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Vdurm Improving_DNN #35

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Vdurm Improving_DNN #35

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vladislavovich-d May 13, 2019
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135 changes: 77 additions & 58 deletions Improving_DNN/GradientChecking/GradientChecking.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -17,10 +17,8 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Packages\n",
Expand Down Expand Up @@ -72,10 +70,8 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# GRADED FUNCTION: forward_propagation\n",
Expand All @@ -93,17 +89,25 @@
" \"\"\"\n",
" \n",
" ### START CODE HERE ### (approx. 1 line)\n",
" J = None\n",
" J = x * theta\n",
" ### END CODE HERE ###\n",
" \n",
" return J"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 3,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"J = 8\n"
]
}
],
"source": [
"x, theta = 2, 4\n",
"J = forward_propagation(x, theta)\n",
Expand Down Expand Up @@ -133,10 +137,8 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# GRADED FUNCTION: backward_propagation\n",
Expand All @@ -154,19 +156,27 @@
" \"\"\"\n",
" \n",
" ### START CODE HERE ### (approx. 1 line)\n",
" dtheta = None\n",
" dtheta = x\n",
" ### END CODE HERE ###\n",
" \n",
" return dtheta"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 5,
"metadata": {
"scrolled": true
},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"dtheta = 2\n"
]
}
],
"source": [
"x, theta = 2, 4\n",
"dtheta = backward_propagation(x, theta)\n",
Expand Down Expand Up @@ -212,10 +222,8 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# GRADED FUNCTION: gradient_check\n",
Expand All @@ -235,22 +243,22 @@
" \n",
" # Compute gradapprox using left side of formula (1). epsilon is small enough, you don't need to worry about the limit.\n",
" ### START CODE HERE ### (approx. 5 lines)\n",
" thetaplus = None # Step 1\n",
" thetaminus = None # Step 2\n",
" J_plus = None # Step 3\n",
" J_minus = None # Step 4\n",
" gradapprox = None # Step 5\n",
" thetaplus = theta+epsilon # Step 1\n",
" thetaminus = theta-epsilon # Step 2\n",
" J_plus = thetaplus*x # Step 3\n",
" J_minus = thetaminus*x # Step 4\n",
" gradapprox = (J_plus-J_minus) / (2*epsilon) # Step 5\n",
" ### END CODE HERE ###\n",
" \n",
" # Check if gradapprox is close enough to the output of backward_propagation()\n",
" ### START CODE HERE ### (approx. 1 line)\n",
" grad = None\n",
" grad = backward_propagation(x, theta)\n",
" ### END CODE HERE ###\n",
" \n",
" ### START CODE HERE ### (approx. 1 line)\n",
" numerator = None # Step 1'\n",
" denominator = None # Step 2'\n",
" difference = None # Step 3'\n",
" numerator = np.linalg.norm(grad-gradapprox) # Step 1'\n",
" denominator = np.linalg.norm(grad)+np.linalg.norm(gradapprox) # Step 2'\n",
" difference = numerator/denominator # Step 3'\n",
" ### END CODE HERE ###\n",
" \n",
" if difference < 1e-7:\n",
Expand All @@ -263,11 +271,20 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 9,
"metadata": {
"scrolled": true
},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The gradient is correct!\n",
"difference = 2.919335883291695e-10\n"
]
}
],
"source": [
"x, theta = 2, 4\n",
"difference = gradient_check(x, theta)\n",
Expand Down Expand Up @@ -320,10 +337,8 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"def forward_propagation_n(X, Y, parameters):\n",
Expand Down Expand Up @@ -380,10 +395,8 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def backward_propagation_n(X, Y, cache):\n",
Expand Down Expand Up @@ -469,10 +482,8 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"# GRADED FUNCTION: gradient_check_n\n",
Expand Down Expand Up @@ -506,28 +517,28 @@
" # Compute J_plus[i]. Inputs: \"parameters_values, epsilon\". Output = \"J_plus[i]\".\n",
" # \"_\" is used because the function you have to outputs two parameters but we only care about the first one\n",
" ### START CODE HERE ### (approx. 3 lines)\n",
" thetaplus = None # Step 1\n",
" thetaplus[i][0] = None # Step 2\n",
" J_plus[i], _ = None # Step 3\n",
" thetaplus = np.copy(parameters_values) # Step 1\n",
" thetaplus[i][0] = thetaplus[i][0]+epsilon # Step 2\n",
" J_plus[i], _ = forward_propagation_n(X,Y, vector_to_dictionary(thetaplus)) # Step 3\n",
" ### END CODE HERE ###\n",
" \n",
" # Compute J_minus[i]. Inputs: \"parameters_values, epsilon\". Output = \"J_minus[i]\".\n",
" ### START CODE HERE ### (approx. 3 lines)\n",
" thetaminus = None # Step 1\n",
" thetaminus[i][0] = None # Step 2 \n",
" J_minus[i], _ = None # Step 3\n",
" thetaminus = np.copy(parameters_values) # Step 1\n",
" thetaminus[i][0] = thetaminus[i][0]-epsilon # Step 2 \n",
" J_minus[i], _ = forward_propagation_n(X,Y, vector_to_dictionary(thetaminus)) # Step 3\n",
" ### END CODE HERE ###\n",
" \n",
" # Compute gradapprox[i]\n",
" ### START CODE HERE ### (approx. 1 line)\n",
" gradapprox[i] = None\n",
" gradapprox[i] = (J_plus[i]-J_minus[i])/(2*epsilon)\n",
" ### END CODE HERE ###\n",
" \n",
" # Compare gradapprox to backward propagation gradients by computing difference.\n",
" ### START CODE HERE ### (approx. 1 line)\n",
" numerator = None # Step 1'\n",
" denominator = None # Step 2'\n",
" difference = None # Step 3'\n",
" numerator = np.linalg.norm(grad-gradapprox) # Step 1'\n",
" denominator = np.linalg.norm(grad)+np.linalg.norm(gradapprox) # Step 2'\n",
" difference = numerator/denominator # Step 3'\n",
" ### END CODE HERE ###\n",
"\n",
" if difference > 2e-7:\n",
Expand All @@ -540,11 +551,19 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 13,
"metadata": {
"scrolled": false
},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[93mThere is a mistake in the backward propagation! difference = 0.2850931567761624\u001b[0m\n"
]
}
],
"source": [
"X, Y, parameters = gradient_check_n_test_case()\n",
"\n",
Expand Down Expand Up @@ -618,7 +637,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.0"
"version": "3.7.1"
}
},
"nbformat": 4,
Expand Down
406 changes: 326 additions & 80 deletions Improving_DNN/Initialization/Initialization.ipynb
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349 changes: 257 additions & 92 deletions Improving_DNN/Regularization/Regularization.ipynb
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