728x90 반응형 ML57 Calculus for Machine Learning and Data Science (7) Gradients and Gradient DescentQuizQ1Given that $f(x,y) = x^2y+3x^2$, find its derivative with respect to $x$, i.e. find ${\partial f\over \partial x}$Answer더보기$2xy+6x$Q2Given that $f(x,y)=xy^2+2x+3y$, its gradient, i.e. $\nabla f(x,y)$ is:$\left[\begin{array}{c} 2xy+3\\ y^2+2 \end{array}\right]$$\left[\begin{array}{c} 2xy\\ 2x+3 \end{array}\right]$$\left[\begin{array}{c} y^2+2\\ 2xy+3 \end{array.. 2024. 8. 28. Calculus for Machine Learning and Data Science (6) Gradients and Gradient DescentGradientsIntroduction to Tangent planesJust like we had a tangent line in a 1-dimensional line by computing derivatives, we have a tangent plane, which is a slope or a derivative of the functions with multiple variables.To find the tangent plane we use gradient descent to speed up the optimization.A tangent is a straight line or plane that touches a curve or curved .. 2024. 8. 27. Calculus for Machine Learning and Data Science (5) Derivatives and OptimizationOptimizationIntroduction to optimizationWe use derivatives for optimization.Using the sauna example, we want to find the coolest place.Optimization is when we want to find the maximum or the minimum of the function.Local minima: Low points with zero slopes that are not the lowest points (orange arrows in the 3rd slide)Global minima: Lowest point with zero slope (blue .. 2024. 8. 26. Calculus for Machine Learning and Data Science (4) Derivatives and OptimizationQuizQ1Consider the following lines.What can be said about the slopes at their intersection?Slope(Line 1) > Slope(Line 2).Slope(Line 1) Slope(Line 1) = Slope(Line 2).It is impossible to infer anything from the given information.Answer더보기2Correct! Line 2 is steeper than Line 1, therefore its slope is higher.Q2Given the following graph, what is the slope of the line? You.. 2024. 8. 25. Calculus for Machine Learning and Data Science (3) Derivatives and OptimizationDerivativesExistence of the derivativeFunctions where we cannot find the derivative at every point are called the non-differentiable functions.더보기x = 1Correct. There is a cusp at x = 1 so the derivative does not exist.더보기x = -1Correct. There is a discontinuity/jump at x=-1, so the derivative does not exist.Vertical tangents are not differentiable at the origin (x = 0).. 2024. 8. 24. Calculus for Machine Learning and Data Science (2) Derivatives and OptimizationDerivativesSome common derivatives - LinesHere are some of the common derivativesSome common derivatives - QuadraticsFor the above slide, plug in the values for $\Delta x$ (the change in $x$) and $x$, where $x = 1$ to get $\Delta f$ and then the slopeSome common derivatives - Higher degree polynomialsSome common derivatives - Other power functionsFor all power functio.. 2024. 8. 23. 이전 1 ··· 3 4 5 6 7 8 9 10 다음 728x90 반응형
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