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