Research intended to estimate the effect of an action, like in randomized trials, often do not have random samples of the intended target population. Instead, estimates can be transported to the desired target population. Methods for transporting between populations are often premised on a positivity assumption, such that all relevant covariate patterns in one population are also present in the other. However, eligibility criteria, particularly in the case of trials, can result in violations of positivity. To address nonpositivity, a synthesis of statistical and mechanistic models was previously proposed in the context of violations by a single binary covariate. Here, we extend the synthesis approach for positivity violations with a continuous covariate. For estimation, two novel augmented inverse probability weighting estimators are proposed, with one based on estimating the parameters of a marginal structural model and the other based on estimating the conditional average causal effect. Both estimators are compared to other common approaches to address nonpositivity via a simulation study. Finally, the competing approaches are illustrated with an example in the context of two-drug versus one-drug antiretroviral therapy on CD4 T cell counts among women with HIV.
相關內容
A general theory of efficient estimation for ergodic diffusion processes sampled at high frequency with an infinite time horizon is presented. High frequency sampling is common in many applications, with finance as a prominent example. The theory is formulated in term of approximate martingale estimating functions and covers a large class of estimators including most of the previously proposed estimators for diffusion processes. Easily checked conditions ensuring that an estimating function is an approximate martingale are derived, and general conditions ensuring consistency and asymptotic normality of estimators are given. Most importantly, simple conditions are given that ensure rate optimality and efficiency. Rate optimal estimators of parameters in the diffusion coefficient converge faster than estimators of drift coefficient parameters because they take advantage of the information in the quadratic variation. The conditions facilitate the choice among the multitude of estimators that have been proposed for diffusion models. Optimal martingale estimating functions in the sense of Godambe and Heyde and their high frequency approximations are, under weak conditions, shown to satisfy the conditions for rate optimality and efficiency. This provides a natural feasible method of constructing explicit rate optimal and efficient estimating functions by solving a linear equation.
The use of alternative operations in differential cryptanalysis, or alternative notions of differentials, are lately receiving increasing attention. Recently, Civino et al. managed to design a block cipher which is secure w.r.t. classical differential cryptanalysis performed using XOR-differentials, but weaker with respect to the attack based on an alternative difference operation acting on the first s-box of the block. We extend this result to parallel alternative operations, i.e. acting on each s-box of the block. First, we recall the mathematical framework needed to define and use such operations. After that, we perform some differential experiments against a toy cipher and compare the effectiveness of the attack w.r.t. the one that uses XOR-differentials.
A technique that allows a formation-enforcing control (FEC) derived from graph rigidity theory to interface with a realistic relative localization system onboard lightweight Unmanned Aerial Vehicles (UAVs) is proposed in this paper. The proposed methodology enables reliable real-world deployment of UAVs in tight formation using real relative localization systems burdened by non-negligible sensory noise, which is typically not fully taken into account in FEC algorithms. The proposed solution is based on decomposition of the gradient descent-based FEC command into interpretable elements, and then modifying these individually based on the estimated distribution of sensory noise, such that the resulting action limits the probability of overshooting the desired formation. The behavior of the system has been analyzed and the practicality of the proposed solution has been compared to pure gradient-descent in real-world experiments where it presented significantly better performance in terms of oscillations, deviation from the desired state and convergence time.
Motivated by the need to model the dependence between regions of interest in functional neuroconnectivity for efficient inference, we propose a new sampling-based Bayesian clustering approach for covariance structures of high-dimensional Gaussian outcomes. The key technique is based on a Dirichlet process that clusters covariance sub-matrices into independent groups of outcomes, thereby naturally inducing sparsity in the whole brain connectivity matrix. A new split-merge algorithm is employed to achieve convergence of the Markov chain that is shown empirically to recover both uniform and Dirichlet partitions with high accuracy. We investigate the empirical performance of the proposed method through extensive simulations. Finally, the proposed approach is used to group regions of interest into functionally independent groups in the Autism Brain Imaging Data Exchange participants with autism spectrum disorder and and co-occurring attention-deficit/hyperactivity disorder.
This survey is concerned with the power of random information for approximation in the (deterministic) worst-case setting, with special emphasis on information consisting of functionals selected independently and identically distributed (iid) at random on a class of admissible information functionals. We present a general result based on a weighted least squares method and derive consequences for special cases. Improvements are available if the information is ``Gaussian'' or if we consider iid function values for Sobolev spaces. We include open questions to guide future research on the power of random information in the context of information-based complexity.
One tuple of probability vectors is more informative than another tuple when there exists a single stochastic matrix transforming the probability vectors of the first tuple into the probability vectors of the other. This is called matrix majorization. Solving an open problem raised by Mu et al, we show that if certain monotones - namely multivariate extensions of R\'{e}nyi divergences - are strictly ordered between the two tuples, then for sufficiently large $n$, there exists a stochastic matrix taking the $n$-fold Kronecker power of each input distribution to the $n$-fold Kronecker power of the corresponding output distribution. The same conditions, with non-strict ordering for the monotones, are also necessary for such matrix majorization in large samples. Our result also gives conditions for the existence of a sequence of statistical maps that asymptotically (with vanishing error) convert a single copy of each input distribution to the corresponding output distribution with the help of a catalyst that is returned unchanged. Allowing for transformation with arbitrarily small error, we find conditions that are both necessary and sufficient for such catalytic matrix majorization. We derive our results by building on a general algebraic theory of preordered semirings recently developed by one of the authors. This also allows us to recover various existing results on majorization in large samples and in the catalytic regime as well as relative majorization in a unified manner.
Accent conversion aims to convert the accent of a source speech to a target accent, meanwhile preserving the speaker's identity. This paper introduces a novel non-autoregressive framework for accent conversion that learns accent-agnostic linguistic representations and employs them to convert the accent in the source speech. Specifically, the proposed system aligns speech representations with linguistic representations obtained from Text-to-Speech (TTS) systems, enabling training of the accent voice conversion model on non-parallel data. Furthermore, we investigate the effectiveness of a pretraining strategy on native data and different acoustic features within our proposed framework. We conduct a comprehensive evaluation using both subjective and objective metrics to assess the performance of our approach. The evaluation results highlight the benefits of the pretraining strategy and the incorporation of richer semantic features, resulting in significantly enhanced audio quality and intelligibility.
For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are typically performed at discrete nodal locations, which is not sufficient to ensure the robustness of the scheme when the solution must be evaluated at arbitrary locations (e.g., for adaptive mesh refinement, remapping in arbitrary Lagragian--Eulerian solvers, overset meshes, etc.). In this work, a novel limiting approach for discontinuous Galerkin methods is presented which ensures that the solution is continuously bounds-preserving (i.e., across the entire solution polynomial) for any arbitrary choice of basis, approximation order, and mesh element type. Through a modified formulation for the constraint functionals, the proposed approach requires only the solution of a single spatial scalar minimization problem per element for which a highly efficient numerical optimization procedure is presented. The efficacy of this approach is shown in numerical experiments by enforcing continuous constraints in high-order unstructured discontinuous Galerkin discretizations of hyperbolic conservation laws, ranging from scalar transport with maximum principle preserving constraints to compressible gas dynamics with positivity-preserving constraints.
The implicit trace estimation problem asks for an approximation of the trace of a square matrix, accessed via matrix-vector products (matvecs). This paper designs new randomized algorithms, XTrace and XNysTrace, for the trace estimation problem by exploiting both variance reduction and the exchangeability principle. For a fixed budget of matvecs, numerical experiments show that the new methods can achieve errors that are orders of magnitude smaller than existing algorithms, such as the Girard-Hutchinson estimator or the Hutch++ estimator. A theoretical analysis confirms the benefits by offering a precise description of the performance of these algorithms as a function of the spectrum of the input matrix. The paper also develops an exchangeable estimator, XDiag, for approximating the diagonal of a square matrix using matvecs.
The homogenization of elliptic divergence-type fourth-order operators with periodic coefficients is studied in a (periodic) domain. The aim is to find an operator with constant coefficients and represent the equation through a perturbation around this operator. The resolvent is found as $L^2 \to L^2$ operator using the Neumann series for the periodic fundamental solution of biharmonic operator. Results are based on some auxiliary Lemmas suggested by Bensoussan in 1986, Zhikov in 1991, Yu. Grabovsky and G. Milton in 1998, Pastukhova in 2016. Operators of the type considered in the paper appear in the study of the elastic properties of thin plates. The choice of the operator with constant coefficients is discussed separately and chosen in an optimal way w.r.t. the spectral radius and convergence of the Neumann series and uses the known bounds for ''homogenized'' coefficients. Similar ideas are usually applied for the construction of preconditioners for iterative solvers for finite dimensional problems resulting from discretized PDEs. The method presented is similar to Cholesky factorization transferred to elliptic operators (as in references mentioned above). Furthermore, the method can be applied to non-linear problems.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191