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