Problem 6: Identifiability of Neural Network ParametersStatement: Investigate the conditions under which the parameters (weights and biases) of a neuralnetwork are identifiable, meaning that different parameter settings do not produce the samefunction. Provide a proof outlining necessary and sufficient conditions for identifiability in multi-layerperceptrons.Key Points for the Proof:•Explore the role of activation functions in parameter identifiability.Examine the impact of network architecture (e.g., number of layers, neurons per layer) onidentifiability.• Address permutation symmetries and scaling ambiguities inherent in neural networkparameters.Establish conditions that eliminate these ambiguities to achieve identifiability.

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Answered: Problem 6: Identifiability of Neural…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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An article in the Journal of Database Management "Experimental Study of a Self-Tuning Algorithm for DBMS Buffer Pools," (2005, Vol. 16, pp. 1-20) provided the workload used in the TPC-C OLTP (Transaction Processing Performance Council's Version C On-Line Transaction Processing) benchmark, which simulates a typical order entry application. Average frequencies and operations in TPC-c Transaction Frequency Selects Updates Inserts Deletes Non-unique Joins Selects New order 43 23 11 12 Payment 44 4.2 3. 0.6 Order Status 4 11.4 0.6 Delivery 5 130 120 10 Stock Level 4 1 The frequency of each type of transaction (in the second column) can be used as the percentage of each type of transaction. Let X, Y, and Z denote the average number of selects, updates, and inserts operations required for each type of transaction, respectively. Calculate the following: (c) P(X < 6, Y < 6|Z = 0) = Round your answer to three decimal places (e.g. i 98.765). (d) E(X | Y = 0, Z = 0) Round your answer to one…
2b
A researcher analyzing the determinants of earnings and she has data on 16 occupation categories that exhausts all possibilities. If the researcher runs a regression of earnings on a binary (dummy variable) for all 16 categories, which least-square assumption is violated?
9. Suppose you use p features X1, ., Xp to predict the probabilities of K classes by the multi- class logistic regression model. Formulate it as a feed-forward neural network. Draw the model and point out the activation function.
In a bumper test, three test vehicles of each of three types of autos were crashed into a barrier at 5 mph, and the resulting damage was estimated. Crashes were from three angles: head-on, slanted, and rear-end. The results are shown below. Research questions: Is the mean repair cost affected by crash type and/or vehicle type? Are the observed effects (if any) large enough to be of practical importance (as opposed to statistical significance)? 5 mph Collision Damage (S) Crash Type Goliath Head-On Slant Rear-end b 730 1,420 810 a 1,400 1,750 1,260 710 1,290 ,910 Varmint 1,710 1,610 1,610 1,860 1,780 1,670 860 1,560 1,240 Weasel 2,230 1,600 1,730 2,040 1,510 2,470 1,660 Click here for the Excel Data File (a-1) Choose the correct row-effect hypotheses. a. Ho: A1 A2 A3 #0 Angle means differ H: All the Ajare equal to zero Angle means are the same b. Ho: A1 A2 A3=0 Angle means are the same. H: Not all the Ajare equal to zero Angle means differ 1,620 1,260 (8-2) Choose the correct…
Describe each of the five “Gauss Markov” assumptions, (define them) and explain in the context of the regression output
(a) State the predictors available in this model. (b) Determine the multiple regression model for this analysis.
The article “Reaction Modeling and Optimization Using Neural Networks and Genetic Algorithms: Case Study Involving TS-1-Catalyzed Hydroxylation of Benzene” (S. Nandi, P. Mukherjee, et al., Industrial and Engineering Chemistry Research, 2002:2159–2169) presents benzene conversions (in mole percent) for 24 different benzenehydroxylation reactions. The results are 52.3 41.1 28.8 67.8 78.6 72.3 9.1 19.0 30.3 41.0 63.0 80.8 26.8 37.3 38.1 33.6 14.3 30.1 33.4 36.2 34.6 40.0 81.2 59.4. a) Can you conclude that the mean conversion is less than 45? Compute the appropriate test statistic and find the P-value. b) Can you conclude that the mean conversion is greater than 30? Compute the appropriate test statistic and find the P-value. c) Can you conclude that the mean conversion differs from 55? Compute the appropriate test statistic and find the P-value.
a. Give the design matrix, the observation vector, and the unknown parameter vector. Choose the correct design matrix X below. b. Find the associated least-squares curve for the data
Can you show that Q is an intensity matrix?
An article presents the results of an experiment in which the surface roughness (in μm) was measured for 15 D2 steel specimens and compared with the roughness predicted by a neural network model. The results are presented in the following table. TRUE Value (x) Predicted Value (y) of 6 0.45 0.400 0.82 0.7 0.54 0.52 0.41 0.39 0.77 0.74 2:30:15 0.79 0.78 0.25 0.27 pped 0.62 0.6 0.91 0.87 0.52 Book 0.51 1.02 0.91 Hint 0.6 0.71 Ask 0.58 0.5 erences 0.87 0.91 1.06 1.04 ۵ To check the accuracy of the prediction method, the linear model y=Bo+B1x+ & is fit. If the prediction method is accurate, the value of Bo will be 0 and the value of ẞ1 will be 1. Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text.
Credit Card Use: Consider the following hypothetical bank data on consumers’ use of credit card credit facilities in Table 11.3. Create a JMP data table using Table 11.3 (File>New>Data Table), and create a neural network model (Analyze>Predictive Modelling>Neural) using your new data table. Use the default validation method (Holdback Portion) and use the random seed 123. (see the screen capture below) TABLE 11.3 Data for Credit Card Example and Variable Descriptions Years Salary Used Credit 43 65 4 18 1 3 15 6 53 95 88 112 0 What is the misclassification rate on the validation set? [ Select ] ["0", "0.4268", "0.012", "0.4"] How many parameters are estimated to build this model? [ Select ] ["14", "15", "13", "12"] (Hint: use the red triangle option "Show Estimates") Use the Profiler (red triangle option) to explore how the predicted response changes as you change values of the predictors. Describe what you observe. Determine whether the statement below is either true or…

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