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