4i

.gitignore

@@ -0,0 +1,3 @@
+*.asv
+.vscode
+*.pdf

assignments/hwk01/Bayes_Learning.m

@@ -0,0 +1,49 @@
+% implements Bayes_Learning, returns the outputs (p1: learned Bernoulli
+% parameters of the first class, p2: learned Bernoulli parameters of the 
+% second class, pc1: best prior of the first class, pc2: best prior of the 
+% second class
+
+function [p1,p2,pc1,pc2] = Bayes_Learning(training_data, validation_data)
+
+[train_row_size, column_size] = size (training_data); % dimension of training data
+[valid_row_size, ~] = size (validation_data); % dimension of validation data
+X = training_data(1:train_row_size, 1:column_size-1); %Training data
+
+% (1) TODO: find label counts of class 1 and class 2
+
+% (2) TODO: get MLE p1, p2
+
+
+% Use different P(C_1) and P(C_2) on validation set
+% We compute g(x) = based on priors P(C_1), P(C_2), MLE estimator p1, p2, and x_{1*D}
+error_table = zeros(11,4); % build an error table with 4 columns of : sigma, P(C1), P(C2), error_rate
+index = 1; % row index of error table
+for sigma = [0.00001,0.0001,0.001,0.01,0.1,1,2,3,4,5,6]
+    P_C1 = 1-(exp(-sigma)); % set priors using formula P(C1)=1-(exp(-sigma))
+    P_C2 = 1 - P_C1; 
+
+    error_count = 0; % total number of errors to be count
+    % (3) TODO: compute likelihood for class1 and class2 , then compute the posterior
+    % probability for both classes (posterior = prior x likelihood). 
+    % Classify each validation sample as whichever class has the higher posterior probability. 
+    % If the sample is misclassified, increment the error count (error_count = error_count + 1);
+
+
+    error_table(index,1) = sigma;
+    error_table(index,2) = P_C1;
+    error_table(index,3) = P_C2;
+    error_table(index,4) = error_count/valid_row_size; % update error table
+    index = index + 1;
+end
+
+% get the best priors
+[~, I] = min(error_table(:,4)); % find row index of the lowest error rate on validation set
+pc1 = error_table(I,2); 
+pc2 = error_table(I,3); % best priors
+
+% print error table to terminal
+fprintf('\n Error rates of all priors on validation set: \n\n');
+fprintf('    sigma     P(C1)     P(C2)     error rate on validation set\n\n');
+disp(error_table);
+
+end

assignments/hwk01/Bayes_Testing.m

@@ -0,0 +1,41 @@
+% implements Bayes Testing, return the test error (p1: learned Bernoulli
+% parameters of the first class, p2: learned Bernoulli parameters of the 
+% second class; pc1: best prior of the first class, pc2: best prior of the 
+% second class
+
+function test_error = Bayes_Testing(test_data, p1, p2, pc1, pc2)
+
+% (1) TODO: classify the test set using the learned parameters p1, p2, pc1, pc2
+
+[test_row_size, column_size] = size(test_data); % dimension of test data
+X = test_data(1:test_row_size, 1:column_size-1); % test data
+y = test_data(:,column_size); % test labels
+
+
+c = 0;
+for i = 1:test_row_size
+    x = X(i, :);
+    correct_label = y(i);
+
+    postc1 = prod(p1 .^ x .* (1 - p1) .^ (1 - x)) * pc1;
+    postc2 = prod(p2 .^ x .* (1 - p2) .^ (1 - x)) * pc2;
+
+    if postc1 > postc2
+        lab = 1;
+    else
+        lab = 2;
+    end
+
+    if lab == correct_label
+        c = c + 1;
+    end
+end
+
+test_error = (test_row_size - c) / test_row_size;
+
+% (2) TODO: compute error rate and print it
+% (test_error = # of incorrectly classified / total number of test samples
+fprintf('Error rate on the test dataset is: \n\n');
+disp(test_error);
+
+end

assignments/hwk01/HW1.md

@@ -0,0 +1,25 @@
+---
+geometry: margin=2cm
+output: pdf_document
+---
+
+\renewcommand{\c}[1]{\textcolor{gray}{#1}}
+
+1.  **(20 points)**
+    \c{Derive the VC dimension of the following classifiers.}
+
+2.
+
+3.  **(20 points)**
+    \c{Let $P (x|C)$ denote a Bernoulli density function for a class $C \in {C_1, C_2}$
+    and $P (C)$ denote the prior}
+
+    a. \c{Given the priors $P (C_1)$ and $P (C_2)$, and the Bernoulli densities
+    specified by $p_1 \equiv p(x = 0|C_1)$ and $p_2 \equiv p(x = 0|C_2)$, derive the
+    classification rules for classifying a sample $x$ into $C_1$ and $C_2$ based on the
+    posteriors $P (C_1|x)$ and $P (C_2|x)$. (Hint: give rules for classifying $x = 0$ and
+    $x = 1$.)}
+
+        For $x=0$, the posteriors $P(C_i | x)$ are given by $P(C_i | x = 0) = \frac{p(x = 0 | C_i) p(C_i)}{p(x = 0)}$.
+
+        - $p(x = 0 | C_i)$ is given to us as $p_1$

assignments/hwk01/HW1_script.m

@@ -0,0 +1,29 @@
+% solves question 1d, Print a table of error rate of each prior on the 
+% validation set and the error rate using the best prior on the test set.
+% use functions MLE_Learning.m, Bayes_Learning.m, Bayes_Testing.m
+
+% load data
+load('training_data.txt');
+load('validation_data.txt');
+load('testing_data.txt');
+
+%Part 1: using the first two columns to test MLE_Learning and Bayes_Testing
+%function
+training2_data = training_data(:,[1,2,end]);
+testing2_data = testing_data(:,[1,2,end]);
+
+[p1,p2,pc1,pc2] = MLE_Learning(training2_data);
+test_error = Bayes_Testing(testing2_data, p1, p2, pc1, pc2); % use parameters to calculate test error
+
+%Part 2: using the compmlete dataset to test MLE_Learning
+[p1,p2,pc1,pc2] = MLE_Learning(training_data);
+test_error = Bayes_Testing(testing_data, p1, p2, pc1, pc2); % use parameters to calculate test error
+
+%Part 3: using validataion set to do Bayes_Learning
+[p1,p2,pc1,pc2] = Bayes_Learning(training_data, validation_data); % get p1, p2, pc1, pc2
+[pc1,pc2] %show the best prior
+test_error = Bayes_Testing(testing_data, p1, p2, pc1, pc2); % use parameters to calculate test error
+
+% by calling Bayes_Learning and Bayes_Testing, the error table of
+% validataion data and test data error is automatically printed to command
+% window

assignments/hwk01/MLE_Learning.m

@@ -0,0 +1,25 @@
+% implements MLE_Learning, returns the outputs (p1: learned Bernoulli
+% parameters of the first class, p2: learned Bernoulli parameters of the 
+% second class; pc1: prior of the first class, pc2: prior of the 
+% second class
+
+function [p1,p2,pc1,pc2] = MLE_Learning(training_data)
+
+[train_row_size, column_size] = size(training_data); % dimension of training data
+X = training_data(1:train_row_size, 1:column_size-1); %Training data
+y = training_data(:,column_size); % training labels
+
+% (1) TODO: find label counts of class 1 and class 2
+class1_rows = find(y == 1);
+class1_count = length(class1_rows);
+class2_rows = find(y == 2);
+class2_count = length(class2_rows);
+
+% (2) TODO: compute priors pc1, pc2
+pc1 = class1_count / train_row_size;
+pc2 = class2_count / train_row_size;
+
+% (3) TODO: compute maximum likelihood estimate (MLE) p1, p2
+p1 = sum(X(class1_rows, :)) / class1_count;
+p2 = sum(X(class2_rows, :)) / class2_count;
+

assignments/hwk01/Makefile

@@ -0,0 +1,2 @@
+watch:
+	watchexec -e md -- pandoc HW1.md -o HW1.pdf

assignments/hwk01/hw1solve.py

@@ -0,0 +1,14 @@
+from sympy.abc import i, k, m, n, x
+import sympy
+
+
+def prob_2a():
+    # f = sympy.Function('f')
+    def f(x, theta): return (1.0 / theta) * sympy.exp(- x / theta)
+
+    log = sympy.Sum(f, (k, 1, n))
+
+    print(log)
+
+
+prob_2a()

assignments/hwk01/testing_data.txt

@@ -0,0 +1,200 @@
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assignments/hwk01/validation_data.txt

@@ -0,0 +1,200 @@
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perceptron/perceptron.m

@@ -35,8 +35,12 @@ while err > 0
         %%% ylim([mny mxy]);
         %ginput(1);
         % pause(0.5); %change the delay
+
+        rate = rate * 0.9;
     end
   end
-  round = round + 1
+  round = round + 1;
-  err = sum(sign(w'*X)~=Y')/N   %show misclassification rate
+  err = sum(sign(w'*X)~=Y')/N;   %show misclassification rate
-end
+end
+
+round

perceptron/runpercep.m

@@ -2,22 +2,26 @@
 % Rui Kuang
 % Run perceptron on random data points in two classes 
 
-n = 20; %set the number of data points
+% n = 200; %set the number of data points
-mydata = rand(n,2);
+% mydata = rand(n,2);
-
+% 
-shiftidx = abs(mydata(:,1)-mydata(:,2))>0.05;
+% shiftidx = abs(mydata(:,1)-mydata(:,2))>0.00005;
-mydata = mydata(shiftidx,:); 
+% mydata = mydata(shiftidx,:); 
-myclasses = mydata(:,1)>mydata(:,2); % labels
+% myclasses = mydata(:,1)>mydata(:,2); % labels
-n = size(mydata,1);
+% n = size(mydata,1);
-X = [mydata ones(1,n)']'; Y=myclasses;
+% X = [mydata ones(1,n)']'; Y=myclasses;
-Y = Y * 2 -1; 
+% Y = Y * 2 -1; 
-
+% 
-% init weigth vector
+% % init weigth vector
-w = [mean(mydata) 0]';
+% %%% w = [mean(mydata) 0]';
+% w = [1 0 0];
 
 for i = 1:1
-    w=rand(1,3)';
+    %%% w=rand(1,3)'
-    w(3,1)=0;%go through the origin for visualization
+    w =   [0.6842
+    0.5148
+         0]
+    w(3,1)=0%go through the origin for visualization
     % call perceptron
     wtag=perceptron(X,Y,w,10);
 end

zoo/.gitignore

@@ -0,0 +1 @@
+trees