The Proximal Bootstrap for Finite-Dimensional Regularized Estimators

2021 ◽  
Vol 111 ◽  
pp. 616-620
Author(s):  
Jessie Li
Keyword(s):  
Optimization Problem ◽  
Closed Form Solution ◽  
Form Solution ◽  
Support Vector ◽  
Computationally Efficient ◽  
L1 Norm ◽  
Efficient Manner ◽  
Finite Dimensional ◽  
Consistent Estimators ◽  
Nuclear Norm Regularization

We propose a proximal bootstrap that can consistently estimate the limiting distribution of sqrt(n)-consistent estimators with nonstandardasymptotic distributions in a computationally efficient manner by formulating the proximal bootstrap estimator as the solution to aconvex optimization problem, which can have a closed-form solution for certain designs. This paper considers the application to finite-dimensionalregularized estimators, such as the lasso, l1-norm regularized quantile regression, l1-norm support vector regression, and trace regression via nuclear norm regularization.

scholarly journals Design of Cut off-Frequency Fixing Filters by Error Compensation of MAXFLAT FIR Filters

Electronics ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 553
Author(s):  
Daewon Chung ◽  
Woon Cho ◽  
Inyeob Jeong ◽  
Joonhyeon Jeon
Keyword(s):  
Closed Form ◽  
Error Compensation ◽  
Finite Impulse Response ◽  
Cutoff Frequency ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fir Filters ◽  
Frequency Error ◽  
Computationally Efficient ◽  
Filter Type

Maximally-flat (MAXFLAT) finite impulse response (FIR) filters often face a problem of the cutoff-frequency error due to approximation of the desired frequency response by some closed-form solution. So far, there have been plenty of efforts to design such a filter with an arbitrarily specified cut off-frequency, but this filter type requires extensive computation and is not MAXFLAT anymore. Thus, a computationally efficient and effective design is needed for highly accurate filters with desired frequency characteristics. This paper describes a new method for designing cutoff-frequency-fixing FIR filters through the cutoff-frequency error compensation of MAXFLAT FIR filters. The proposed method provides a closed-form Chebyshev polynomial containing a cutoff-error compensation function, which can characterize the “cutoff-error-free” filters in terms of the degree of flatness for a given order of filter and cut off-frequency. This method also allows a computationally efficient and accurate formula to directly determine the degree of flatness, so that this filter type has a flat magnitude characteristic both in the passband and the stopband. The remarkable effectiveness of the proposed method in design efficiency and accuracy is clearly demonstrated through various examples, indicating that the cutoff-fixing filters exhibit amplitude distortion error of less than 10−14 and no cut off-frequency error. This new approach is shown to provide significant advantages over the previous works in design flexibility and accuracy.

Real Time Trajectory Modification Using a Closed Form Solution

1992 ◽  
Author(s):  
Michael R. Hummels ◽  
Raymond J. Cipra
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Interval ◽  
Efficient Manner ◽  
Planning Strategy ◽  
Higher Derivatives ◽  
On Line ◽  
Line Trajectory

Abstract An on-line trajectory modification and path planning strategy is developed which will allow a robot to respond in an efficient manner to real time sensory input. The approach developed here eliminates the need for solving many equations by developing a closed form algorithm. It uses two fourth order curves for the transition phases with a constant velocity section in between. Although this is done by providing additional constraints to the curve, it makes the problem of determining the trajectory much easier to solve, while providing continuous higher derivatives. It also provides a safe and efficient way of modifying trajectories based on the robots joint rate limits, joint acceleration limits, jerk limits, and desired time interval between trajectory modifications for a 4-1-4 trajectory. This method involves the solution of one second order equation and is directed toward real time applications.

A New Approach to the Control Design of Fuzzy Dynamical Systems

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Ye-Hwa Chen
Keyword(s):  
Dynamical Systems ◽  
Optimization Problem ◽  
Closed Form Solution ◽  
Control Design ◽  
Form Solution ◽  
Bottom Line ◽  
New Approach ◽  
Fuzzy Dynamical System ◽  
The Cost ◽  
Fuzzy Dynamical Systems

A new approach to the control design for fuzzy dynamical systems is proposed. For a fuzzy dynamical system, the uncertainty lies within a fuzzy set. The desirable system performance is twofold: one deterministic and one fuzzy. While the deterministic performance assures the bottom line, the fuzzy performance enhances the cost consideration. Under this setting, a class of robust controls is proposed. The control is deterministic and is not if-then rules-based. An optimal design problem associated with the control is then formulated as a constrained optimization problem. We show that the problem can be solved and the solution exists and is unique. The closed-form solution and cost are explicitly shown. The resulting control is able to guarantee the prescribed deterministic performance and minimize the average fuzzy performance.

scholarly journals Closed form solution in buckling optimization problem of twisted rod

2021 ◽  
Author(s):  
Vladimir Kobelev
Keyword(s):  
Closed Form ◽  
Cross Section ◽  
Cross Sections ◽  
Optimization Problem ◽  
Closed Form Solution ◽  
Form Solution ◽  
Optimal Shape ◽  
Actual Problem ◽  
The Cross ◽  
Simply Connected

Abstract The applications of this method for stability problems are illustrated in this manuscript. In the context of twisted rods, the counterpart for Euler’s buckling problem is Greenhill's problem, which studies the forming of a loop in an elastic bar under torsion (Greenhill, 1883). We search the optimal shape of the rod along its axis. A priori form of the cross-section remains unknown. For the solution of the actual problem the stability equations take into account all possible convex, simply connected shapes of the cross-section. Thus, we drop the assumption about the equality of principle moments of inertia for the cross-section. The cross-sections are similar geometric figures related by a homothetic transformation with respect to a homothetic center on the axis of the rod and vary along its axis. The distribution of material along the length of a twisted rod is optimized so that the rod is of the constant volume T and will support the maximal moment without spatial buckling. The cross section that delivers the maximum or the minimum for the critical eigenvalue must be determined among all convex, simply connected domains. We demonstrate at the beginning the validity of static Euler’s approach for simply supported rod (hinged), twisted by the conservative moment. The applied method for integration of the optimization criteria delivers different length and volumes of the optimal twisted rods. Instead of the seeking for the twisted rods of the fixed length and volume, we directly compare the twisted rods with the different lengths and cross-sections using the invariant factors. The solution of optimization problem for twisted rod is stated in closed form in terms of the higher transcendental functions. In the torsion stability problem, the optimal shape of cross-section is the equilateral triangle.

Combined Expansion and Orthogonalization of Experimental Modeshapes

2004 ◽  
Vol 127 (2) ◽  
pp. 188-196 ◽  
Author(s):  
Y. Halevi ◽  
C. A. Morales ◽  
D. J. Inman
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Model Updating ◽  
Mass Matrix ◽  
Closed Form Solution ◽  
Form Solution ◽  
Entire Structure ◽  
Error Localization ◽  
Procrustes Problem

The paper describes a method of combined expansion and orthogonalization (CEO) of experimental modeshapes. Most model updating and error localization methods require a set of full length, orthogonal with respect to the mass matrix, eigenvectors. In practically every modal experiment, the number of measurements is less than the order of the model, and hence modeshape expansion, i.e., adding the unmeasured degrees of freedom, is required. This step is then followed by orthogonalization with respect to the mass matrix. Most current methods use two separate steps for expansion and orthogonalization, each one optimal by itself, but their combination is not optimal. The suggested method combines the two steps into one optimization problem for both steps, and minimizes a quadratic criterion. In the case of an equal number of analytical and experimental modeshapes, the problem coincides with the Procrustes problem and has a closed form solution. Otherwise the solution involves nonlinear equations. Several examples show the advantage of CEO, especially in cases where the measurements are limited either in number or in space, i.e., not spanned through the entire structure.

Closed-Form Solution for Computationally Efficient Symbol-Level Precoding

2018 ◽  
Author(s):  
Jevgenij Krivochiza ◽  
J.C. Merlano-Duncan ◽  
Stefano Andrenacci ◽  
Symeon Chatzinotas ◽  
Bjorn Ottersten
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Computationally Efficient

scholarly journals Above-Threshold Queries of Environmental Conditions Based on Bilinear Interpolation in Wireless Sensor Networks

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4203
Author(s):  
Yaxi Liu ◽  
Wei Huangfu ◽  
Haijun Zhang ◽  
Keping Long
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Closed Form Solution ◽  
Database Systems ◽  
Form Solution ◽  
Sensor Data ◽  
Wireless Sensor ◽  
Bilinear Interpolation ◽  
Efficient Manner ◽  
Aggregate Queries

Wireless sensor networks can be regarded as sensor database systems, which permit users to query sensor data of interest. Among various spatial database queries, we focus the area-wise aggregate queries in the region where the sensor values are above a predefined threshold, which are summarized as above-threshold queries. In this paper, we propose a novel Bilinear Interpolation-Based (BIB) algorithm, which utilizes the bilinear interpolation to estimate the environmental variables inside a grid with the known sensor values at the vertexes, to support the above-threshold queries for regularly-deployed sensor networks and provide the closed-form solution of the above-threshold ratio. We designate experiments with both the artificially-constructed environment data and the real temperature data. Experiment results manifest that the proposed BIB algorithm shows a good performance in estimating the above-threshold ratios to support the above-threshold queries in an accurate and efficient manner.

scholarly journals An Efficient and Robust Unsupervised Anomaly Detection Method Using Ensemble Random Projection in Surveillance Videos

Sensors ◽  
2019 ◽  
Vol 19 (19) ◽  
pp. 4145 ◽  
Author(s):  
Jingtao Hu ◽  
En Zhu ◽  
Siqi Wang ◽  
Xinwang Liu ◽  
Xifeng Guo ◽  
...  
Keyword(s):  
Anomaly Detection ◽  
Detection Method ◽  
Computational Cost ◽  
Closed Form Solution ◽  
Random Projection ◽  
Form Solution ◽  
Least Square ◽  
Support Vector ◽  
Regression Problem ◽  
Unsupervised Anomaly Detection

Video anomaly detection is widely applied in modern society, which is achieved by sensors such as surveillance cameras. This paper learns anomalies by exploiting videos under the fully unsupervised setting. To avoid massive computation caused by back-prorogation in existing methods, we propose a novel efficient three-stage unsupervised anomaly detection method. In the first stage, we adopt random projection instead of autoencoder or its variants in previous works. Then we formulate the optimization goal as a least-square regression problem which has a closed-form solution, leading to less computational cost. The discriminative reconstruction losses of normal and abnormal events encourage us to roughly estimate normality that can be further sifted in the second stage with one-class support vector machine. In the third stage, to eliminate the instability caused by random parameter initializations, ensemble technology is performed to combine multiple anomaly detectors’ scores. To the best of our knowledge, it is the first time that unsupervised ensemble technology is introduced to video anomaly detection research. As demonstrated by the experimental results on several video anomaly detection benchmark datasets, our algorithm robustly surpasses the recent unsupervised methods and performs even better than some supervised approaches. In addition, we achieve comparable performance contrast with the state-of-the-art unsupervised method with much less running time, indicating the effectiveness, efficiency, and robustness of our proposed approach.

Provisions for bank deposit withdrawals and portfolio selection

2020 ◽  
Vol 07 (01) ◽  
pp. 1950037
Author(s):  
Ryle S. Perera
Keyword(s):  
Portfolio Selection ◽  
Closed Form Solution ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Form Solution ◽  
Investment Portfolio ◽  
Efficient Manner ◽  
Selection For ◽  
Mean Variance Portfolio ◽  
Mean Variance

The primary economic function of a bank is to redirect funds from savers to borrowers in an efficient manner, while increasing the value of the bank’s asset holdings in absolute terms. Within the regulatory framework of the Basel III accord, banks are required to maintain minimum liquidity to guard against withdrawals/liquidity risks. In this paper, we analyze a continuous-time mean-variance portfolio selection for a bank with stochastic withdrawal provisioning by relating the reserves as a proxy for the assets held by the bank. We then formulate an optimal investment portfolio selection for a banker by constructing a special Riccati equation as a continuous solution to the Hamilton–Jacobi–Bellman (HJB) equation under mean-variance paradigm. We obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier. The aforementioned modeling enables us to formulate a stochastic optimal control problem related to the minimization of the reserve, depository, and intrinsic risk that are associated with the reserve process.

Sign in / Sign up

Export Citation Format

Share Document