[proj2] implement Softmax

Project 2 Digit Recognition/mnist/part1/softmax.py

@@ -31,8 +31,20 @@ def compute_probabilities(X, theta, temp_parameter):
     Returns:
         H - (k, n) NumPy array, where each entry H[j][i] is the probability that X[i] is labeled as j
     """
-    #YOUR CODE HERE
-    raise NotImplementedError
+    # Compute the scaled dot product: (n, d) dot (k, d).T -> (n, k)
+    scaled_scores = np.dot(X, theta.T) / temp_parameter
+
+    # Prevent numerical overflow by subtracting the max score from each score
+    scaled_scores -= np.max(scaled_scores, axis=1, keepdims=True)
+
+    # Exponentiate the adjusted scores
+    exp_scores = np.exp(scaled_scores)
+
+    # Normalize the scores to get probabilities: (n, k)
+    probabilities = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
+
+    # Transpose to match the expected output shape (k, n)
+    return probabilities.T
 
 def compute_cost_function(X, Y, theta, lambda_factor, temp_parameter):
     """

catchup.md

@@ -3,4 +3,4 @@
 - Homework: Homework 1 (write python for all problems)
 - Project 1: Classification accuracy of each algorithm do not match with expectation (5,7,8 and 9)
 - extra assignments at the end of Project 1 (9 Feature Engineering)
-- Eigenvalues, Eigenvectors and Determinants (Unit 0 - Optional)
+- Softmax 5 Prespective videos and notes (Project 2, section 4, "Multinomial (Softmax) Regression and Gradient Descent")