scholarly journals Sparse Density Estimation with Measurement Errors

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 30
Author(s):  
Xiaowei Yang ◽  
Huiming Zhang ◽  
Haoyu Wei ◽  
Shouzheng Zhang
Keyword(s):  
Measurement Errors ◽  
High Probability ◽  
Density Estimator ◽  
Oracle Inequalities ◽  
Distance Method ◽  
Adaptive Weights ◽  
Tuning Parameters ◽  
Sharp Concentration ◽  
Multi Mode ◽  
Theoretical Results

This paper aims to estimate an unknown density of the data with measurement errors as a linear combination of functions from a dictionary. The main novelty is the proposal and investigation of the corrected sparse density estimator (CSDE). Inspired by the penalization approach, we propose the weighted Elastic-net penalized minimal ℓ2-distance method for sparse coefficients estimation, where the adaptive weights come from sharp concentration inequalities. The first-order conditions holding a high probability obtain the optimal weighted tuning parameters. Under local coherence or minimal eigenvalue assumptions, non-asymptotic oracle inequalities are derived. These theoretical results are transposed to obtain the support recovery with a high probability. Some numerical experiments for discrete and continuous distributions confirm the significant improvement obtained by our procedure when compared with other conventional approaches. Finally, the application is performed in a meteorology dataset. It shows that our method has potency and superiority in detecting multi-mode density shapes compared with other conventional approaches.

REVIEW ON DECOMPOSED FUZZY PID STRUCTURE FOR POWER INVERTERS REGULATION

2016 ◽  
Vol 78 (7) ◽  
Author(s):  
M. S. Arif ◽  
S. M. Ayob ◽  
Z. Salam
Keyword(s):  
Fuzzy Controller ◽  
Design Flow ◽  
Fuzzy Pid ◽  
Fuzzy Pid Control ◽  
Distance Method ◽  
Control Laws ◽  
Control Structures ◽  
Tuning Parameters ◽  
Fuzzy Pid Controller ◽  
Parameters Tuning

The aim of this paper is to critically review prominent decomposed Fuzzy PID control structures. Structural construction and output control laws of these controllers will be discussed.  Their merits and drawbacks are highlighted.  Based on the critical discussions, a new structure of Fuzzy PID controller is proposed.  It is based on cascaded structure, which yields simpler design flow and parameters tuning.  Other advantages of the proposed Fuzzy PID structure are the reduction of tuning parameters and rules of the Fuzzy controller. In addition, the proposed structure allows the usage of signed distance method. The application of the method reduces the computation burden significantly as the power inverter regulation needs very fast and precise computations.

scholarly journals NUMERICAL EXPERIMENTS FOR THE ESTIMATION OF MEAN DENSITIES OF RANDOM SETS

2014 ◽  
Vol 33 (2) ◽  
pp. 83 ◽  
Author(s):  
Federico Camerlenghi ◽  
Vincenzo Capasso ◽  
Elena Villa
Keyword(s):  
Numerical Experiments ◽  
Random Sets ◽  
Density Estimator ◽  
Absolutely Continuous ◽  
Minkowski Content ◽  
Closed Sets ◽  
Random Closed Sets ◽  
Spatially Inhomogeneous ◽  
The Subject ◽  
Theoretical Results

Many real phenomena may be modelled as random closed sets in ℝd, of different Hausdorff dimensions. The problem of the estimation of pointwise mean densities of absolutely continuous, and spatially inhomogeneous, random sets with Hausdorff dimension n < d, has been the subject of extended mathematical analysis by the authors. In particular, two different kinds of estimators have been recently proposed, the first one is based on the notion of Minkowski content, the second one is a kernel-type estimator generalizing the well-known kernel density estimator for random variables. The specific aim of the present paper is to validate the theoretical results on statistical properties of those estimators by numerical experiments. We provide a set of simulations which illustrates their valuable properties via typical examples of lower dimensional random sets.

scholarly journals Estimating Stochastic Linear Combination of Non-Linear Regressions

2020 ◽  
Vol 34 (04) ◽  
pp. 6137-6144
Author(s):  
Di Wang ◽  
Xiangyu Guo ◽  
Chaowen Guan ◽  
Shi Li ◽  
Jinhui Xu
Keyword(s):  
Machine Learning ◽  
Linear Combination ◽  
Statistical Models ◽  
High Probability ◽  
Estimation Errors ◽  
Zero Bias ◽  
Multi Index ◽  
Non Linear ◽  
Linear Regressions ◽  
Theoretical Results

In this paper we study the problem of estimating stochastic linear combination of non-linear regressions, which has a close connection with many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks. Specifically, we first show that with some mild assumptions, if the variate vector x is multivariate Gaussian, then there is an algorithm whose output vectors have ℓ2-norm estimation errors of O(√p/n) with high probability, where p is the dimension of x and n is the number of samples. Then we extend our result to the case where x is sub-Gaussian using the zero-bias transformation, which could be seen as a generalization of the classic Stein's lemma. We also show that with some additional assumptions there is an algorithm whose output vectors have ℓ∞-norm estimation errors of O(1/√p + √p/n) with high probability. Finally, for both Gaussian and sub-Gaussian cases we propose a faster sub-sampling based algorithm and show that when the sub-sample sizes are large enough then the estimation errors will not be sacrificed by too much. Experiments for both cases support our theoretical results. To the best of our knowledge, this is the first work that studies and provides theoretical guarantees for the stochastic linear combination of non-linear regressions model.

scholarly journals Blocks in Constrained Random Graphs with Fixed Average Degree

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Konstantinos Panagiotou
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
High Probability ◽  
Average Degree ◽  
Additional Restriction ◽  
Structural Constraints ◽  
Analytic Framework ◽  
Discrete Algorithms ◽  
International Audience ◽  
Sharp Concentration

International audience This work is devoted to the study of typical properties of random graphs from classes with structural constraints, like for example planar graphs, with the additional restriction that the average degree is fixed. More precisely, within a general analytic framework, we provide sharp concentration results for the number of blocks (maximal biconnected subgraphs) in a random graph from the class in question. Among other results, we discover that essentially such a random graph belongs with high probability to only one of two possible types: it either has blocks of at most logarithmic size, or there is a \emphgiant block that contains linearly many vertices, and all other blocks are significantly smaller. This extends and generalizes the results in the previous work [K. Panagiotou and A. Steger. Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '09), pp. 432-440, 2009], where similar statements were shown without the restriction on the average degree.

Adaptive Tracking Control without Image Velocity Measurement

2015 ◽  
Vol 734 ◽  
pp. 147-152
Author(s):  
Su Ye ◽  
Yu Tang Ye ◽  
Juan Xiu Liu ◽  
Lin Liu ◽  
Chun Lei Du
Keyword(s):  
Parameter Estimation ◽  
Measurement Errors ◽  
Visual Servoing ◽  
Sliding Mode ◽  
Adaptive Controller ◽  
Reference Trajectory ◽  
Image Velocity ◽  
Adaptive Tracking Control ◽  
Tuning Parameters ◽  
Image Position

This paper presents a adaptive controller for visual servoing systems to allow the tracking of a 2D reference trajectory without using image velocity measurements when the kinematics and dynamics parameters are uncertain. To avoid performance decaying caused by measurement errors of the image velocity, we proposed the adaptive controller, with which image velocity need not be directly measured. The first derivative of designed sliding mode vector is not affected by actual image speed. The parameter estimation of image position is used to replace the parameter estimation of image speed. We removed the filter structure in controller, which is used to predict the image velocity. The method makes the controller structure is simpler and more reliable, and reduces the difficulty of project implementation and tuning parameters. The asymptotic stability of the system is proved by using the Lyapunov’s method. Simulation results show that the SCARA robot end effector is able to converge to a desired trajectory.

scholarly journals The Phase Transition Analysis for the Random Regular Exact 2-(d,k)-SAT Problem

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1231
Author(s):  
Guoxia Nie ◽  
Daoyun Xu ◽  
Xiaofeng Wang ◽  
Xi Wang
Keyword(s):  
Phase Transition ◽  
High Probability ◽  
Solution Space ◽  
Regular Structure ◽  
Generation Model ◽  
Transition Analysis ◽  
Sat Problem ◽  
Second Moments ◽  
Instance Generation ◽  
Theoretical Results

In a regular (d,k)-CNF formula, each clause has length k and each variable appears d times. A regular structure such as this is symmetric, and the satisfiability problem of this symmetric structure is called the (d,k)-SAT problem for short. The regular exact 2-(d,k)-SAT problem is that for a (d,k)-CNF formula F, if there is a truth assignment T, then exactly two literals of each clause in F are true. If the formula F contains only positive or negative literals, then there is a satisfiable assignment T with a size of 2n/k such that F is 2-exactly satisfiable. This paper introduces the (d,k)-SAT instance generation model, constructs the solution space, and employs the method of the first and second moments to present the phase transition point d* of the 2-(d,k)-SAT instance with only positive literals. When d<d*, the 2-(d,k)-SAT instance can be satisfied with high probability. When d>d*, the 2-(d,k)-SAT instance can not be satisfied with high probability. Finally, the verification results demonstrate that the theoretical results are consistent with the experimental results.

Analysis of the influence sensitivity for the regulator parameters with approximating control on the factors of the regulation quality

2021 ◽  
Author(s):  
Keyword(s):  
Control Systems ◽  
Quality Indicators ◽  
Control Function ◽  
Sensitivity Coefficient ◽  
Quality Factors ◽  
Tuning Parameters ◽  
Parametric Sensitivity ◽  
Mode Control ◽  
Multi Mode ◽  
Transient And Steady State

The parametric sensitivity of the control quality factors is investigated; the most significant parameters of the regulator settings for the transient and steady-state modes of the system are validated. The range of minimum and maximum values of the sensitivity coefficient, at which the quality indicators are sensitive to variations in the tuning parameters of the investigated regulator is established. The results of the analysis permit to choose acceptable ranges for the parameters variation of the regulator settings at the stage of developing multi-mode control systems. Keywords sensitivity of quality indicators; regulator with approximating control function; multi-mode control system

scholarly journals Matchability of heterogeneous networks pairs

2020 ◽  
Vol 9 (4) ◽  
pp. 749-783 ◽  
Author(s):  
Vince Lyzinski ◽  
Daniel L Sussman
Keyword(s):  
Network Model ◽  
Heterogeneous Networks ◽  
General Class ◽  
High Probability ◽  
Distributed Networks ◽  
Singular Value ◽  
Synthetic Simulation ◽  
Singular Value Thresholding ◽  
Theoretical Results

Abstract We consider the problem of graph matchability in non-identically distributed networks. In a general class of edge-independent networks, we demonstrate that graph matchability can be lost with high probability when matching the networks directly. We further demonstrate that under mild model assumptions, matchability is almost perfectly recovered by centering the networks using universal singular value thresholding before matching. These theoretical results are then demonstrated in both real and synthetic simulation settings. We also recover analogous core-matchability results in a very general core-junk network model, wherein some vertices do not correspond between the graph pair.

Lateral Dynamics of a Rail Transit Vehicle: A Comparison of Experimental and Theoretical Results

1981 ◽  
Vol 103 (1) ◽  
pp. 39-48 ◽  
Author(s):  
J. A. Young ◽  
T. A. P. S. AppaRao
Keyword(s):  
Measurement Errors ◽  
Dynamic Models ◽  
Theoretical Models ◽  
Test Results ◽  
Experimental Frequency ◽  
Lateral Dynamics ◽  
Measured Time ◽  
Time Histories ◽  
Theoretical Results ◽  
Theory And Experiment

A subway rail vehicle was tested on tangent and curved track sections to provide dynamics data for validation of theoretical models. Tests were done with three combinations of primary suspension and wheel profiles which were selected using a simplified truck stability/curving trade off analysis. The test results of one configuration are compared with two lateral dynamic models. Experimental frequency and damping results are compared with the predictions of a linear Lateral Stability model for a number of vehicle speeds. The measured time histories of vehicle responses on a spiral and a 122 m (400 ft) radius curve are compared with the results obtained from a Curve Entry Dynamics model. The agreement between theory and experiment varied from good to poor depending on the parameter being compared. The discrepancies between theory and experiment can be attributed to four major sources: limitations of models, errors in vehicle parameters used in obtaining theoretical results, measurement errors and data analysis limitations.

Multi-mode light microscopy of microtubule assembly dynamics and chromosome movement in vivo and In vitro

1996 ◽  
Vol 54 ◽  
pp. 730-731
Author(s):  
E. D. Salmon ◽  
J. C. Waters ◽  
C. Waterman-Storer
Keyword(s):  
Imaging System ◽  
Ccd Camera ◽  
Transmitted Light ◽  
Microtubule Assembly ◽  
Live Cells ◽  
Optical Efficiency ◽  
Multiple Band ◽  
Multi Mode

We have developed a multi-mode digital imaging system which acquires images with a cooled CCD camera (Figure 1). A multiple band pass dichromatic mirror and robotically controlled filter wheels provide wavelength selection for epi-fluorescence. Shutters select illumination either by epi-fluorescence or by transmitted light for phase contrast or DIC. Many of our experiments involve investigations of spindle assembly dynamics and chromosome movements in live cells or unfixed reconstituted preparations in vitro in which photodamage and phototoxicity are major concerns. As a consequence, a major factor in the design was optical efficiency: achieving the highest image quality with the least number of illumination photons. This principle applies to both epi-fluorescence and transmitted light imaging modes. In living cells and extracts, microtubules are visualized using X-rhodamine labeled tubulin. Photoactivation of C2CF-fluorescein labeled tubulin is used to locally mark microtubules in studies of microtubule dynamics and translocation. Chromosomes are labeled with DAPI or Hoechst DNA intercalating dyes.

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