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