Note: exercize one id the follwoing: Derive that the gradient of the cross entropy loss function used
Fantastic news! We've Found the answer you've been seeking!
Question:
Note: exercize one id the follwoing: Derive that the gradient of the cross entropy loss function used in binary logistic regression takes the form:
????=1/????∑????????=1[(????????^−????????)∗????????]
Transcribed Image Text:
4. Stochastic Gradient. In this exercise, we will design and perform a small numerical experiment to verify that the expected value of the stochastic gradient is the true gradient. Consider the setup where we are given the MNIST data and our goal is to write a binary logistic classifier the predict whether a given image is the digit 5 (label "1") or not (label "0"). We start our learning from a random point in parameter space (say, generated from a normal distribution using torch.randn) using the result of Exercise 1, compute the gradient of the loss J at that point. using pytorch, write an expression for the loss J and compute its gradient at that point using backward (). Do you get the same answer? ● using a batch size of b = 32, write a function that returns a stochastic gradient of J by choosing b randomly chosen images from the dataset. • call the stochastic gradient function a large number of times to obtain an estimate of its expected value. Compare with the full gradient. 4. Stochastic Gradient. In this exercise, we will design and perform a small numerical experiment to verify that the expected value of the stochastic gradient is the true gradient. Consider the setup where we are given the MNIST data and our goal is to write a binary logistic classifier the predict whether a given image is the digit 5 (label "1") or not (label "0"). We start our learning from a random point in parameter space (say, generated from a normal distribution using torch.randn) using the result of Exercise 1, compute the gradient of the loss J at that point. using pytorch, write an expression for the loss J and compute its gradient at that point using backward (). Do you get the same answer? ● using a batch size of b = 32, write a function that returns a stochastic gradient of J by choosing b randomly chosen images from the dataset. • call the stochastic gradient function a large number of times to obtain an estimate of its expected value. Compare with the full gradient.
Expert Answer:
Related Book For
Intermediate Accounting
ISBN: 978-0470161012
9th Canadian Edition, Volume 2
Authors: Donald E. Kieso, Jerry J. Weygandt, Terry D. Warfield.
Posted Date:
Students also viewed these programming questions
-
Accounting EGNMENT RESOURCES Hitical Thinking 4-05 - PRINTER VERSO MY NEED counting Cycle view 4-01 okie Creations ercise 4-03 ata 4-06 URION bownloadable Textbook ent Open Assignment ENT RESOURCES...
-
Describe the capacity of the MS teams to make e-learning accessible. You have to provide information on general accessibility features, and also specific opportunities for assistive technologies to...
-
In this exercise we will show that a hypothesis test involving a binomial experiment is equivalent to a hypothesis test for a proportion (Section 7-5). Assume that a particular experiment has only...
-
The dehydration butanol of alumina is carried out over a silica-alumina catalyst at 680K. CH3CH2CH2CH20H------->cat CH3CH=CHCH3 + H2O The rate law is -r Bu = KPBU/(1+KBuPBul with k= 0.054...
-
Does a company "publicly perform" a copyrighted television program if it is distributed to paid subscribers over the Internet? That is the issue behind the American Broadcasting Companies, Inc. v....
-
What are the major tenets of this understanding of human development? Is there a key person who developed this approach? Who were they? Who did they study to form the theory/ approach? Do humans...
-
Why might a plaintiff want to seek a provisional remedy?
-
The following information pertains to peak heights company: Required: Present the operation activities section of the statement of cash flows for peak heights company using the indirectmethod. Income...
-
An airplane with a loading of 1 8 . 2 lb / ft 2 uses a wing section whose CLMAX is 1 . 5 . What is the stalling speed in a 4 0 \ deg banked turn at standard sea level conditions?
-
Chumpy Lighting Limited manufactures a wide variety of light bulbs which it sells to lighting shops and builders merchants through wholesale distributors. It also sells direct to the big UK...
-
How would a professional option seller utilize the various option greeks to manage their underlying risk exposure?
-
You short sale a common stock on margin at $40 per share with $90,000 of your own money. Assume the initial margin is 75% and the stock pays no dividend. What would the maintenance margin be if a...
-
What risk management frameworks can be applied to resource management to anticipate, identify, and mitigate potential threats to project success?
-
Define Virtual Memory and elucidate its significance in modern computing architectures. How does it facilitate efficient memory management and address the limitations of physical memory?
-
Assume that Paraison has zero marginal costs, and its fixed costs are sunk. What are the profit maximizing prices if Paraison offers each service separately, as well as the package? (PC = price for...
-
A high-speed rail line is proposed to connect two large cities 200 miles apart. The "constant speed" is expected to be 110 mph, with acceleration and deceleration rates at 3 ft/sec/sec.. A. How much...
-
Question 615 points: 1 pts each]: Answer the questions given below. 1. The time elapsed from the point the machine fails to perform its function to the point it is repaired and brought into operating...
-
For the following arrangements, discuss whether they are 'in substance' lease transactions, and thus fall under the ambit of IAS 17.
-
Write a brief essay highlighting the difference between IFRS and accounting standards for private enterprises and the contract-based approach noted in this chapter, discussing the conceptual...
-
Access the financial statements of Bombardier Inc. for the year ended January 31, 2010, and January 31, 2008, from the companys website or SEDAR (www.sedar.com). Instructions Changes in non-cash...
-
Accent Capital Ltd. issued 500 $1,000 bonds at 103. Each bond was issued with one detachable stock warrant. After issuance, the bonds were selling in the market at 97, and the warrants had a market...
-
Explain the limitations that auditors face when they perform the attest function.
-
Indicate whether you think the following third-party groups would normally represent a (1) primary beneficiary, (2) foreseen party, or (3) foreseeable party. Give reasons for your answers. a. A...
-
Use and Dispose Company was organized to manufacture and sell inexpensive golf clubs that can be used during the golf round and then thrown away at the end of the round. In order to keep the business...
Study smarter with the SolutionInn App