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

We propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in settings that also include heavy-tailed covariates and errors. Moreover, our procedure can be valid under clustered errors, which is important in practice, but has been largely overlooked by earlier work. Through extensive simulations, we illustrate our method's wider range of applicability as suggested by theory. In particular, we show that our method outperforms state-of-art methods in challenging, yet more realistic, settings where the distribution of covariates is heavy-tailed or the sample size is small, while it remains competitive in standard, ``well behaved" settings previously studied in the literature.

Continuously-indexed flows (CIFs) have recently achieved improvements over baseline normalizing flows on a variety of density estimation tasks. CIFs do not possess a closed-form marginal density, and so, unlike standard flows, cannot be plugged in directly to a variational inference (VI) scheme in order to produce a more expressive family of approximate posteriors. However, we show here how CIFs can be used as part of an auxiliary VI scheme to formulate and train expressive posterior approximations in a natural way. We exploit the conditional independence structure of multi-layer CIFs to build the required auxiliary inference models, which we show empirically yield low-variance estimators of the model evidence. We then demonstrate the advantages of CIFs over baseline flows in VI problems when the posterior distribution of interest possesses a complicated topology, obtaining improved results in both the Bayesian inference and surrogate maximum likelihood settings.

Learning the causal structure that underlies data is a crucial step towards robust real-world decision making. The majority of existing work in causal inference focuses on determining a single directed acyclic graph (DAG) or a Markov equivalence class thereof. However, a crucial aspect to acting intelligently upon the knowledge about causal structure which has been inferred from finite data demands reasoning about its uncertainty. For instance, planning interventions to find out more about the causal mechanisms that govern our data requires quantifying epistemic uncertainty over DAGs. While Bayesian causal inference allows to do so, the posterior over DAGs becomes intractable even for a small number of variables. Aiming to overcome this issue, we propose a form of variational inference over the graphs of Structural Causal Models (SCMs). To this end, we introduce a parametric variational family modelled by an autoregressive distribution over the space of discrete DAGs. Its number of parameters does not grow exponentially with the number of variables and can be tractably learned by maximising an Evidence Lower Bound (ELBO). In our experiments, we demonstrate that the proposed variational posterior is able to provide a good approximation of the true posterior.

Multi-modal distributions are commonly used to model clustered data in statistical learning tasks. In this paper, we consider the Mixed Linear Regression (MLR) problem. We propose an optimal transport-based framework for MLR problems, Wasserstein Mixed Linear Regression (WMLR), which minimizes the Wasserstein distance between the learned and target mixture regression models. Through a model-based duality analysis, WMLR reduces the underlying MLR task to a nonconvex-concave minimax optimization problem, which can be provably solved to find a minimax stationary point by the Gradient Descent Ascent (GDA) algorithm. In the special case of mixtures of two linear regression models, we show that WMLR enjoys global convergence and generalization guarantees. We prove that WMLR's sample complexity grows linearly with the dimension of data. Finally, we discuss the application of WMLR to the federated learning task where the training samples are collected by multiple agents in a network. Unlike the Expectation Maximization algorithm, WMLR directly extends to the distributed, federated learning setting. We support our theoretical results through several numerical experiments, which highlight our framework's ability to handle the federated learning setting with mixture models.

The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm retains the attractive properties of the standard GP as a nonparametric and flexible regression method, it can greatly improve the model accuracy for contaminated data even in the presence of extreme or abundant outliers. It is also easier to implement compared with previous robust GP variants that rely on approximate inference. Applied to a wide range of experiments with different contamination levels, the proposed method significantly outperforms the standard GP and the popular robust GP variant with the Student-t likelihood in most test cases. In addition, as a practical example in the astrophysical study, we show that this method can precisely determine the main-sequence ridge line in the color-magnitude diagram of star clusters.

We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with $d$ states. We propose a data-driven distributionally robust optimization model to estimate the problem's objective function and optimal solution. By leveraging results from large deviations theory, we derive statistical guarantees on the quality of these estimators. The underlying worst-case expectation problem is nonconvex and involves $\mathcal O(d^2)$ decision variables. Thus, it cannot be solved efficiently for large $d$. By exploiting the structure of this problem, we devise a customized Frank-Wolfe algorithm with convex direction-finding subproblems of size $\mathcal O(d)$. We prove that this algorithm finds a stationary point efficiently under mild conditions. The efficiency of the method is predicated on a dimensionality reduction enabled by a dual reformulation. Numerical experiments indicate that our approach has better computational and statistical properties than the state-of-the-art methods.

Sometimes, it is possible to represent a complicated polytope as a projection of a much simpler polytope. To quantify this phenomenon, the extension complexity of a polytope $P$ is defined to be the minimum number of facets in a (possibly higher-dimensional) polytope from which $P$ can be obtained as a (linear) projection. This notion has been studied for several decades, motivated by its relevance for combinatorial optimisation problems. It is an important question to understand the extent to which the extension complexity of a polytope is controlled by its dimension, and in this paper we prove three different results along these lines. First, we prove that for a fixed dimension $d$, the extension complexity of a random $d$-dimensional polytope (obtained as the convex hull of random points in a ball or on a sphere) is typically on the order of the square root of its number of vertices. Second, we prove that any cyclic $n$-vertex polygon (whose vertices lie on a circle) has extension complexity at most $24\sqrt n$. This bound is tight up to the constant factor $24$. Finally, we show that there exists an $n^{o(1)}$-dimensional polytope with at most $n$ facets and extension complexity $n^{1-o(1)}$.

It is becoming increasingly common to study complex associations between multiple phenotypes and high-dimensional genomic features in biomedicine. However, it requires flexible and efficient joint statistical models if there are correlations between multiple response variables and between high-dimensional predictors. We propose a structured multivariate Bayesian variable selection model to identify sparse predictors associated with multiple correlated response variables. The approach makes use of known structure information between the multiple response variables and high-dimensional predictors via a Markov random field (MRF) prior for the latent indicator variables of the coefficient matrix of a sparse seemingly unrelated regressions (SSUR). The structure information included in the MRF prior can improve the model performance (i.e., variable selection and response prediction) compared to other common priors. In addition, we employ random effects to capture heterogeneity of grouped samples. The proposed approach is validated by simulation studies and applied to a pharmacogenomic study which includes pharmacological profiling and multi-omics data (i.e., gene expression, copy number variation and mutation) from in vitro anti-cancer drug sensitivity screening.

Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regressions remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more parsimonious way than nonparametric smoothing methods. However, while deep learning brought breakthroughs in prediction, it often lacks interpretability due to the black-box nature of multilayer structure with millions of parameters, hence it is not well suited for statistical inference. In this paper, we leverage the advantages of deep learning to apply it to quantile regression where the goal to produce interpretable results and perform statistical inference. We achieve this by adopting a semiparametric approach based on the partially linear quantile regression model, where covariates of primary interest for statistical inference are modelled linearly and all other covariates are modelled nonparametrically by means of a deep neural network. In addition to the new methodology, we provide theoretical justification for the proposed model by establishing the root-$n$ consistency and asymptotically normality of the parametric coefficient estimator and the minimax optimal convergence rate of the neural nonparametric function estimator. Across several simulated and real data examples, our proposed model empirically produces superior estimates and more accurate predictions than various alternative approaches.

We propose a new diffusion-asymptotic analysis for sequentially randomized experiments, including those that arise in solving multi-armed bandit problems. In an experiment with $ n $ time steps, we let the mean reward gaps between actions scale to the order $1/\sqrt{n}$ so as to preserve the difficulty of the learning task as $n$ grows. In this regime, we show that the behavior of a class of sequentially randomized Markov experiments converges to a diffusion limit, given as the solution of a stochastic differential equation. The diffusion limit thus enables us to derive refined, instance-specific characterization of the stochastic dynamics of adaptive experiments. As an application of this framework, we use the diffusion limit to obtain several new insights on the regret and belief evolution of Thompson sampling. We show that a version of Thompson sampling with an asymptotically uninformative prior variance achieves nearly-optimal instance-specific regret scaling when the reward gaps are relatively large. We also demonstrate that, in this regime, the posterior beliefs underlying Thompson sampling are highly unstable over time.