the performance of the serendipitous weights.

Knowledge graphs represent factual knowledge about the world as relationships between concepts and are critical for intelligent decision making in enterprise applications. New knowledge is inferred from the existing facts in the knowledge graphs by encoding the concepts and relations into low-dimensional feature vector representations. The most effective representations for this task, called Knowledge Graph Embeddings (KGE), are learned through neural network architectures. Due to their impressive predictive performance, they are increasingly used in high-impact domains like healthcare, finance and education. However, are the black-box KGE models adversarially robust for use in domains with high stakes? This thesis argues that state-of-the-art KGE models are vulnerable to data poisoning attacks, that is, their predictive performance can be degraded by systematically crafted perturbations to the training knowledge graph. To support this argument, two novel data poisoning attacks are proposed that craft input deletions or additions at training time to subvert the learned model's performance at inference time. These adversarial attacks target the task of predicting the missing facts in knowledge graphs using KGE models, and the evaluation shows that the simpler attacks are competitive with or outperform the computationally expensive ones. The thesis contributions not only highlight and provide an opportunity to fix the security vulnerabilities of KGE models, but also help to understand the black-box predictive behaviour of KGE models.

Seeking the equivalent entities among multi-source Knowledge Graphs (KGs) is the pivotal step to KGs integration, also known as \emph{entity alignment} (EA). However, most existing EA methods are inefficient and poor in scalability. A recent summary points out that some of them even require several days to deal with a dataset containing 200,000 nodes (DWY100K). We believe over-complex graph encoder and inefficient negative sampling strategy are the two main reasons. In this paper, we propose a novel KG encoder -- Dual Attention Matching Network (Dual-AMN), which not only models both intra-graph and cross-graph information smartly, but also greatly reduces computational complexity. Furthermore, we propose the Normalized Hard Sample Mining Loss to smoothly select hard negative samples with reduced loss shift. The experimental results on widely used public datasets indicate that our method achieves both high accuracy and high efficiency. On DWY100K, the whole running process of our method could be finished in 1,100 seconds, at least 10* faster than previous work. The performances of our method also outperform previous works across all datasets, where Hits@1 and MRR have been improved from 6% to 13%.

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.

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.

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.

Multivariate time series forecasting is extensively studied throughout the years with ubiquitous applications in areas such as finance, traffic, environment, etc. Still, concerns have been raised on traditional methods for incapable of modeling complex patterns or dependencies lying in real word data. To address such concerns, various deep learning models, mainly Recurrent Neural Network (RNN) based methods, are proposed. Nevertheless, capturing extremely long-term patterns while effectively incorporating information from other variables remains a challenge for time-series forecasting. Furthermore, lack-of-explainability remains one serious drawback for deep neural network models. Inspired by Memory Network proposed for solving the question-answering task, we propose a deep learning based model named Memory Time-series network (MTNet) for time series forecasting. MTNet consists of a large memory component, three separate encoders, and an autoregressive component to train jointly. Additionally, the attention mechanism designed enable MTNet to be highly interpretable. We can easily tell which part of the historic data is referenced the most.