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 parameter vector has a fixed \(L_\infty\) norm.
defined by a collection of planes.
within a torus of fixed radius.
inside an axis-aligned box.
where the minima are.
3. An objective function is nonconvex, iff:
It is discontinuous.
It more than one minimum.
It has two maxima.
It is incomputable.
It is partially differentiable.
4. The
feasible set
in an optimisation problem is:
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
the best solutions to the problem
5. In an approximation problem, we'd often have a loss function of the form:
\(L(\theta) = \|\theta - \vec{x}\|\)
\(L(\theta) = \theta \vec{x}\)
\(L(\theta) = \|f(\vec{x};\theta)-y\|\)
\(L(\theta) = \frac{1}{\theta}\)
\(L(\theta) = \frac{\theta}{f(\vec{x}-\vec{\theta})}\)
6. The definition of an eigenvector is:
\(A\lambda = \vec{x}A\)
\(A\vec{x} = \lambda x\)
\(A\vec{x} = x\)
\(\lambda = \|\vec{x}\|_2\)
\(A^{-1}\vec{x} = A^{+}\lambda\)
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