Consider the two-dimensional AND dataset D that contains the following 4 examples with binary labels D...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider the two-dimensional AND dataset D that contains the following 4 examples with binary labels D = {(x1,t1), (x2, t2), (X3, t3), (x4, t4)} = {([0,0], -1), ([1, 1], +1), ([0, 1], 1), ([1,0], -1)}, i.e., the truth table of the logical AND function. Φι $2 t 0 0 -1 0 1 -1 1 0 -1 1 1 +1 (a) Prove that D is linearly separable. • Do not forget to add the bias feature 0 = 1 to each example. (b) (*) Prove that the Perceptron algorithm makes at most 51 mistakes when trained on this dataset before it converges. • Hint: Use u = [-1.5, 1, 1]/√4.25 in Theorem 1 (Block, Novikoff) from this paper that proves the Perceptron convergence property. [Bonus, 10p] Find a different vector u that results in a tighter bound at (b) above, i.e. a smaller number of mistakes. (c) [Bonus, 5p] Let u and v be two vectors such that ||v|| = 1. Prove that ||u|| > uTv. Consider the two-dimensional AND dataset D that contains the following 4 examples with binary labels D = {(x1,t1), (x2, t2), (X3, t3), (x4, t4)} = {([0,0], -1), ([1, 1], +1), ([0, 1], 1), ([1,0], -1)}, i.e., the truth table of the logical AND function. Φι $2 t 0 0 -1 0 1 -1 1 0 -1 1 1 +1 (a) Prove that D is linearly separable. • Do not forget to add the bias feature 0 = 1 to each example. (b) (*) Prove that the Perceptron algorithm makes at most 51 mistakes when trained on this dataset before it converges. • Hint: Use u = [-1.5, 1, 1]/√4.25 in Theorem 1 (Block, Novikoff) from this paper that proves the Perceptron convergence property. [Bonus, 10p] Find a different vector u that results in a tighter bound at (b) above, i.e. a smaller number of mistakes. (c) [Bonus, 5p] Let u and v be two vectors such that ||v|| = 1. Prove that ||u|| > uTv.
Expert Answer:
Answer rating: 100% (QA)
a We must demonstrate the existence of a hyperplane that divides the positive cases from the negative examples in order to demonstrate that dataset D ... View the full answer
Posted Date:
Students also viewed these civil engineering questions
-
A triangular corner lot has perpendicular sides of length 120ft and 160ft. Find the dimensions of the largest rectangular building that can be constructed on the lot with sides parallel to the...
-
The area of a circle increases at a rate of 1 cm 2 /s. a. How fast is the radius changing when the radius is 2 cm? b. How fast is the radius changing when the circumference is 2 cm?
-
The radius of a circle is measured to be (10.5 0.2) m. Calculate the (a) Area and (b) Circumference of the circle and give the uncertainty in each value.
-
TABLE 6A-1 General Depreciation System: 200% or 150% Declining Balance Switching to Straight-Line* Half-Year Convention Recovery Year 3-Year 5-Year 7-Year 10-Year 15-Year 20-Year 1 33.33 20.00 14.29...
-
The following data show the curb weight, horsepower, and -mile speed for 16 popular sports and GT cars. Suppose that the price of each sports and GT car is also available. The complete data set is as...
-
How do the two cost accounting systems differ in accounting for each of the following items? a. materials b. labor c. factory overhead
-
A proton (inertia \(1.67 \times 10^{-27} \mathrm{~kg}\) ) and an electron (inertia \(9.11 \times 10^{-31} \mathrm{~kg}\) ) are being separately subjected to an electric force of \(3.2 \times 10^{-14}...
-
LRF Printing provides printing services to many different corporate clients. Although LRF bids most jobs, some jobs, particularly new ones, are negotiated on a cost-plus basis. Cost-plus means that...
-
6. 7. 8. If one of the diameters of the circle x + y-2x-6y+6=0 is a chord of another circle 'C', whose centre is at (2, 1), then its radius is Let Bi (i = 1, 2, 3) be three independent events in a...
-
Ellipses Corp is a small business that operates in Herndon, VA. The company is located at10 Period Lane, Herndon, VA 20170. Its federal Employer Identification Number is 77-7777777, and its...
-
= Calculate the wave height at Point O which is sheltered by the island PQ shown in Fig. 1. Assume incident wave height is H. - 5 m, wave period is T, 10 s, bathymetry contours are parallel to...
-
An adhesion contract will never be deemed unconscionable. (True/False)
-
Under the doctrine of strict liability, liability is imposed for reasons other than fault. (True/False)
-
An illegal contract is valid unless it is executory. (True/False)
-
All individualsregardless of their knowledge, skill, or intelligencemust exercise the same duty of care if they wish to avoid liability for negligence. (True/False)
-
A person who borrows a friends car and fails to return it at the friends request is guilty of conversion. (True/False)
-
3. Arrays and Matrices - (Marks: 25 Marks) Create a vector x which consists of 20 equally spaced points in the range from - to +. reate a y vector which is equal to sin(x).
-
For the data in Exercise 17-19, use the FIFO method to summarize total costs to account for, and assign these costs to units completed and transferred out, and to units in ending work in process....
-
The codon change (Gly-12 to Val-12) in human H-ras that converts it to oncogenic H-ras has been associated with many types of cancers. For this reason, researchers would like to develop drugs to...
-
Outline the general strategy used in metagenomics.
-
You need to understand the approach described in question 3 in More Genetic TIPS before answering this question. A muscle-specific gene was cloned and then subjected to promoter bashing. As shown...
Study smarter with the SolutionInn App