Machine Learning You are given the scatter of points (x,y) = (1, 1.5), (4, 3.5), (7, 9), (10, 8). Set up an optimization problem to perform linear regression by hand along the lines of the previous problem by defining theta, etc. Then perform hand calculations to implement linear regression using gradient descent, and report the optimal value of theta that you obtain and what that means. Again, list all the steps - 1, 2,...etc. without omitting any details.

Machine Learning You are given the scatter of points (x,y) = (1, 1.5), (4, 3.5), (7, 9), (10, 8). Set up an optimization problem to perform linear regression by hand along the lines of the previous problem by defining theta, etc. Then perform hand calculations to implement linear regression using gradient descent, and report the optimal value of theta that you obtain and what that means. Again, list all the steps - 1, 2,...etc. without omitting any details.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

Implement a simple linear regression model using Python without using any machine learning libraries like scikit-learn. Your model should take a dataset of input features X and corresponding target values y, and it should output the coefficients w and b for the linear equation y =wX + b
The task is to implement density estimation using the K-NN method. Obtain an iidsample of N ≥ 1 points from a univariate normal (Gaussian) distribution (let us callthe random variable X) centered at 1 and with variance 2. Now, empirically obtain anestimate of the density from the sample points using the K-NN method, for any valueof K, where 1 ≤ K ≤ N. Produce one plot for each of the following cases (each plotshould show the following three items: the N data points (instances or realizations ofX) and the true and estimated densities versus x for a large number – e.g., 1000, 10000– of discrete, linearly-spaced x values): (i) K = N = 1, (ii) K = 2, N = 10, (iii) K = 10,N = 10, (iv) K = 10, N= 1000, (v) K = 100, N= 1000, (vi) K = N = 50,000. Pleaseprovide appropriate axis labels and legends. Thus there should be a total of six ﬁgures(plots),
Consider the same house rent prediction problem where you are supposed to predict price of a house based on just its area. Suppose you have n samples with their respective areas, x(1), x(2), ... , x(n), their true house rents y(1), y(2),..., y(n). Let's say, you train a linear regres- sor that predicts f(x()) = 00 + 01x(e). The parameters 6o and 0, are scalars and are learned by minimizing mean-squared-error loss with L2-regularization through gradient descent with a learning rate a and the regularization strength constant A. Answer the following questions. 1. Express the loss function(L) in terms of x), y@), n, 0, 01, A. 2. Compute L 3. Compute 4. Write update rules for 6, and O1
Consider the same house rent prediction problem where you are supposed to predict price of a house based on just its area. Suppose you have n samples with their respective areas, x(¹), x(²),...,x(n), their true house rents y(¹), y(2),..., y(n). Let's say, you train a linear regres- sor that predicts f(x)) = 0 + 0₁x). The parameters, and 0₁ are scalars and are learned by minimizing mean-squared-error loss with L1-regularization through gradient descent with a learning rate a and the regularization strength constant A. Answer the following questions. 1. Express the loss function(L) in terms of x(i),y(i), n, 00, 01, X. 2. Compute L 200 ƏL 3. Compute 20₁ 4. Write update rules for 0o and 0₁ Hint: d|w| dw undefined -1 w>0 w=0 w <0
We create a simple regression model and call the fit function as follows: Im=LinearRegression() Im.fit(X,Y) in a multilinear model we proceed in the same way: mlm=LinearRegression() mlm.fit(Z,Y) How does the linear regression model knows if we are doing a simple or multiple linear regression? Answer:
"When conducting a binary regression with a skewed predictor, it is often easiest to assess the need for x and log(x) by including them both in the model so that their relative contributions can be assessed directly." Show that indeed the log odds are a function of x and log(x) for the gamma distribution.
Consider a linear regression setting. Given a model's weights W E RD, we incorporate regularisation into the loss function by adding an la regularisation function of the form-W;|*. Select all true statements from below. a. When q = 1, a solution to this problem tends to be sparse. I.e., most weights are driven to zero with only a few weights that are not close to zero. b. When q = 2, a solution to this problem tends to be sparse. I.e., most weights are driven to zero with only a few weights that are not close to zero. c. When q = 1, the problem can be solved analytically as in closed form. d. When q = 2, the problem can be solved analytically as in closed form.
Find out other univariant linear regression models and compare between them
We are interested in estimating the total BEEF consumption per person given BEEF and POPULATION totals for n countries. One obvious way to estimate this is using a ratio estimator with y = BEEF and x = POPULATION. How can a linear regression estimator, Hansen-Hurwitz and Horwitz-Thompson estimator be used to do this?
We are intrested in predicting the percentage of people commuting to work by walking given some input variables. Each observation corresponds to a different city and each input variable summarizes some characteristic of a given city, such as density, urban sprawl and average income per capita. This is 1. not a machine learning problem. Only social scientists would be interested in such a problem. 2. both a classification and a regression problem as it depends on the way one codes the output variable as either 0, 1 or a a particular number in the [0,1] interval. 3. a regression problem. The output variable is continuous. 4. a classification problem. Walking to work is a discrete variable and can only take two values: to walk to work and not to walk to wor
Please implement Multinomial Logistic Regression on the following data. Please continue from the given code:
Three points (xi, yi) are given: (−π, 0), (0, 1) and (π, 2). Calculate the parameters a and b in the model y = a sin (x / 2) + b cos (x) adapted with the least squares method to the three points. The answer is a=1 and b=-1/3 show me the way how to solve it