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Related Concept Videos

Downsampling01:20

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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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An adaptive shortest-solution guided decimation approach to sparse high-dimensional linear regression.

Xue Yu1, Yifan Sun2, Hai-Jun Zhou3,4,5

  • 1Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, 100872, China.

Scientific Reports
|December 16, 2021
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Summary
This summary is machine-generated.

We introduce ASSD, a novel heuristic algorithm for sparse high-dimensional linear regression. ASSD excels in accuracy and robustness, particularly with correlated data, outperforming existing methods like LASSO.

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • High-dimensional linear regression is crucial for analyzing large datasets.
  • Achieving sparse regression coefficients is a significant challenge.
  • Existing methods like LASSO struggle with highly correlated data.

Purpose of the Study:

  • To propose a novel heuristic algorithm, ASSD, for constructing sparse high-dimensional linear regression models.
  • To enhance the accuracy and robustness of sparse regression, especially for correlated data.
  • To provide a competitive alternative to existing sparse regression techniques.

Main Methods:

  • ASSD algorithm adapted from shortest-solution guided decimation.
  • Utilizes shortest least-squares solutions of recursively decimated models.
  • Incorporates an early-stopping criterion and a second-stage thresholding for refinement.

Main Results:

  • ASSD demonstrates superior performance over LASSO, adaptive LASSO, and VAMP.
  • Achieves higher solution accuracy and robustness in numerical experiments.
  • ASSD is particularly effective for linear regression with highly correlated measurement matrices.

Conclusions:

  • ASSD offers a robust and accurate approach to sparse high-dimensional linear regression.
  • The algorithm is well-suited for real-world applications with correlated data.
  • ASSD presents a significant advancement in sparse modeling techniques.