bryanesmith

% - - - - - - - - - - - - - 
% hVal, yVal are scalar values
% yVal ∈ { 0, 1 }
% - - - - - - - - - - - - - 
function cost = calcCostTerm(hVal, yVal)
  % equivalent to:
  % if yVal == 1, sum -= log(hVal);
  % elseif yVal == 0, sum -= log(1 - hVal);
  cost = -yVal * log(hVal) - (1 - yVal) * log(1 - hVal);
endfunction

bryanesmith

% - - - - - - - - - - - - - 
% h is R^1,m
% y is R^1,m
% - - - - - - - - - - - - - 
function cost = calcCost(h, y) 
  costs = -y .* log(h) - (1 - y) .* log(1 - h);
  cost = sum(costs) / length(h);
endfunction

% - - - - - - - - - - - - - 

bryanesmith

function [theta, J] = runGradientDescent(x, y, theta, alpha, iters) 
  J = 0;
  for i=0:iters-1

    h = calcH(theta, x);
  
    errors = h - y;	
    matrix = errors * x';
    theta = theta - ( alpha / length(y) ) * matrix;

bryanesmith

%
% x is R^n,m
% y is R^1,m
% theta is R^1,n
% alpha is float (e.g., 0.01)
% alpha is int (e.g., 10000)
%
function [theta, J] = runGradientDescent(x, y, theta, alpha, iters) 
  J = 0;
  for i=0:iters-1

bryanesmith

% H(theta) = theta1 + x1 * theta2 + x2 * theta3
global x = ...; % load R^n,m data
global y = ...; % load R^1,m outcomes

global n = length(x(:,1));
global m = length(x(1,:));

function cost = cost(h, y)
  costs = -y .* log(h) - (1 - y) .* log(1 - h);
  cost = sum(costs) / length(h);

bryanesmith

function [theta, J] = runGradientDescent(x, y, theta, alpha, lambda, iters) 
  J = 0;
  m = length(y);
  for i=0:iters-1

    h = calcH(theta, x);
  
    % todo: theta(0) should not include regularization: (lambda * theta) / m
    theta = theta - alpha * ( (1 / m) * (h - y) * x' + (lambda * theta) / m );

bryanesmith

% 
% Assume network input layer of size s1,
%   one hidden layer of size s2,
%   and an output layer of size s3.
%
% Note a bias unit is added to input and hidden layers.
% 
% Theta1 and Theta2 are pre-calculated weights.
%  (This example just performs forward propogation.)
% 

bryanesmith

% Given:
%   X ϵ R^m,n
%   y ϵ R^m,1

% - - - - - - - - - - - - - - - 
%   X ϵ R^m,n
%   theta ϵ R^n,1
% - - - - - - - - - - - - - - - 
function h = calcH(X, theta)
  h =  X * theta;

bryanesmith

{
  "@context": "https://purl.imsglobal.org/ctx/extended-transcript/v1p0",
  "obi:validation": [
    {
      "obi:validatesType": "obi:extensions/ExtendedTranscript",
      "obi:validationSchema": "https://purl.imsglobal.org/ctx/extended-transcript/v1p0/schema.json"
    }
  ]
}

bryanesmith

{
  "@context": { ... }, 
  "obi:validation": [
    {
      "obi:validatesType": "obi:extensions/SecuredExtendedTranscript",
      "obi:validationSchema": "https://openbadgespec.org/extensions/securedExtendedTranscript/schema.json"
    }
  ]
}