Add Problem #40: Linear Regression

README.md

@@ -26,7 +26,7 @@ Practice implementing operators and architectures from scratch — the exact ski
 
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@@ -97,6 +97,7 @@ The bread and butter of ML coding interviews. You'll be asked to write these wit
 | 20 | <a href="https://github.com/duoan/TorchCode/blob/master/templates/20_weight_init.ipynb" target="_blank">Kaiming Init</a> <a href="https://colab.research.google.com/github/duoan/TorchCode/blob/master/templates/20_weight_init.ipynb" target="_blank"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab" height="20"></a> | `kaiming_init(weight)` | ![Easy](https://img.shields.io/badge/Easy-4CAF50?style=flat-square) | ⭐ | `std = sqrt(2/fan_in)`, variance scaling |
 | 21 | <a href="https://github.com/duoan/TorchCode/blob/master/templates/21_gradient_clipping.ipynb" target="_blank">Gradient Clipping</a> <a href="https://colab.research.google.com/github/duoan/TorchCode/blob/master/templates/21_gradient_clipping.ipynb" target="_blank"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab" height="20"></a> | `clip_grad_norm(params, max_norm)` | ![Easy](https://img.shields.io/badge/Easy-4CAF50?style=flat-square) | ⭐ | Norm-based clipping, direction preservation |
 | 31 | <a href="https://github.com/duoan/TorchCode/blob/master/templates/31_gradient_accumulation.ipynb" target="_blank">Gradient Accumulation</a> <a href="https://colab.research.google.com/github/duoan/TorchCode/blob/master/templates/31_gradient_accumulation.ipynb" target="_blank"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab" height="20"></a> | `accumulated_step(model, opt, ...)` | ![Easy](https://img.shields.io/badge/Easy-4CAF50?style=flat-square) | 💡 | Micro-batching, loss scaling |
+| 40 | <a href="https://github.com/duoan/TorchCode/blob/master/templates/40_linear_regression.ipynb" target="_blank">Linear Regression</a> <a href="https://colab.research.google.com/github/duoan/TorchCode/blob/master/templates/40_linear_regression.ipynb" target="_blank"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab" height="20"></a> | `LinearRegression` (3 methods) | ![Medium](https://img.shields.io/badge/Medium-FF9800?style=flat-square) | 🔥 | Normal equation, GD from scratch, nn.Linear |
 | 3 | <a href="https://github.com/duoan/TorchCode/blob/master/templates/03_linear.ipynb" target="_blank">Linear Layer</a> <a href="https://colab.research.google.com/github/duoan/TorchCode/blob/master/templates/03_linear.ipynb" target="_blank"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab" height="20"></a> | `SimpleLinear` (nn.Module) | ![Medium](https://img.shields.io/badge/Medium-FF9800?style=flat-square) | 🔥 | `y = xW^T + b`, Kaiming init, `nn.Parameter` |
 | 4 | <a href="https://github.com/duoan/TorchCode/blob/master/templates/04_layernorm.ipynb" target="_blank">LayerNorm</a> <a href="https://colab.research.google.com/github/duoan/TorchCode/blob/master/templates/04_layernorm.ipynb" target="_blank"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab" height="20"></a> | `my_layer_norm(x, γ, β)` | ![Medium](https://img.shields.io/badge/Medium-FF9800?style=flat-square) | 🔥 | Normalization, running stats, affine transform |
 | 7 | <a href="https://github.com/duoan/TorchCode/blob/master/templates/07_batchnorm.ipynb" target="_blank">BatchNorm</a> <a href="https://colab.research.google.com/github/duoan/TorchCode/blob/master/templates/07_batchnorm.ipynb" target="_blank"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab" height="20"></a> | `my_batch_norm(x, γ, β)` | ![Medium](https://img.shields.io/badge/Medium-FF9800?style=flat-square) | ⭐ | Batch vs layer statistics, train/eval behavior |

solutions/40_linear_regression_solution.ipynb

@@ -0,0 +1,125 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "# 🟡 Solution: Linear Regression\n",
+        "\n",
+        "Reference solution demonstrating closed-form, gradient descent, and nn.Linear approaches."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {},
+      "outputs": [],
+      "source": [
+        "import torch\n",
+        "import torch.nn as nn"
+      ],
+      "execution_count": null
+    },
+    {
+      "cell_type": "code",
+      "metadata": {},
+      "outputs": [],
+      "source": [
+        "# ✅ SOLUTION\n",
+        "\n",
+        "class LinearRegression:\n",
+        "    def closed_form(self, X: torch.Tensor, y: torch.Tensor):\n",
+        "        \"\"\"Normal equation via augmented matrix.\"\"\"\n",
+        "        N, D = X.shape\n",
+        "        # Augment X with ones column for bias\n",
+        "        X_aug = torch.cat([X, torch.ones(N, 1)], dim=1)  # (N, D+1)\n",
+        "        # Solve (X^T X) theta = X^T y\n",
+        "        theta = torch.linalg.lstsq(X_aug, y).solution      # (D+1,)\n",
+        "        w = theta[:D]\n",
+        "        b = theta[D]\n",
+        "        return w.detach(), b.detach()\n",
+        "\n",
+        "    def gradient_descent(self, X: torch.Tensor, y: torch.Tensor,\n",
+        "                         lr: float = 0.01, steps: int = 1000):\n",
+        "        \"\"\"Manual gradient computation — no autograd.\"\"\"\n",
+        "        N, D = X.shape\n",
+        "        w = torch.zeros(D)\n",
+        "        b = torch.tensor(0.0)\n",
+        "\n",
+        "        for _ in range(steps):\n",
+        "            pred = X @ w + b          # (N,)\n",
+        "            error = pred - y           # (N,)\n",
+        "            grad_w = (2.0 / N) * (X.T @ error)  # (D,)\n",
+        "            grad_b = (2.0 / N) * error.sum()     # scalar\n",
+        "            w = w - lr * grad_w\n",
+        "            b = b - lr * grad_b\n",
+        "\n",
+        "        return w, b\n",
+        "\n",
+        "    def nn_linear(self, X: torch.Tensor, y: torch.Tensor,\n",
+        "                  lr: float = 0.01, steps: int = 1000):\n",
+        "        \"\"\"PyTorch nn.Linear with autograd training loop.\"\"\"\n",
+        "        N, D = X.shape\n",
+        "        layer = nn.Linear(D, 1)\n",
+        "        optimizer = torch.optim.SGD(layer.parameters(), lr=lr)\n",
+        "        loss_fn = nn.MSELoss()\n",
+        "\n",
+        "        for _ in range(steps):\n",
+        "            optimizer.zero_grad()\n",
+        "            pred = layer(X).squeeze(-1)  # (N,)\n",
+        "            loss = loss_fn(pred, y)\n",
+        "            loss.backward()\n",
+        "            optimizer.step()\n",
+        "\n",
+        "        w = layer.weight.data.squeeze(0)  # (D,)\n",
+        "        b = layer.bias.data.squeeze(0)    # scalar ()\n",
+        "        return w, b"
+      ],
+      "execution_count": null
+    },
+    {
+      "cell_type": "code",
+      "metadata": {},
+      "outputs": [],
+      "source": [
+        "# Verify\n",
+        "torch.manual_seed(42)\n",
+        "X = torch.randn(100, 3)\n",
+        "true_w = torch.tensor([2.0, -1.0, 0.5])\n",
+        "y = X @ true_w + 3.0\n",
+        "\n",
+        "model = LinearRegression()\n",
+        "for name, method in [(\"Closed-form\", model.closed_form),\n",
+        "                      (\"Grad Descent\", lambda X, y: model.gradient_descent(X, y, lr=0.05, steps=2000)),\n",
+        "                      (\"nn.Linear\", lambda X, y: model.nn_linear(X, y, lr=0.05, steps=2000))]:\n",
+        "    w, b = method(X, y)\n",
+        "    print(f\"{name:13s}  w={w.tolist()}  b={b.item():.4f}\")\n",
+        "print(f\"{'True':13s}  w={true_w.tolist()}  b=3.0000\")"
+      ],
+      "execution_count": null
+    },
+    {
+      "cell_type": "code",
+      "metadata": {},
+      "outputs": [],
+      "source": [
+        "# ✅ SUBMIT\n",
+        "from torch_judge import check\n",
+        "check(\"linear_regression\")"
+      ],
+      "execution_count": null
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "name": "python",
+      "version": "3.11.0"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 4
+}