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 paper proposes a general procedure to analyse high-dimensional spatio-temporal count data, with special emphasis on relative risks estimation in cancer epidemiology. Model fitting is carried out using integrated nested Laplace approximations over a partition of the spatio-temporal domain. This is a simple idea that works very well in this context as the models are defined to borrow strength locally in space and time, providing reliable risk estimates. Parallel and distributed strategies are proposed to speed up computations in a setting where Bayesian model fitting is generally prohibitively time-consuming and even unfeasible. We evaluate the whole procedure in a simulation study with a twofold objective: to estimate risks accurately and to detect extreme risk areas while avoiding false positives/negatives. We show that our method outperforms classical global models. A real data analysis comparing the global models and the new procedure is also presented.

Data structures known as $k$-d trees have numerous applications in scientific computing, particularly in areas of modern statistics and data science such as range search in decision trees, clustering, nearest neighbors search, local regression, and so forth. In this article we present a scalable mechanism to construct $k$-d trees for distributed data, based on approximating medians for each recursive subdivision of the data. We provide theoretical guarantees of the quality of approximation using this approach, along with a simulation study quantifying the accuracy and scalability of our proposed approach in practice.

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization properties of neural networks. Many recent works analyze such models in a certain high-dimensional regime where the covariates are independent and the number of samples and the number of covariates grow at a fixed ratio (i.e. proportional asymptotics). In this work we show that for a large class of kernels, including the neural tangent kernel of fully connected networks, kernel methods can only perform as well as linear models in this regime. More surprisingly, when the data is generated by a kernel model where the relationship between input and the response could be very nonlinear, we show that linear models are in fact optimal, i.e. linear models achieve the minimum risk among all models, linear or nonlinear. These results suggest that more complex models for the data other than independent features are needed for high-dimensional analysis.

This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient matrix is proposed. Our method first utilizes the multivariate nature of the responses by estimating and adjusting the hidden effect to construct an initial estimator of the coefficient matrix. By further deploying a low-dimensional projection procedure to reduce the bias introduced by the regularization in the previous step, a refined estimator is proposed and shown to be asymptotically normal. The asymptotic variance of the resulting estimator is derived with closed-form expression and can be consistently estimated. In addition, we propose a testing procedure for the existence of hidden effects and provide its theoretical justification. Both our procedures and their analyses are valid even when the feature dimension and the number of responses exceed the sample size. Our results are further backed up via extensive simulations and a real data analysis.

The recently proposed statistical finite element (statFEM) approach synthesises measurement data with finite element models and allows for making predictions about the true system response. We provide a probabilistic error analysis for a prototypical statFEM setup based on a Gaussian process prior under the assumption that the noisy measurement data are generated by a deterministic true system response function that satisfies a second-order elliptic partial differential equation for an unknown true source term. In certain cases, properties such as the smoothness of the source term may be misspecified by the Gaussian process model. The error estimates we derive are for the expectation with respect to the measurement noise of the $L^2$-norm of the difference between the true system response and the mean of the statFEM posterior. The estimates imply polynomial rates of convergence in the numbers of measurement points and finite element basis functions and depend on the Sobolev smoothness of the true source term and the Gaussian process model. A numerical example for Poisson's equation is used to illustrate these theoretical results.

Local differential privacy (LDP), which perturbs the data of each user locally and only sends the noisy version of her information to the aggregator, is a popular privacy-preserving data collection mechanism. In LDP, the data collector could obtain accurate statistics without access to original data, thus guaranteeing privacy. However, a primary drawback of LDP is its disappointing utility in high-dimensional space. Although various LDP schemes have been proposed to reduce perturbation, they share the same and naive aggregation mechanism at the side of the collector. In this paper, we first bring forward an analytical framework to generally measure the utilities of LDP mechanisms in high-dimensional space, which can benchmark existing and future LDP mechanisms without conducting any experiment. Based on this, the framework further reveals that the naive aggregation is sub-optimal in high-dimensional space, and there is much room for improvement. Motivated by this, we present a re-calibration protocol HDR4ME for high-dimensional mean estimation, which improves the utilities of existing LDP mechanisms without making any change to them. Both theoretical analysis and extensive experiments confirm the generality and effectiveness of our framework and protocol.

Acquisition of data is a difficult task in many applications of machine learning, and it is only natural that one hopes and expects the population risk to decrease (better performance) monotonically with increasing data points. It turns out, somewhat surprisingly, that this is not the case even for the most standard algorithms that minimize the empirical risk. Non-monotonic behavior of the risk and instability in training have manifested and appeared in the popular deep learning paradigm under the description of double descent. These problems highlight the current lack of understanding of learning algorithms and generalization. It is, therefore, crucial to pursue this concern and provide a characterization of such behavior. In this paper, we derive the first consistent and risk-monotonic (in high probability) algorithms for a general statistical learning setting under weak assumptions, consequently answering some questions posed by Viering et al. 2019 on how to avoid non-monotonic behavior of risk curves. We further show that risk monotonicity need not necessarily come at the price of worse excess risk rates. To achieve this, we derive new empirical Bernstein-like concentration inequalities of independent interest that hold for certain non-i.i.d.~processes such as Martingale Difference Sequences.

The paper addresses joint sparsity selection in the regression coefficient matrix and the error precision (inverse covariance) matrix for high-dimensional multivariate regression models in the Bayesian paradigm. The selected sparsity patterns are crucial to help understand the network of relationships between the predictor and response variables, as well as the conditional relationships among the latter. While Bayesian methods have the advantage of providing natural uncertainty quantification through posterior inclusion probabilities and credible intervals, current Bayesian approaches either restrict to specific sub-classes of sparsity patterns and/or are not scalable to settings with hundreds of responses and predictors. Bayesian approaches which only focus on estimating the posterior mode are scalable, but do not generate samples from the posterior distribution for uncertainty quantification. Using a bi-convex regression based generalized likelihood and spike-and-slab priors, we develop an algorithm called Joint Regression Network Selector (JRNS) for joint regression and covariance selection which (a) can accommodate general sparsity patterns, (b) provides posterior samples for uncertainty quantification, and (c) is scalable and orders of magnitude faster than the state-of-the-art Bayesian approaches providing uncertainty quantification. We demonstrate the statistical and computational efficacy of the proposed approach on synthetic data and through the analysis of selected cancer data sets. We also establish high-dimensional posterior consistency for one of the developed algorithms.

Self-training algorithms, which train a model to fit pseudolabels predicted by another previously-learned model, have been very successful for learning with unlabeled data using neural networks. However, the current theoretical understanding of self-training only applies to linear models. This work provides a unified theoretical analysis of self-training with deep networks for semi-supervised learning, unsupervised domain adaptation, and unsupervised learning. At the core of our analysis is a simple but realistic ``expansion'' assumption, which states that a low-probability subset of the data must expand to a neighborhood with large probability relative to the subset. We also assume that neighborhoods of examples in different classes have minimal overlap. We prove that under these assumptions, the minimizers of population objectives based on self-training and input-consistency regularization will achieve high accuracy with respect to ground-truth labels. By using off-the-shelf generalization bounds, we immediately convert this result to sample complexity guarantees for neural nets that are polynomial in the margin and Lipschitzness. Our results help explain the empirical successes of recently proposed self-training algorithms which use input consistency regularization.

The superior performance of Deformable Convolutional Networks arises from its ability to adapt to the geometric variations of objects. Through an examination of its adaptive behavior, we observe that while the spatial support for its neural features conforms more closely than regular ConvNets to object structure, this support may nevertheless extend well beyond the region of interest, causing features to be influenced by irrelevant image content. To address this problem, we present a reformulation of Deformable ConvNets that improves its ability to focus on pertinent image regions, through increased modeling power and stronger training. The modeling power is enhanced through a more comprehensive integration of deformable convolution within the network, and by introducing a modulation mechanism that expands the scope of deformation modeling. To effectively harness this enriched modeling capability, we guide network training via a proposed feature mimicking scheme that helps the network to learn features that reflect the object focus and classification power of R-CNN features. With the proposed contributions, this new version of Deformable ConvNets yields significant performance gains over the original model and produces leading results on the COCO benchmark for object detection and instance segmentation.