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Propagation of Uncertainty from Systematic Error01:10

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
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Propagation of Uncertainty from Random Error00:59

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Uncertainty: Confidence Intervals00:54

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Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
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Related Experiment Video

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Improving Uncertainty Quantification of Variance Networks by Tree-Structured Learning.

Wenxuan Ma, Xing Yan, Kun Zhang

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    We introduce the Uncertainty-Splitting Neural Regression Tree (USNRT), a novel model for improved uncertainty quantification. USNRT effectively partitions feature spaces to better predict variance and enhance model reliability.

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    Area of Science:

    • Machine Learning
    • Statistical Modeling
    • Artificial Intelligence

    Background:

    • Uncertainty quantification is crucial for reliable machine learning models.
    • Existing variance network methods face limitations in capturing complex uncertainty patterns.

    Purpose of the Study:

    • To develop a novel tree-structured neural network model for enhanced uncertainty quantification.
    • To address the challenge of heterogeneity in uncertainty within feature spaces.

    Main Methods:

    • Proposed the Uncertainty-Splitting Neural Regression Tree (USNRT) model.
    • USNRT partitions feature space into regions based on uncertainty heterogeneity.
    • Region-specific neural networks predict mean and variance; novel splitting criteria based on residual analysis are employed.

    Main Results:

    • USNRT demonstrates superior performance in uncertainty quantification compared to existing methods on UCI datasets.
    • The model effectively identifies and learns from uncertainty heterogeneity.
    • USNRT is computationally efficient with no need for pruning.

    Conclusions:

    • USNRT offers a robust and efficient approach to uncertainty quantification.
    • The model's ability to learn uncertainty heterogeneity improves prediction reliability.
    • Ensemble versions can capture both aleatory and epistemic uncertainty.