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