Multidimensional Signal Interpolation Based on Factorization and Dimension Reduction of Decision Rules

2019 ◽  
Vol 28 (4) ◽  
pp. 332-342
Author(s):  
M. V. Gashnikov
Author(s):  
A I Maksimov ◽  
M V Gashnikov

We propose a new adaptive multidimensional signal interpolator for differential compression tasks. To increase the efficiency of interpolation, we optimize its parameters space by the minimum absolute interpolation error criterion. To reduce the complexity of interpolation optimization, we reduce the dimension of its parameter range. The correspondence between signal samples in a local neighbourhood is parameterized. Besides, we compare several methods for such parameterization. The developed adaptive interpolator is embedded in the differential compression method. Computational experiments on real multidimensional signals confirm that the use of the proposed interpolator can increase the compression ratio.


Biometrika ◽  
2020 ◽  
Author(s):  
Wenzhuo Zhou ◽  
Ruoqing Zhu ◽  
Donglin Zeng

Abstract Learning an individualized dose rule in personalized medicine is a challenging statistical problem. Existing methods often suffer from the curse of dimensionality, especially when the decision function is estimated nonparametrically. To tackle this problem, we propose a dimension reduction framework that effectively reduces the estimation to a lower-dimensional subspace of the covariates. We exploit that the individualized dose rule can be defined in a subspace spanned by a few linear combinations of the covariates, leading to a more parsimonious model. The proposed framework does not require the inverse probability of the propensity score under observational studies due to a direct maximization of the value function. This distinguishes us from the outcome weighted learning framework, which also solves decision rules directly. Under the same framework, we further propose a pseudo-direct learning approach that focuses more on estimating the dimensionality-reduced subspace of the treatment outcome. Parameters in both approaches can be estimated efficiently using an orthogonality constrained optimization algorithm on the Stiefel manifold. Under mild regularity assumptions, the results on the asymptotic normality of the proposed estimators are established, respectively. We also derive the consistency and convergence rate for the value function under the estimated optimal dose rule. We evaluate the performance of the proposed approaches through extensive simulation studies and a warfarin pharmacogenetic dataset.


2020 ◽  
Vol 14 (2) ◽  
pp. 273-280
Author(s):  
Meng Wang ◽  
Shiyuan Zhou ◽  
Zhankui Dong ◽  
Xiupeng Li

Background: With the explosive growth of the manufacturing data, the manufacturing enterprises paid more and more attention to dealing with the manufacturing big data. The manufacturing big data also can be summarized as "5Vs”, volume, variety, velocity, veracity and value. Recently, the researchers are focused on proposing better knowledge discovery algorithms to handling the manufacturing big data. Objective: The high dimensional data can be reduced from two directions. The one was the dimension reduction. It makes the data set simple and overcome the problem of curse dimensionality. This method reduced the data set form the data width. Methods: We proposed a hybrid data reduction and knowledge extraction algorithm (HDRKE) for quality prediction. There are 5 steps in the algorithm: Step 1: Data preprocessing; Step 2: Dimension reduction; Step 3: Extract SVs by SVM; Step 4: Extract rules from the subset; Step 5: Prediction by the rules extracted in step 3. Results: The presented HDRKE method reduced the data scales from the data dimensions and the data attributions. Then, the prediction method was used on the subset of reduced data. At last, the HDRKE method was applied to a enterprise sample, the validation of the method can be validated on the enterprise sample. Conclusion: Quality prediction and control was an important procedure in manufacturing. The HDRKE algorithm was a novel method based on the attribution reduction and dimensionality reduce. The data set simplified from double direction made the data set easily to calculate. The HDRKE method also proposed a new thought of decision rules extracting on the low-embeddings. The HDRKE method also applied to a manufacturing instance and proved its validity.


2004 ◽  
Author(s):  
Kevin D. Carlson ◽  
Mary L. Connerley ◽  
Arlise P. McKinney ◽  
Ross L. Mecham

Sign in / Sign up

Export Citation Format

Share Document