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

For deep ordinal classification, learning a well-structured feature space specific to ordinal classification is helpful to properly capture the ordinal nature among classes. Intuitively, when Euclidean distance metric is used, an ideal ordinal layout in feature space would be that the sample clusters are arranged in class order along a straight line in space. However, enforcing samples to conform to a specific layout in the feature space is a challenging problem. To address this problem, in this paper, we propose a novel Constrained Proxies Learning (CPL) method, which can learn a proxy for each ordinal class and then adjusts the global layout of classes by constraining these proxies. Specifically, we propose two kinds of strategies: hard layout constraint and soft layout constraint. The hard layout constraint is realized by directly controlling the generation of proxies to force them to be placed in a strict linear layout or semicircular layout (i.e., two instantiations of strict ordinal layout). The soft layout constraint is realized by constraining that the proxy layout should always produce unimodal proxy-to-proxies similarity distribution for each proxy (i.e., to be a relaxed ordinal layout). Experiments show that the proposed CPL method outperforms previous deep ordinal classification methods under the same setting of feature extractor.

We consider random sample splitting for estimation and inference in high dimensional generalized linear models, where we first apply the lasso to select a submodel using one subsample and then apply the debiased lasso to fit the selected model using the remaining subsample. We show that, no matter including a prespecified subset of regression coefficients or not, the debiased lasso estimation of the selected submodel after a single splitting follows a normal distribution asymptotically. Furthermore, for a set of prespecified regression coefficients, we show that a multiple splitting procedure based on the debiased lasso can address the loss of efficiency associated with sample splitting and produce asymptotically normal estimates under mild conditions. Our simulation results indicate that using the debiased lasso instead of the standard maximum likelihood estimator in the estimation stage can vastly reduce the bias and variance of the resulting estimates. We illustrate the proposed multiple splitting debiased lasso method with an analysis of the smoking data of the Mid-South Tobacco Case-Control Study.

Stochastic models with global parameters $\bm{\theta}$ and latent variables $\bm{z}$ are common, and variational inference (VI) is popular for their estimation. This paper uses a variational approximation (VA) that comprises a Gaussian with factor covariance matrix for the marginal of $\bm{\theta}$, and the exact conditional posterior of $\bm{z}|\bm{\theta}$. Stochastic optimization for learning the VA only requires generation of $\bm{z}$ from its conditional posterior, while $\bm{\theta}$ is updated using the natural gradient, producing a hybrid VI method. We show that this is a well-defined natural gradient optimization algorithm for the joint posterior of $(\bm{z},\bm{\theta})$. Fast to compute expressions for the Tikhonov damped Fisher information matrix required to compute a stable natural gradient update are derived. We use the approach to estimate probabilistic Bayesian neural networks with random output layer coefficients to allow for heterogeneity. Simulations show that using the natural gradient is more efficient than using the ordinary gradient, and that the approach is faster and more accurate than two leading benchmark natural gradient VI methods. In a financial application we show that accounting for industry level heterogeneity using the deep model improves the accuracy of probabilistic prediction of asset pricing models.

The widely used 'Counterfactual' definition of Causal Effects was derived for unbiasedness and accuracy - and not generalizability. We propose a simple definition for the External Validity (EV) of interventions and counterfactuals. The definition leads to EV statistics for individual counterfactuals, and to non-parametric effect estimators for sets of counterfactuals (i.e., for samples). We use this definition to discuss several issues that have baffled the original counterfactual formulation: out-of-sample validity, reliance on independence assumptions or estimation, concurrent estimation of multiple effects and full-models, bias-variance tradeoffs, statistical power, omitted variables, and connections to current predictive and explaining techniques. Methodologically, the definition also allows us to replace the parametric, and generally ill-posed, estimation problems that followed the counterfactual definition by combinatorial enumeration problems in non-experimental samples. We use this framework to generalize popular supervised, explaining, and causal-effect estimators, improving their performance across three dimensions (External Validity, Unconfoundness and Accuracy), and enabling their use in non-i.i.d. samples. We demonstrate gains in out-of-sample prediction, intervention effect prediction, and causal effect estimation tasks. The COVID19 pandemic highlighted the need for learning solutions to provide general predictions in small samples - many times with missing variables. We also demonstrate applications in this pressing problem.

Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak stationarity, this paper derives the asymptotic distribution of the maximum of sample autocovariances and sample autocorrelations under weak conditions by using Gaussian approximation techniques. The asymptotic theory for parameter estimation obtained by fitting a (linear) autoregressive model to a general weakly stationary time series is revisited and a Gaussian approximation theorem for the maximum of the estimators of the autoregressive coefficients is derived. To perform statistical inference for the second order parameters considered, a bootstrap algorithm, the so-called second-order wild bootstrap, is applied. Consistency of this bootstrap procedure is proven. In contrast to existing bootstrap alternatives, validity of the second-order wild bootstrap does not require the imposition of strict stationary conditions or structural process assumptions, like linearity. The good finite sample performance of the second-order wild bootstrap is demonstrated by means of simulations.

This work considers the low-rank approximation of a matrix $A(t)$ depending on a parameter $t$ in a compact set $D \subset \mathbb{R}^d$. Application areas that give rise to such problems include computational statistics and dynamical systems. Randomized algorithms are an increasingly popular approach for performing low-rank approximation and they usually proceed by multiplying the matrix with random dimension reduction matrices (DRMs). Applying such algorithms directly to $A(t)$ would involve different, independent DRMs for every $t$, which is not only expensive but also leads to inherently non-smooth approximations. In this work, we propose to use constant DRMs, that is, $A(t)$ is multiplied with the same DRM for every $t$. The resulting parameter-dependent extensions of two popular randomized algorithms, the randomized singular value decomposition and the generalized Nystr\"{o}m method, are computationally attractive, especially when $A(t)$ admits an affine linear decomposition with respect to $t$. We perform a probabilistic analysis for both algorithms, deriving bounds on the expected value as well as failure probabilities for the $L^2$ approximation error when using Gaussian random DRMs. Both, the theoretical results and numerical experiments, show that the use of constant DRMs does not impair their effectiveness; our methods reliably return quasi-best low-rank approximations.

The recent literature on online learning to rank (LTR) has established the utility of prior knowledge to Bayesian ranking bandit algorithms. However, a major limitation of existing work is the requirement for the prior used by the algorithm to match the true prior. In this paper, we propose and analyze adaptive algorithms that address this issue and additionally extend these results to the linear and generalized linear models. We also consider scalar relevance feedback on top of click feedback. Moreover, we demonstrate the efficacy of our algorithms using both synthetic and real-world experiments.

Learning causal relationships from empirical observations is a central task in scientific research. A common method is to employ structural causal models that postulate noisy functional relations among a set of interacting variables. To ensure unique identifiability of causal directions, researchers consider restricted subclasses of structural causal models. Post-nonlinear (PNL) causal models constitute one of the most flexible options for such restricted subclasses, containing in particular the popular additive noise models as a further subclass. However, learning PNL models is not well studied beyond the bivariate case. The existing methods learn non-linear functional relations by minimizing residual dependencies and subsequently test independence from residuals to determine causal orientations. However, these methods can be prone to overfitting and, thus, difficult to tune appropriately in practice. As an alternative, we propose a new approach for PNL causal discovery that uses rank-based methods to estimate the functional parameters. This new approach exploits natural invariances of PNL models and disentangles the estimation of the non-linear functions from the independence tests used to find causal orientations. We prove consistency of our method and validate our results in numerical experiments.

This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of stochastic systems affected by external manipulation (interventions). This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust (out-of-distribution generalizing) prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. Our proposed estimators show, in certain settings, mean squared error improvements compared to both canonical and state-of-the-art estimators. We show that recent research on distributionally robust prediction methods has connections to well-studied estimators from econometrics. This connection leads us to prove that general K-class estimators possess distributional robustness properties. We, furthermore, propose a general framework for distributional robustness with respect to intervention-induced distributions. In this framework, we derive sufficient conditions for the identifiability of distributionally robust prediction methods and present impossibility results that show the necessity of several of these conditions. We present a new structure learning method applicable in additive noise models with directed trees as causal graphs. We prove consistency in a vanishing identifiability setup and provide a method for testing substructure hypotheses with asymptotic family-wise error control that remains valid post-selection. Finally, we present heuristic ideas for learning summary graphs of nonlinear time-series models.

Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple iterative methods such as gradient descent have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently. In this tutorial-style overview, we highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: (1) two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and (2) global landscape analysis and initialization-free algorithms. Several canonical matrix factorization problems are discussed, including but not limited to matrix sensing, phase retrieval, matrix completion, blind deconvolution, robust principal component analysis, phase synchronization, and joint alignment. Special care is taken to illustrate the key technical insights underlying their analyses. This article serves as a testament that the integrated consideration of optimization and statistics leads to fruitful research findings.