Mathematics for Machine Learning20

Solution to Mathematics for Machine Learning Exercise 4.12
Solution: By SVD (Singular Value Decomposition), we have $A=U\Sigma V^T$. Let $y=V^T x$, then \[\|y\...
Solution to Mathematics for Machine Learning Exercise 2.6
$ \newcommand{\colvec}[1]{\begin{bmatrix} #1 \end{bmatrix}} \newcommand{\rowvec}[1]{\begin{bmatrix} ...
Solution to Mathematics for Machine Learning Exercise 7.7
Consider the quadratic program illustrated in Figure 7.4, $$ \min _{\boldsymbol{x} \in \mathbb{R}^{2...
Solution to Mathematics for Machine Learning Exercise 7.6
Consider the linear program illustrated in Figure 7.9, $$ \min _{\boldsymbol{x} \in \mathbb{R}^{2}}\...
Solution to Mathematics for Machine Learning Exercise 7.2
Consider the update equation for stochastic gradient descent (Equation (7.15)). Write down the updat...
Solution to Mathematics for Machine Learning Exercise 7.4
Consider whether the following statements are true or false: (a) The sum of any two convex functions...
Solution to Mathematics for Machine Learning Exercise 7.3
Consider whether the following statements are true or false: (a) The intersection of any two convex ...
Solution to Mathematics for Machine Learning Exercise 7.1
Consider the univariate function $$f(x)=x^3+6x^2-3x-5.$$Find its stationary points and indicate whet...
Solution to Mathematics for Machine Learning Exercise 5.4
Compute the Taylor polynomials $T_n$, $n=0,\dots,5$ of $f(x)=\sin x+\cos x$ at $x_0=0$. Solution: By...
Solution to Mathematics for Machine Learning Exercise 5.3
Compute the derivative $f’(x)$ of the function $$f(x)=\exp\left(-\frac{1}{2\sigma^2}(x-\mu)^2\right)...