From 943e29030a213180044a6dad2eb7f2a07d99c72b Mon Sep 17 00:00:00 2001 From: Yadunand Prem Date: Sat, 30 Mar 2024 10:56:58 +0800 Subject: [PATCH] feat: 2109s PS5 done --- cs2109s/labs/ps5/ps5.ipynb | 231 +++++++++++++++++++++++++------------ 1 file changed, 158 insertions(+), 73 deletions(-) diff --git a/cs2109s/labs/ps5/ps5.ipynb b/cs2109s/labs/ps5/ps5.ipynb index c4dc986..c5cb278 100644 --- a/cs2109s/labs/ps5/ps5.ipynb +++ b/cs2109s/labs/ps5/ps5.ipynb @@ -65,7 +65,7 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -116,7 +116,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 30, "metadata": {}, "outputs": [ { @@ -314,7 +314,7 @@ "[5 rows x 23 columns]" ] }, - "execution_count": 56, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -332,7 +332,7 @@ }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 31, "metadata": {}, "outputs": [ { @@ -343,7 +343,7 @@ "Name: Class, dtype: int64" ] }, - "execution_count": 57, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -376,7 +376,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 32, "metadata": {}, "outputs": [ { @@ -396,7 +396,7 @@ "Name: Class, Length: 284807, dtype: int64" ] }, - "execution_count": 58, + "execution_count": 32, "metadata": {}, "output_type": "execute_result" } @@ -415,7 +415,7 @@ }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 33, "metadata": {}, "outputs": [ { @@ -532,7 +532,7 @@ "[2 rows x 23 columns]" ] }, - "execution_count": 59, + "execution_count": 33, "metadata": {}, "output_type": "execute_result" } @@ -551,7 +551,7 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 34, "metadata": {}, "outputs": [ { @@ -571,7 +571,7 @@ "Name: Class, Length: 284807, dtype: bool" ] }, - "execution_count": 60, + "execution_count": 34, "metadata": {}, "output_type": "execute_result" } @@ -582,7 +582,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 35, "metadata": {}, "outputs": [ { @@ -955,7 +955,7 @@ "[284315 rows x 23 columns]" ] }, - "execution_count": 61, + "execution_count": 35, "metadata": {}, "output_type": "execute_result" } @@ -974,7 +974,7 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 36, "metadata": {}, "outputs": [ { @@ -1145,7 +1145,7 @@ "[4 rows x 23 columns]" ] }, - "execution_count": 62, + "execution_count": 36, "metadata": {}, "output_type": "execute_result" } @@ -1212,7 +1212,7 @@ }, { "cell_type": "code", - "execution_count": 63, + "execution_count": 37, "metadata": {}, "outputs": [], "source": [ @@ -1238,7 +1238,7 @@ }, { "cell_type": "code", - "execution_count": 64, + "execution_count": 38, "metadata": {}, "outputs": [], "source": [ @@ -1284,7 +1284,7 @@ }, { "cell_type": "code", - "execution_count": 65, + "execution_count": 39, "metadata": {}, "outputs": [], "source": [ @@ -1311,7 +1311,7 @@ }, { "cell_type": "code", - "execution_count": 66, + "execution_count": 40, "metadata": {}, "outputs": [], "source": [ @@ -1387,7 +1387,7 @@ }, { "cell_type": "code", - "execution_count": 67, + "execution_count": 41, "metadata": {}, "outputs": [], "source": [ @@ -1429,7 +1429,7 @@ }, { "cell_type": "code", - "execution_count": 68, + "execution_count": 42, "metadata": {}, "outputs": [], "source": [ @@ -1544,7 +1544,7 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 90, "metadata": {}, "outputs": [], "source": [ @@ -1569,16 +1569,16 @@ " # Machine epsilon for numpy `float64` type\n", " eps = np.finfo(np.float64).eps\n", "\n", - " y_predicted = 1/(1+np.exp(-X @ weight_vector)) + eps\n", - " first = -y * np.log(y_predicted)\n", - " second = (1-y) * np.log(1-y_predicted)\n", + " y_predicted = 1/(1+np.exp(-X @ weight_vector))\n", + " first = -y * np.log(y_predicted+eps)\n", + " second = (1-y) * np.log(1-y_predicted+eps)\n", "\n", " return np.mean(first-second)" ] }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 91, "metadata": {}, "outputs": [], "source": [ @@ -1602,7 +1602,7 @@ }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 92, "metadata": {}, "outputs": [], "source": [ @@ -1632,7 +1632,7 @@ }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 93, "metadata": {}, "outputs": [], "source": [ @@ -1660,7 +1660,7 @@ }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 94, "metadata": {}, "outputs": [], "source": [ @@ -1687,7 +1687,7 @@ }, { "cell_type": "code", - "execution_count": 74, + "execution_count": 95, "metadata": {}, "outputs": [], "source": [ @@ -1715,7 +1715,7 @@ }, { "cell_type": "code", - "execution_count": 75, + "execution_count": 96, "metadata": {}, "outputs": [], "source": [ @@ -1753,7 +1753,7 @@ }, { "cell_type": "code", - "execution_count": 76, + "execution_count": 97, "metadata": {}, "outputs": [], "source": [ @@ -1780,7 +1780,7 @@ }, { "cell_type": "code", - "execution_count": 77, + "execution_count": 98, "metadata": {}, "outputs": [], "source": [ @@ -1792,7 +1792,7 @@ }, { "cell_type": "code", - "execution_count": 78, + "execution_count": 99, "metadata": {}, "outputs": [], "source": [ @@ -1813,7 +1813,7 @@ }, { "cell_type": "code", - "execution_count": 79, + "execution_count": 100, "metadata": {}, "outputs": [], "source": [ @@ -1858,12 +1858,12 @@ }, { "cell_type": "code", - "execution_count": 81, + "execution_count": 101, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ "
" ] @@ -1876,7 +1876,7 @@ "import matplotlib.pyplot as plt\n", "from time import time\n", "\n", - "X_sample, y_sample = X[:1000], y[:1000].flatten()\n", + "X_sample, y_sample = X[:2000], y[:2000].flatten()\n", "num_interations = 2000\n", "batch_times = []\n", "batch_costs = []\n", @@ -1907,6 +1907,57 @@ "plt.show()" ] }, + { + "cell_type": "code", + "execution_count": 102, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "from time import time\n", + "\n", + "X_sample, y_sample = X[:2000], y[:2000].flatten()\n", + "num_interations = 2000\n", + "batch_times = []\n", + "batch_costs = []\n", + "\n", + "for i in range(50, num_interations + 1, 50):\n", + " start = time()\n", + " weight_vector = logistic_regression_batch_gradient_descent(X_sample, y_sample, i, 0, 1e-5)\n", + " stop = time()\n", + " batch_times.append(i)\n", + " batch_costs.append(cost_function(X_sample, y_sample, weight_vector))\n", + "plt.plot(batch_times, batch_costs, 'g^', label=\"Batch Gradient Descent\")\n", + "\n", + "stochastic_times = []\n", + "stochastic_costs = []\n", + "for i in range(50, num_interations + 1, 50):\n", + " start = time()\n", + " weight_vector = logistic_regression_stochastic_gradient_descent(X_sample, y_sample, i, 0, 1e-5)\n", + " stop = time()\n", + " stochastic_times.append(i)\n", + " stochastic_costs.append(cost_function(X_sample, y_sample, weight_vector))\n", + "plt.plot(stochastic_times, stochastic_costs, 'bs', label=\"Stochastic Gradient Descent\")\n", + "\n", + "plt.xlabel('Number of Update Rounds')\n", + "plt.ylabel('Cross Entropy Loss')\n", + "plt.legend()\n", + "plt.title('Plot of cross entropy loss against number of update rounds')\n", + "\n", + "plt.show()" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1916,6 +1967,13 @@ "With reference to the 2 plots that you have made in task 3.6.1, what do you observe about the relationship between the cross entropy loss vs the number of update rounds and/or the runtime it takes to run the update for both batch gradient descent (task 3.4) and stochastic gradient descent (task 3.5)? Explain your observations in terms of the effect of size of data, number of update rounds, runtime and whether the algorithm will be stuck in a local minima and so on." ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Stochastic Gradient Descent runs significantly faster than batch gradient descent. Especially as the batch size increases, the speed of Stochastic over batch Gradient Descent can be seen. However, looking at the number of update rounds, batch gradient descent attains a lower CEL with lesser updates as compared to Stochastic Gradient descent. However, over time and over 2000 updates, both stochastic and batch gradient descent converges. The graph of stochastic gradient descent doesn't look as smooth and tends to 'overcorrect', when the randomly seleced variable. Since batch gradient descent considers the entire set of data, and stochastic gradient descent randomly samplies from the given dataset, this will not be stuck in a local minima. " + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1936,7 +1994,7 @@ }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 107, "metadata": {}, "outputs": [], "source": [ @@ -1966,36 +2024,23 @@ " -------\n", " The final (n,) weight parameters\n", " '''\n", - " X_sel = X_train[(y_train == class_i)]\n", - " Y_sel = y_train[(y_train == class_i)]\n", + " \n", + " X_sel = X_train\n", + " y_sel = (y_train == class_i).astype(int)\n", "\n", " weights = np.zeros(X_sel.shape[1])\n", " for _ in range(max_num_epochs):\n", - " weights = weight_update(X_sel, Y_sel, alpha, weights)\n", - " if cost_function(X_sel, Y_sel, weights) <= threshold:\n", + " weights = weight_update(X_sel, y_sel, alpha, weights)\n", + " if cost_function(X_sel, y_sel, weights) <= threshold:\n", " break\n", " return weights\n" ] }, { "cell_type": "code", - "execution_count": 74, + "execution_count": 108, "metadata": {}, - "outputs": [ - { - "ename": "TypeError", - "evalue": "unsupported operand type(s) for -: 'float' and 'str'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn[74], line 10\u001b[0m\n\u001b[1;32m 8\u001b[0m max_num_epochs1 \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m20\u001b[39m\n\u001b[1;32m 9\u001b[0m expected1 \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mtranspose([\u001b[38;5;241m6.75\u001b[39m, \u001b[38;5;241m0.125\u001b[39m, \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m6.0\u001b[39m])\n\u001b[0;32m---> 10\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m np\u001b[38;5;241m.\u001b[39marray_equal(\u001b[43mmulti_class_logistic_regression_batch_gradient_descent\u001b[49m\u001b[43m(\u001b[49m\u001b[43mX1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmax_num_epochs1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0.05\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43msome\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m, expected1)\n", - "Cell \u001b[0;32mIn[73], line 32\u001b[0m, in \u001b[0;36mmulti_class_logistic_regression_batch_gradient_descent\u001b[0;34m(X_train, y_train, max_num_epochs, threshold, alpha, class_i)\u001b[0m\n\u001b[1;32m 30\u001b[0m weights \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mzeros(X_sel\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m1\u001b[39m])\n\u001b[1;32m 31\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m _ \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(max_num_epochs):\n\u001b[0;32m---> 32\u001b[0m weights \u001b[38;5;241m=\u001b[39m \u001b[43mweight_update\u001b[49m\u001b[43m(\u001b[49m\u001b[43mX_sel\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mY_sel\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43malpha\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mweights\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 33\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m cost_function(X_sel, Y_sel, weights) \u001b[38;5;241m<\u001b[39m\u001b[38;5;241m=\u001b[39m threshold:\n\u001b[1;32m 34\u001b[0m \u001b[38;5;28;01mbreak\u001b[39;00m\n", - "Cell \u001b[0;32mIn[18], line 22\u001b[0m, in \u001b[0;36mweight_update\u001b[0;34m(X, y, alpha, weight_vector)\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m'''\u001b[39;00m\n\u001b[1;32m 3\u001b[0m \u001b[38;5;124;03mDo the weight update for one step in gradient descent\u001b[39;00m\n\u001b[1;32m 4\u001b[0m \n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;124;03mNew weight vector after one round of update.\u001b[39;00m\n\u001b[1;32m 19\u001b[0m \u001b[38;5;124;03m'''\u001b[39;00m\n\u001b[1;32m 20\u001b[0m y_predicted \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\u001b[38;5;241m/\u001b[39m(\u001b[38;5;241m1\u001b[39m\u001b[38;5;241m+\u001b[39mnp\u001b[38;5;241m.\u001b[39mexp(\u001b[38;5;241m-\u001b[39mX \u001b[38;5;241m@\u001b[39m weight_vector))\n\u001b[0;32m---> 22\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m weight_vector \u001b[38;5;241m-\u001b[39m alpha \u001b[38;5;241m*\u001b[39m X\u001b[38;5;241m.\u001b[39mT \u001b[38;5;241m@\u001b[39m (\u001b[43my_predicted\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m) \u001b[38;5;241m/\u001b[39m \u001b[38;5;28mlen\u001b[39m(y)\n", - "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for -: 'float' and 'str'" - ] - } - ], + "outputs": [], "source": [ "data1 = [[26, 9, 69, 'full'],\n", " [54, 3, 16, 'some'],\n", @@ -2020,7 +2065,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 155, "metadata": {}, "outputs": [], "source": [ @@ -2044,14 +2089,22 @@ " -------\n", " Classification result as an (m,) np.ndarray. Eg ['some', 'none', 'full', ... ,'none'].\n", " '''\n", + " m = X.shape[0]\n", + " y_none = (1/(1+np.exp(-X @ weight_vector_none))).reshape(m, 1)\n", + " y_some = (1/(1+np.exp(-X @ weight_vector_some))).reshape(m, 1)\n", + " y_full = (1/(1+np.exp(-X @ weight_vector_full))).reshape(m, 1)\n", "\n", - " # TODO: add your solution here and remove `raise NotImplementedError`\n", - " raise NotImplementedError" + " combined = np.hstack((y_none, y_some, y_full))\n", + " result = np.argmax(combined, axis=1).astype('object')\n", + " result[result == 0] = 'none'\n", + " result[result == 1] = 'some'\n", + " result[result == 2] = 'full'\n", + " return result\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 156, "metadata": {}, "outputs": [], "source": [ @@ -2120,7 +2173,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -2143,16 +2196,31 @@ " acc: np.float64\n", " The accuracy on a scale up to 100.\n", " '''\n", + " from sklearn.metrics import accuracy_score\n", + " X_train, X_test, y_train, y_test = model_selection.train_test_split(X, y, test_size=0.3, random_state=42)\n", + " \n", + " clf = svm.SVC(kernel='linear', random_state=42)\n", + " clf.fit(X_train, y_train)\n", + " predictions = clf.predict(X_test)\n", + " accuracy = accuracy_score(y_test, predictions) * 100\n", "\n", - " # TODO: add your solution here and remove `raise NotImplementedError`\n", - " raise NotImplementedError" + " return predictions, accuracy" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(array([0, 0, 1]), 66.66666666666666)\n", + "(array([1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]), 80.0)\n" + ] + } + ], "source": [ "# small data\n", "data1 = [[111.1, 10, 0], [111.2, 20, 0], [111.3, 10, 0], [111.4, 10, 0], [111.5, 10, 0], [211.6, 80, 1],\n", @@ -2163,6 +2231,7 @@ "expected1_y = np.transpose([0, 0, 1])\n", "expected1_accuracy = 66.66666666666666\n", "result1 = linear_svm(X1, y1)\n", + "print(result1)\n", "assert (result1[0] == expected1_y).all() and (result1[0]).shape == expected1_y.shape and round(result1[1], 5) == round(expected1_accuracy, 5)\n", "\n", "# subset of credit card data\n", @@ -2178,6 +2247,7 @@ "expected_pred = np.transpose([1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])\n", "expected_accuracy = 80.0\n", "result = linear_svm(X, y.ravel())\n", + "print(result)\n", "assert (result[0] == expected_pred).all() and (result[0]).shape == expected_pred.shape and round(result[1], 5) == round(expected_accuracy, 5)" ] }, @@ -2196,7 +2266,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -2219,16 +2289,30 @@ " acc: np.float64\n", " The accuracy on a scale up to 100.\n", " '''\n", + " from sklearn.metrics import accuracy_score\n", + " X_train, X_test, y_train, y_test = model_selection.train_test_split(X, y, test_size=0.3, random_state=42)\n", + " \n", + " clf = svm.SVC(kernel='rbf', random_state=42)\n", + " clf.fit(X_train, y_train)\n", + " predictions = clf.predict(X_test)\n", + " accuracy = accuracy_score(y_test, predictions) * 100\n", "\n", - " # TODO: add your solution here and remove `raise NotImplementedError`\n", - " raise NotImplementedError" + " return predictions, accuracy" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]), 80.0)\n" + ] + } + ], "source": [ "# small data\n", "data1 = [[111.1, 10, -1], [111.2, 20, -1], [111.3, 10, -1], [111.4, 10, -1], [111.5, 10, -1], [211.6, 80, 1],\n", @@ -2255,6 +2339,7 @@ "expected_pred = np.transpose([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])\n", "expected_accuracy = 80.0\n", "result = gaussian_kernel_svm(X, y.ravel())\n", + "print(result)\n", "assert (result[0] == expected_pred).all() and (result[0]).shape == expected_pred.shape and round(result[1], 5) == round(expected_accuracy, 5)" ] },