Question

Please fill the blanks:

clearvars
clc
addpath('../Generation')
addpath('../Basic_blocks')
addpath('../Algorithms')

% Loading scenarios
% ===========================
scenario=1;
[data_class set_up]=scenarios_classification(scenario);

% Definition of the problem
%===================================
loss_logistic = --------------------;
loss_logistic_L1 = -----------------;
loss_logistic_L2 = -----------------;

% Different ways to solve theoreticaly
%=========================================
% Solution of the empirical risk using CVX
x_cvx=solver_cvx(-------------------);
x_L1_cvx=solver_cvx(----------------);
x_L2_cvx=solver_cvx(----------------);

% Analytic solution
C=toeplitz(data_class.Var_v1*data_class.Coef_corr_v1.^(0:data_class.M-1));
wij=inv(C)*(data_class.Mean_v1-data_class.Mean_v2);
bij=-.5*wij'*(data_class.Mean_v1+data_class.Mean_v2);
[x_cvx x_L1_cvx x_L2_cvx [wij;bij]]
pause

figure(1),
i1=find(set_up.ytrain(:,1)==1);
i2=find(set_up.ytrain(:,1)==-1);
plot(set_up.Utrain(i1,1),set_up.Utrain(i1,2),'+r'),hold on
plot(set_up.Utrain(i2,1),set_up.Utrain(i2,2),'+b'),
e_cvx=test_phase_class(set_up,'g',x_cvx)
e_L2_cvx=test_phase_class(set_up,'m',x_L2_cvx)
e_theo=test_phase_class(set_up,'k',[wij;bij])
hold off
xlabel('Coefficient 1')
ylabel('Coefficient 2')
legend('Class 1','Class 2','Logistic','Logistic L2','Optimum Gaussian')
grid
pause

% % We draw the surface
figure(2),S1=plot_surface(set_up,@(N,U,x,y,lambda) loss_logistic(N,U,x,y,lambda),x_L2_cvx);pause
figure(2),S2=plot_surface(set_up,@(N,U,x,y,lambda) loss_logistic_L2(N,U,x,y,lambda),x_L2_cvx);

Answer 1

Levels of Measurement

In statistics, there's a variety of ways in which quantities or attributes of objects can be measured and calculated, all of which involve numbers in quantitative data sets. These datasets do not always involve numbers that can be calculated, which is determined by each datasets' level of measurement:

• Nominal: Any numerical values at the nominal level of measurement should not be treated as a quantitative variable. An example of this would be a jersey number or student ID number. It makes no sense to do any calculation upon these types of numbers.
• Ordinal: Quantitative data at the ordinal level of measurement can be ordered, however, differences between values are meaningless. An example of data at this level of measurement is any form of ranking.
• Interval: Data at the interval level can be ordered and differences can be meaningfully calculated. However, data at this level typically lacks a starting point. Moreover, ratios between data values are meaningless. For example, 90 degrees Fahrenheit is not three times as hot as when it is 30 degrees.
• Ratio: Data at the ratio level of measurement can not only be ordered and subtracted, but it may also be divided. The reason for this is that this data does have a zero value or starting point. For example, the Kelvin temperature scale does have an absolute zero.