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assignment_1
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@kgogina
kgogina committed Aug 3, 2024
1 parent 0542d62 commit 2bc0809
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157 changes: 130 additions & 27 deletions 01_materials/labs/lab_2.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -22,7 +22,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -36,9 +36,20 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 3,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 300x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sample_index = 45\n",
"plt.figure(figsize=(3, 3))\n",
Expand All @@ -58,7 +69,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
Expand Down Expand Up @@ -91,7 +102,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -101,18 +112,43 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 6,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"array([0., 0., 0., 1., 0., 0., 0., 0., 0., 0.])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"one_hot(n_classes=10, y=3)"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 7,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"array([[1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],\n",
" [0., 0., 0., 0., 0., 0., 0., 0., 0., 1.],\n",
" [0., 1., 0., 0., 0., 0., 0., 0., 0., 0.]])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"one_hot(n_classes=10, y=[0, 4, 9, 1])"
]
Expand Down Expand Up @@ -143,7 +179,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 8,
"metadata": {
"collapsed": false
},
Expand All @@ -164,9 +200,17 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 9,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[9.99662391e-01 3.35349373e-04 2.25956630e-06]\n"
]
}
],
"source": [
"print(softmax([10, 2, -3]))"
]
Expand All @@ -181,9 +225,18 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 10,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[9.99662391e-01 3.35349373e-04 2.25956630e-06]\n",
" [2.47262316e-03 9.97527377e-01 1.38536042e-11]]\n"
]
}
],
"source": [
"X = np.array([[10, 2, -3],\n",
" [-1, 5, -20]])\n",
Expand All @@ -199,18 +252,36 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 11,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.0\n"
]
}
],
"source": [
"print(np.sum(softmax([10, 2, -3])))"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 12,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"softmax of 2 vectors:\n",
"[[9.99662391e-01 3.35349373e-04 2.25956630e-06]\n",
" [2.47262316e-03 9.97527377e-01 1.38536042e-11]]\n"
]
}
],
"source": [
"print(\"softmax of 2 vectors:\")\n",
"X = np.array([[10, 2, -3],\n",
Expand All @@ -227,9 +298,17 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 13,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1. 1.]\n"
]
}
],
"source": [
"print(np.sum(softmax(X), axis=1))"
]
Expand All @@ -251,9 +330,17 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 15,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.01005033585350145\n"
]
}
],
"source": [
"def nll(Y_true, Y_pred):\n",
" Y_true = np.asarray(Y_true)\n",
Expand All @@ -279,9 +366,17 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 16,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4.605170185988091\n"
]
}
],
"source": [
"print(nll([1, 0, 0], [0.01, 0.01, .98]))"
]
Expand All @@ -295,9 +390,17 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 17,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.010050335853503449\n"
]
}
],
"source": [
"# Check that the average NLL of the following 3 almost perfect\n",
"# predictions is close to 0\n",
Expand Down Expand Up @@ -809,7 +912,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.8"
"version": "3.9.15"
}
},
"nbformat": 4,
Expand Down
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