Problems tagged with "histogram estimators"

Consider the data set of ten points shown below:

Suppose this data is used to build a histogram density estimator, \(f\), with bins: \([0,2), [2, 6), [6, 10)\). Note that the bins are not evenly sized.

Consider this data set of points \(x\) from two classes \(Y = 1\) and \(Y = 0\).

Suppose a histogram estimator with bins \([0,1)\), \([1, 2)\), \([2, 3)\) is used to estimate the densities \(p_1(x \given Y = 1)\) and \(p_0(x \given Y = 0)\), and these estimates are used in the Bayes classifier to make a prediction.

What will be the predicted class of a new point, \(x = 2.2\)?

Suppose a density estimate \(f : \mathbb R^3 \to\mathbb R^1\) is made using histogram estimators with bins having a length of 2 units, a width of 3 units, and a height of 1 unit.

What is the largest value that \(f(\vec x)\) can possibly have?

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Consider this data set of points \(x\) from two classes \(Y = 1\) and \(Y = 0\).

Suppose a histogram estimator with bins \([0,2)\), \([2, 4)\), \([4, 6)\) is used to estimate the densities \(p_1(x \given Y = 1)\) and \(p_0(x \given Y = 0)\).

What will be the predicted class-conditional density for class 0 at a new point, \(x = 2.2\)? That is, what is the estimated \(p_0(2.2 \given Y = 0)\)?

Suppose \(\mathcal D\) is a data set of 100 points. Suppose a density estimate \(f : \mathbb R^3 \to\mathbb R^1\) is constructed from \(\mathcal D\) using histogram estimators with bins having a length of 2 units, a width of 2 units, and a height of 2 units.

The density estimate within a particular bin of the histogram is 0.2. How many data points from \(\mathcal D\) fall within that histogram bin?

160 Show Answer