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Regresja jądrowa
\n", + "\n", + "####
Karolina Oparczyk, Tomasz Grzybowski, Jan Nowak
\n" + ] + }, + { + "cell_type": "markdown", + "id": "f792be04", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Regresja jądrowa używana jest jako funkcja wagi do opracowania modelu regresji nieparametrycznej. Nadaje ona niektórym elementom zbioru większą \"wagę\", która ma wpływ na ostateczny wynik. \n", + "\n", + "Można ją porównać do rysowania krzywej na wykresie punktowym tak, aby była jak najlepiej do nich dopasowana. Jest mniej wrażliwa na wartości odstające, niż na przykład regresja liniowa." + ] + }, + { + "cell_type": "markdown", + "id": "ce35888e", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Właściwości regresji jądrowej:\n", + "* symetryczna - wartość maksymalna leży pośrodku krzywej\n", + "\n", + "* powierzchnia pod krzywą funkcji wynosi 1\n", + "* wartość funkcji jądrowej nie jest ujemna" + ] + }, + { + "cell_type": "markdown", + "id": "dbe6165c", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Przykłady:\n", + "* jądro Gaussa\n", + "\\begin{equation}\n", + "K(x) = (2\\pi)^{-\\frac12} \\text{ exp } (-\\frac{{x}^{2}}2) \\text{ lg}(x)\n", + "\\end{equation}\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "f46e92e5", + "metadata": {}, + "source": [ + "* jądro Epanechnikova\n", + "\\begin{equation}\n", + "K(x) = (\\frac34)(1-x^2)l_{|x|\\leq1}(x)\n", + "\\end{equation}\n", + "" + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}