Generalize the minimax decision rule in order to classify patterns from three categories having triangle densities as follows: where δi > 0 is the half-width of the distribution (i = 1, 2, 3). Assume for convenience that µ1 <>2 <>3, and make some minor simplifying assumptions about the δi’s as needed, to answer the following: (a) In terms of the priors P(ωi), means and half-widths, find the optimal decision points x∗ 1 and x∗ 2 under a zero-one (categorization) loss. (b) Generalize the minimax decision rule to two decision points, x∗ 1 and x∗ 2 for such triangular distributions. (c) Let {µi, δi} = {0, 1}, {.5, .5}, and {1, 1}. Find the minimax decision rule (i.e., x∗ 1 and x∗ 2) for this case. (d) What is the minimax risk?

Question
Asked Mar 10, 2020
2 views

Generalize the minimax decision rule in order to classify patterns from three categories having triangle densities as follows:

where δi > 0 is the half-width of the distribution (i = 1, 2, 3). Assume for convenience that µ1 <>2 <>3, and make some minor simplifying assumptions about the δi’s as needed, to answer the following:

(a) In terms of the priors P(ωi), means and half-widths, find the optimal decision points x∗ 1 and x∗ 2 under a zero-one (categorization) loss.

(b) Generalize the minimax decision rule to two decision points, x∗ 1 and x∗ 2 for such triangular distributions.

(c) Let {µi, δi} = {0, 1}, {.5, .5}, and {1, 1}. Find the minimax decision rule (i.e., x∗ 1 and x∗ 2) for this case. (d) What is the minimax risk?

 

Expert Answer

This question hasn't been answered yet.

Ask an expert

Check out a sample Q&A here.

The solution to your study problems

Solutions are written by subject matter experts who are available 24/7. Questions are typically answered within 1 hour.*

Get Started
*Response times may vary by subject and question.

Related Physics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: An air-filled spherical capacitor is constructed with an inner-shell radius of 6.70 cm and an outer-...

A: a) The required capacitance of the device is,  

question_answer

Q: 3. Several years ago, NASA conducted the Lunar CRater Observation and Sensing Satellite (LCROSS)miss...

A: Let V1 be the velocity of the rocket, V2 is the velocity of the spacecraft, the mass of the moon as ...

question_answer

Q: = -3x N, where x is in meters. The velocity of the body at The only force acting on a 3.8 kg body as...

A: a)The equation for x-component of the acceleration of the body is given by, Substitute the numerica...

question_answer

Q: Given four masses with their mass and height relative to the ground shown. Which mass has the most g...

A: Click to see the answer

question_answer

Q: (a) Find the direction of the force on a proton (a positively charged particle) moving through the m...

A: a) Considering proton and applying the right hand rule to get the direction of force for the given f...

question_answer

Q: it's more difficult to start moving a heavy carton from rest than it is to keep pushing it with cons...

A: For an object required to move, it is necessary to overcome the frictional force. Frictional force d...

question_answer

Q: Question 5.14 (resubmit)

A: (a)The total tension acting on the system  is,    

question_answer

Q: Positive charge is distributed with a uniform density λ along the positive x-axis from r to ∞, along...

A: Click to see the answer

question_answer

Q: a spring with a spring constant of 2500n/m. is stretched 4.00 cm. what is the work required to stret...

A: Click to see the answer