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 colour of the surface.
The surface area of the object.
The shape of the object.
None of the above.
The amount of water the object holds.
2. A convex constraint is equivalent to a restriction to a portion of the parameter space:
inside an axis-aligned box.
where the minima are.
defined by a collection of planes.
within a torus of fixed radius.
where the parameter vector has a fixed \(L_\infty\) norm.
3. An objective function is nonconvex, iff:
It has two maxima.
It is incomputable.
It is discontinuous.
It more than one minimum.
It is partially differentiable.
4. The
feasible set
in an optimisation problem is:
the best solutions to the problem
the possible configurations of the parameters
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:
\(L(\theta) = \|\theta - \vec{x}\|\)
\(L(\theta) = \frac{1}{\theta}\)
\(L(\theta) = \|f(\vec{x};\theta)-y\|\)
\(L(\theta) = \theta \vec{x}\)
\(L(\theta) = \frac{\theta}{f(\vec{x}-\vec{\theta})}\)
6. The definition of an eigenvector is:
\(A\vec{x} = \lambda x\)
\(A^{-1}\vec{x} = A^{+}\lambda\)
\(\lambda = \|\vec{x}\|_2\)
\(A\vec{x} = x\)
\(A\lambda = \vec{x}A\)
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