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Related Concept Videos

Approximate Integration01:24

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In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
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Apart from the measures of central tendency, distribution, outliers, and the changing characteristics of data with time, an important characteristic of any data set is its variation or spread. In some data sets, the data values are concentrated closely near the mean; in others, the data values are more widely spread out from the mean.
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Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
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A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
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Universal Approximation Capability of Broad Learning System and Its Structural Variations.

C L Philip Chen, Zhulin Liu, Shuang Feng

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    This summary is machine-generated.

    A novel Broad Learning System (BLS) demonstrates universal approximation capabilities. Its variants show superior performance in regression tasks, outperforming existing algorithms on complex datasets like MS-Celeb-1M.

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    Area of Science:

    • Machine Learning
    • Artificial Intelligence
    • Deep Learning

    Background:

    • A fast and efficient discriminative Broad Learning System (BLS) leveraging a flattened structure and incremental learning has been developed.
    • The universal approximation property of BLS requires rigorous mathematical validation.

    Purpose of the Study:

    • To provide a mathematical proof for the universal approximation property of the Broad Learning System (BLS).
    • To introduce and mathematically model variants of BLS, including cascade, recurrent, and broad-deep structures.
    • To evaluate the performance of BLS and its variants against existing learning algorithms.

    Main Methods:

    • Mathematical proof of universal approximation.
    • Development of mathematical models for BLS variants (cascade, recurrent, broad-deep).
    • Empirical evaluation on function approximation, time series prediction, and face recognition datasets, including MS-Celeb-1M.

    Main Results:

    • The mathematical proof confirms the universal approximation property of BLS.
    • BLS variants demonstrate superior regression performance compared to existing algorithms.
    • Effectiveness and efficiency of BLS variants are validated against convolutional networks on challenging datasets.

    Conclusions:

    • The Broad Learning System (BLS) possesses universal approximation capabilities.
    • BLS variants offer enhanced performance and efficiency for various machine learning tasks.
    • BLS presents a competitive alternative to traditional deep learning models, particularly convolutional networks.