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Fix inconsistency between loss and gradient in linear regression (use… #25

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99 changes: 62 additions & 37 deletions src/MLC/notebooks/linear_regression_md.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -27,19 +27,27 @@
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-19T19:19:47.882779Z",
"start_time": "2026-04-19T19:19:47.830456Z"
}
},
"source": [
"import numpy as np\n",
"import random"
]
],
"outputs": [],
"execution_count": 1
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-19T19:19:47.898601Z",
"start_time": "2026-04-19T19:19:47.886784Z"
}
},
"source": [
"n, k, p=100, 8, 3 \n",
"X=np.random.random([n,k])\n",
Expand All @@ -48,7 +56,9 @@
"max_itr=1000\n",
"alpha=0.0001\n",
"Lambda=0.01"
]
],
"outputs": [],
"execution_count": 2
},
{
"cell_type": "markdown",
Expand All @@ -60,27 +70,35 @@
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-19T19:19:48.821568Z",
"start_time": "2026-04-19T19:19:48.812569Z"
}
},
"source": [
"# F(x)= w[0]*x + w[1]\n",
"def F(X, W):\n",
" return np.matmul(X,W)\n",
"\n",
"def cost(Y_est, Y, W, Lambda):\n",
" E=Y_est-Y\n",
" return E, np.linalg.norm(E,2)+ Lambda * np.linalg.norm(W,2)\n",
" return E, np.sum(E**2)+ Lambda * np.sum(W**2)\n",
"\n",
"def gradient(E,X, W, Lambda):\n",
" return 2* np.matmul(X.T, E) + Lambda* 2* W"
]
],
"outputs": [],
"execution_count": 3
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-19T19:19:49.571069Z",
"start_time": "2026-04-19T19:19:49.557557Z"
}
},
"source": [
"def fit(W, X, Y, alpha, Lambda, max_itr):\n",
" for i in range(max_itr):\n",
Expand All @@ -93,7 +111,9 @@
" print(c)\n",
" \n",
" return W"
]
],
"outputs": [],
"execution_count": 4
},
{
"cell_type": "markdown",
Expand All @@ -104,32 +124,37 @@
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-19T19:19:53.696191Z",
"start_time": "2026-04-19T19:19:53.668683Z"
}
},
"source": [
"X=np.concatenate( (X, np.ones((n,1))), axis=1 ) \n",
"W=np.concatenate( (W, np.random.random((1,p)) ), axis=0 )\n",
"\n",
"W = fit(W, X, Y, alpha, Lambda, max_itr)"
],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"34.3004759224227\n",
"4.265835757989014\n",
"4.052505749060854\n",
"3.8807845759072968\n",
"3.7422281683979812\n",
"3.6303399157863434\n",
"3.5398708528835554\n",
"3.4665749938168915\n",
"3.4070257924246747\n",
"3.3584711183863862\n"
"36.12367727723764\n",
"24.98447306141867\n",
"24.7012193432722\n",
"24.469568919452147\n",
"24.278540046071015\n",
"24.11987305387688\n",
"23.987270232362814\n",
"23.87586573984402\n",
"23.781852150630172\n",
"23.702214614741322\n"
]
}
],
"source": [
"X=np.concatenate( (X, np.ones((n,1))), axis=1 ) \n",
"W=np.concatenate( (W, np.random.random((1,p)) ), axis=0 )\n",
"\n",
"W = fit(W, X, Y, alpha, Lambda, max_itr)"
]
"execution_count": 6
},
{
"cell_type": "code",
Expand All @@ -148,9 +173,9 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "Python (d2l)",
"language": "python",
"name": "python3"
"name": "d2l"
},
"language_info": {
"codemirror_mode": {
Expand Down