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

The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of methods, only a few of them allow for rigorous error control. In this paper, we propose a rigorous error bound for the reduction of linear systems with balancing-related reduction methods. More specifically, we consider the simulation over a finite time interval and provide an a posteriori adaption of the standard a priori bound for Balanced Truncation and Balanced Singular Perturbation Approximation in that setting, which improves the error estimation while still yielding a rigorous bound. Our result is based on an error splitting induced by a Fourier series approximation of the input and a subsequent refined error analysis. We make use of system-theoretic concepts, such as the notion of signal generator driven systems, steady-states and observability. Our bound is also applicable in the presence of nonzero initial conditions. Numerical evidence for the sharpness of the bound is given.

Complex projects developed under the paradigm of model-driven engineering nowadays often involve several interrelated models, which are automatically processed via a multitude of model operations. Modular and incremental construction and execution of such networks of models and model operations are required to accommodate efficient development with potentially large-scale models. The underlying problem is also called Global Model Management. In this report, we propose an approach to modular and incremental Global Model Management via an extension to the existing technique of Generalized Discrimination Networks (GDNs). In addition to further generalizing the notion of query operations employed in GDNs, we adapt the previously query-only mechanism to operations with side effects to integrate model transformation and model synchronization. We provide incremental algorithms for the execution of the resulting extended Generalized Discrimination Networks (eGDNs), as well as a prototypical implementation for a number of example eGDN operations. Based on this prototypical implementation, we experiment with an application scenario from the software development domain to empirically evaluate our approach with respect to scalability and conceptually demonstrate its applicability in a typical scenario. Initial results confirm that the presented approach can indeed be employed to realize efficient Global Model Management in the considered scenario.

This work considers stationary vector count time series models defined via deterministic functions of a latent stationary vector Gaussian series. The construction is very general and ensures a pre-specified marginal distribution for the counts in each dimension, depending on unknown parameters that can be marginally estimated. The vector Gaussian series injects flexibility into the model's temporal and cross-dimensional dependencies, perhaps through a parametric model akin to a vector autoregression. We show that the latent Gaussian model can be estimated by relating the covariances of the counts and the latent Gaussian series. In a possibly high-dimensional setting, concentration bounds are established for the differences between the estimated and true latent Gaussian autocovariances, in terms of those for the observed count series and the estimated marginal parameters. The results are applied to the case where the latent Gaussian series is a vector autoregression, and its parameters are estimated sparsely through a LASSO-type procedure.

We study estimation and testing in the Poisson regression model with noisy high dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a non-convex target function to minimize. Treating the high dimensional issue further leads us to augment an amenable penalty term to the target function. We propose to estimate the regression parameter through minimizing the penalized target function. We derive the L1 and L2 convergence rates of the estimator and prove the variable selection consistency. We further establish the asymptotic normality of any subset of the parameters, where the subset can have infinitely many components as long as its cardinality grows sufficiently slow. We develop Wald and score tests based on the asymptotic normality of the estimator, which permits testing of linear functions of the members if the subset. We examine the finite sample performance of the proposed tests by extensive simulation. Finally, the proposed method is successfully applied to the Alzheimer's Disease Neuroimaging Initiative study, which motivated this work initially.

Computational differential privacy (CDP) is a natural relaxation of the standard notion of (statistical) differential privacy (SDP) proposed by Beimel, Nissim, and Omri (CRYPTO 2008) and Mironov, Pandey, Reingold, and Vadhan (CRYPTO 2009). In contrast to SDP, CDP only requires privacy guarantees to hold against computationally-bounded adversaries rather than computationally-unbounded statistical adversaries. Despite the question being raised explicitly in several works (e.g., Bun, Chen, and Vadhan, TCC 2016), it has remained tantalizingly open whether there is any task achievable with the CDP notion but not the SDP notion. Even a candidate such task is unknown. Indeed, it is even unclear what the truth could be! In this work, we give the first construction of a task achievable with the CDP notion but not the SDP notion. More specifically, under strong but plausible cryptographic assumptions, we construct a task for which there exists an $\varepsilon$-CDP mechanism with $\varepsilon = O(1)$ achieving $1-o(1)$ utility, but any $(\varepsilon, \delta)$-SDP mechanism, including computationally unbounded ones, that achieves a constant utility must use either a super-constant $\varepsilon$ or a non-negligible $\delta$. To prove this, we introduce a new approach for showing that a mechanism satisfies CDP: first we show that a mechanism is "private" against a certain class of decision tree adversaries, and then we use cryptographic constructions to "lift" this into privacy against computational adversaries. We believe this approach could be useful to devise further tasks separating CDP from SDP.

Augmenting the control arm of a randomized controlled trial (RCT) with external data may increase power at the risk of introducing bias. Existing data fusion estimators generally rely on stringent assumptions or may have decreased coverage or power in the presence of bias. Framing the problem as one of data-adaptive experiment selection, potential experiments include the RCT only or the RCT combined with different candidate real-world datasets. To select and analyze the experiment with the optimal bias-variance tradeoff, we develop a novel experiment-selector cross-validated targeted maximum likelihood estimator (ES-CVTMLE). The ES-CVTMLE uses two bias estimates: 1) a function of the difference in conditional mean outcome under control between the RCT and combined experiments and 2) an estimate of the average treatment effect on a negative control outcome (NCO). We define the asymptotic distribution of the ES-CVTMLE under varying magnitudes of bias and construct confidence intervals by Monte Carlo simulation. In simulations involving violations of identification assumptions, the ES-CVTMLE had better coverage than test-then-pool approaches and an NCO-based bias adjustment approach and higher power than one implementation of a Bayesian dynamic borrowing approach. We further demonstrate the ability of the ES-CVTMLE to distinguish biased from unbiased external controls through a re-analysis of the effect of liraglutide on glycemic control from the LEADER trial. The ES-CVTMLE has the potential to improve power while providing relatively robust inference for future hybrid RCT-RWD studies.

Causal discovery and causal reasoning are classically treated as separate and consecutive tasks: one first infers the causal graph, and then uses it to estimate causal effects of interventions. However, such a two-stage approach is uneconomical, especially in terms of actively collected interventional data, since the causal query of interest may not require a fully-specified causal model. From a Bayesian perspective, it is also unnatural, since a causal query (e.g., the causal graph or some causal effect) can be viewed as a latent quantity subject to posterior inference -- other unobserved quantities that are not of direct interest (e.g., the full causal model) ought to be marginalized out in this process and contribute to our epistemic uncertainty. In this work, we propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning, which jointly infers a posterior over causal models and queries of interest. In our approach to ABCI, we focus on the class of causally-sufficient, nonlinear additive noise models, which we model using Gaussian processes. We sequentially design experiments that are maximally informative about our target causal query, collect the corresponding interventional data, and update our beliefs to choose the next experiment. Through simulations, we demonstrate that our approach is more data-efficient than several baselines that only focus on learning the full causal graph. This allows us to accurately learn downstream causal queries from fewer samples while providing well-calibrated uncertainty estimates for the quantities of interest.

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.

Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.

Analyzing observational data from multiple sources can be useful for increasing statistical power to detect a treatment effect; however, practical constraints such as privacy considerations may restrict individual-level information sharing across data sets. This paper develops federated methods that only utilize summary-level information from heterogeneous data sets. Our federated methods provide doubly-robust point estimates of treatment effects as well as variance estimates. We derive the asymptotic distributions of our federated estimators, which are shown to be asymptotically equivalent to the corresponding estimators from the combined, individual-level data. We show that to achieve these properties, federated methods should be adjusted based on conditions such as whether models are correctly specified and stable across heterogeneous data sets.