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 study the robust mean estimation problem in high dimensions, where less than half of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, we formulate the robust mean estimation problem as the minimization of the $\ell_0$-`norm' of an \emph{outlier indicator vector}, under a second moment constraint on the datapoints. We further relax the $\ell_0$-`norm' to the $\ell_p$-norm ($0<p\leq 1$) in the objective and prove that the global minima for each of these objectives are order-optimal for the robust mean estimation problem. Then we propose a computationally tractable iterative $\ell_p$-minimization and hard thresholding algorithm that outputs an order-optimal robust estimate of the population mean. Both synthetic and real data experiments demonstrate that the proposed algorithm outperforms state-of-the-art robust mean estimation methods. The source code will be made available at GitHub.

We formulate an efficient approximation for multi-agent batch reinforcement learning, the approximated multi-agent fitted Q iteration (AMAFQI). We present a detailed derivation of our approach. We propose an iterative policy search and show that it yields a greedy policy with respect to multiple approximations of the centralized, learned Q-function. In each iteration and policy evaluation, AMAFQI requires a number of computations that scales linearly with the number of agents whereas the analogous number of computations increase exponentially for the fitted Q iteration (FQI), a commonly used approaches in batch reinforcement learning. This property of AMAFQI is fundamental for the design of a tractable multi-agent approach. We evaluate the performance of AMAFQI and compare it to FQI in numerical simulations. The simulations illustrate the significant computation time reduction when using AMAFQI instead of FQI in multi-agent problems and corroborate the similar performance of both approaches.

The quadrature error associated with a regular quadrature rule for evaluation of a layer potential increases rapidly when the evaluation point approaches the surface and the integral becomes nearly singular. Error estimates are needed to determine when the accuracy is insufficient and a more costly special quadrature method should be utilized. The final result of this paper are such quadrature error estimates for the composite Gauss-Legendre rule and the global trapezoidal rule, when applied to evaluate layer potentials defined over smooth curved surfaces in R^3. The estimates have no unknown coefficients and can be efficiently evaluated given the discretization of the surface, invoking a local one-dimensional root-finding procedure. They are derived starting with integrals over curves, using complex analysis involving contour integrals, residue calculus and branch cuts. By complexifying the parameter plane, the theory can be used to derive estimates also for curves in in R^3. These results are then used in the derivation of the estimates for integrals over surfaces. In this procedure, we also obtain error estimates for layer potentials evaluated over curves in R^2. Such estimates combined with a local root-finding procedure for their evaluation were earlier derived for the composite Gauss-Legendre rule for layer potentials written on complex form [4]. This is here extended to provide quadrature error estimates for both complex and real formulations of layer potentials, both for the Gauss-Legendre and the trapezoidal rule. Numerical examples are given to illustrate the performance of the quadrature error estimates. The estimates for integration over curves are in many cases remarkably precise, and the estimates for curved surfaces in R^3 are also sufficiently precise, with sufficiently low computational cost, to be practically useful.

Linear minimum mean square error (LMMSE) estimation is often ill-conditioned, suggesting that unconstrained minimization of the mean square error is an inadequate principle for filter design. To address this, we first develop a unifying framework for studying constrained LMMSE estimation problems. Using this framework, we expose an important structural property of constrained LMMSE filters: They generally involve an inherent preconditioning step. This parameterizes all such filters only by their preconditioners. Moreover, each filters is invariant to invertible linear transformations of its preconditioner. We then clarify that merely constraining the rank of the filter does not suitably address the problem of ill-conditioning. Instead, we adopt a constraint that explicitly requires solutions to be well-conditioned in a certain specific sense. We introduce two well-conditioned filters and show that they converge to the unconstrained LMMSE filter as their truncated-power loss goes to zero, at the same rate as the low-rank Wiener filter. We also show extensions to the case of weighted trace and determinant of the error covariance as objective functions. Finally, we show quantitative results with historical VIX data to demonstrate that our two well-conditioned filters have stable performance while the standard LMMSE filter deteriorates with increasing condition number.

Multicopters are among the most versatile mobile robots. Their applications range from inspection and mapping tasks to providing vital reconnaissance in disaster zones and to package delivery. The range, endurance, and speed a multirotor vehicle can achieve while performing its task is a decisive factor not only for vehicle design and mission planning, but also for policy makers deciding on the rules and regulations for aerial robots. To the best of the authors' knowledge, this work proposes the first approach to estimate the range, endurance, and optimal flight speed for a wide variety of multicopters. This advance is made possible by combining a state-of-the-art first-principles aerodynamic multicopter model based on blade-element-momentum theory with an electric-motor model and a graybox battery model. This model predicts the cell voltage with only 1.3% relative error (43.1 mV), even if the battery is subjected to non-constant discharge rates. Our approach is validated with real-world experiments on a test bench as well as with flights at speeds up to 65 km/h in one of the world's largest motion-capture systems. We also present an accurate pen-and-paper algorithm to estimate the range, endurance and optimal speed of multicopters to help future researchers build drones with maximal range and endurance, ensuring that future multirotor vehicles are even more versatile.

In this paper, we study a non-local approximation of the time-dependent (local) Eikonal equation with Dirichlet-type boundary conditions, where the kernel in the non-local problem is properly scaled. Based on the theory of viscosity solutions, we prove existence and uniqueness of the viscosity solutions of both the local and non-local problems, as well as regularity properties of these solutions in time and space. We then derive error bounds between the solution to the non-local problem and that of the local one, both in continuous-time and Backward Euler time discretization. We then turn to studying continuum limits of non-local problems defined on random weighted graphs with $n$ vertices. In particular, we establish that if the kernel scale parameter decreases at an appropriate rate as $n$ grows, then almost surely, the solution of the problem on graphs converges uniformly to the viscosity solution of the local problem as the time step vanishes and the number vertices $n$ grows large.

Personalized decision-making, aiming to derive optimal individualized treatment rules (ITRs) based on individual characteristics, has recently attracted increasing attention in many fields, such as medicine, social services, and economics. Current literature mainly focuses on estimating ITRs from a single source population. In real-world applications, the distribution of a target population can be different from that of the source population. Therefore, ITRs learned by existing methods may not generalize well to the target population. Due to privacy concerns and other practical issues, individual-level data from the target population is often not available, which makes ITR learning more challenging. We consider an ITR estimation problem where the source and target populations may be heterogeneous, individual data is available from the source population, and only the summary information of covariates, such as moments, is accessible from the target population. We develop a weighting framework that tailors an ITR for a given target population by leveraging the available summary statistics. Specifically, we propose a calibrated augmented inverse probability weighted estimator of the value function for the target population and estimate an optimal ITR by maximizing this estimator within a class of pre-specified ITRs. We show that the proposed calibrated estimator is consistent and asymptotically normal even with flexible semi/nonparametric models for nuisance function approximation, and the variance of the value estimator can be consistently estimated. We demonstrate the empirical performance of the proposed method using simulation studies and a real application to an eICU dataset as the source sample and a MIMIC-III dataset as the target sample.

We study the off-policy evaluation (OPE) problem in an infinite-horizon Markov decision process with continuous states and actions. We recast the $Q$-function estimation into a special form of the nonparametric instrumental variables (NPIV) estimation problem. We first show that under one mild condition the NPIV formulation of $Q$-function estimation is well-posed in the sense of $L^2$-measure of ill-posedness with respect to the data generating distribution, bypassing a strong assumption on the discount factor $\gamma$ imposed in the recent literature for obtaining the $L^2$ convergence rates of various $Q$-function estimators. Thanks to this new well-posed property, we derive the first minimax lower bounds for the convergence rates of nonparametric estimation of $Q$-function and its derivatives in both sup-norm and $L^2$-norm, which are shown to be the same as those for the classical nonparametric regression (Stone, 1982). We then propose a sieve two-stage least squares estimator and establish its rate-optimality in both norms under some mild conditions. Our general results on the well-posedness and the minimax lower bounds are of independent interest to study not only other nonparametric estimators for $Q$-function but also efficient estimation on the value of any target policy in off-policy settings.

We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.

In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective function, and (2) the Lipschitz continuity of local individual functions. Under the local regularity assumption, we provide the first optimal first-order decentralized algorithm called multi-step primal-dual (MSPD) and its corresponding optimal convergence rate. A notable aspect of this result is that, for non-smooth functions, while the dominant term of the error is in $O(1/\sqrt{t})$, the structure of the communication network only impacts a second-order term in $O(1/t)$, where $t$ is time. In other words, the error due to limits in communication resources decreases at a fast rate even in the case of non-strongly-convex objective functions. Under the global regularity assumption, we provide a simple yet efficient algorithm called distributed randomized smoothing (DRS) based on a local smoothing of the objective function, and show that DRS is within a $d^{1/4}$ multiplicative factor of the optimal convergence rate, where $d$ is the underlying dimension.