Data Fundamentals (H) - Week 06 Quiz
1. I want to find the shape of an object, with constant surface area, that holds the least water. What is the objective function?
The shape of the object.
The colour of the surface.
The amount of water the object holds.
None of the above.
The surface area of the object.
2. A convex constraint is equivalent to a restriction to a portion of the parameter space:
where the parameter vector has a fixed \(L_\infty\) norm.
defined by a collection of planes.
where the minima are.
inside an axis-aligned box.
within a torus of fixed radius.
3. An objective function is nonconvex, iff:
It more than one minimum.
It is partially differentiable.
It has two maxima.
It is incomputable.
It is discontinuous.
4. The
feasible set
in an optimisation problem is:
the possible configurations of the parameters
the best solutions to the problem
the most distant configurations in the parameter space
a kind of metaheuristic
the possible values of the objective function
5. In an approximation problem, we'd often have a loss function of the form:
\(L(\theta) = \frac{1}{\theta}\)
\(L(\theta) = \frac{\theta}{f(\vec{x}-\vec{\theta})}\)
\(L(\theta) = \|f(\vec{x};\theta)-y\|\)
\(L(\theta) = \|\theta - \vec{x}\|\)
\(L(\theta) = \theta \vec{x}\)
6. The definition of an eigenvector is:
\(\lambda = \|\vec{x}\|_2\)
\(A^{-1}\vec{x} = A^{+}\lambda\)
\(A\lambda = \vec{x}A\)
\(A\vec{x} = x\)
\(A\vec{x} = \lambda x\)
Submit Quiz