diff --git a/Polynomial Regression.ipynb b/Polynomial Regression.ipynb index 1bc9fc4..4d82e39 100644 --- a/Polynomial Regression.ipynb +++ b/Polynomial Regression.ipynb @@ -12,7 +12,7 @@ "metadata": {}, "source": [ "Skład grupy:\n", - "- Nowak Ania,\n", + "- Nowak Anna,\n", "- Łaźna Patrycja,\n", "- Bregier Damian" ] @@ -108,8 +108,38 @@ "metadata": { "scrolled": true }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "BGD:\n", + "f(x) = -65.64506277392492x^0 + 68.77648241255974x^1 + 114.75349304333467x^2 + 102.20675310280696x^3 + 52.800146520467116^4\n", + "82705 updates\n", + "\n", + "MBGD:\n", + "f(x) = -44.80297112432834x^0 + 44.010396798783276x^1 + 87.16025462485948x^2 + 99.3042290245095x^3 + 91.09402012892289^4\n", + "37501 updates\n", + "\n", + "SGD:\n", + "f(x) = 33.46300047596074x^0 + 42.75465449013618x^1 + 48.38013898892164x^2 + 51.32380253289521x^3 + 52.33242989471253^4\n", + "600001 updates\n", + "\n", + "momentum:\n", + "f(x) = 8.015549563834165x^0 + 38.12997860471219x^1 + 58.33870778356615x^2 + 71.22019895802777x^3 + 78.72511869002682^4\n", + "61 updates\n", + "\n" + ] + } + ], "source": [ + "def print_theta(theta):\n", + " print(\"f(x) = \", end=\"\")\n", + " for i,x in enumerate(theta.tolist()[:-1]):\n", + " x = x[0]\n", + " print(f\"{x}x^{i}\", end=\" + \")\n", + " print(f\"{theta.tolist()[-1][0]}^{len(theta) - 1}\")\n", + "\n", "# Implementacja wzrosu na regresję wielomianową\n", "def polynomial_regression(theta, x):\n", " x = x/data[\"Height\"].max()\n", @@ -125,12 +155,12 @@ " return 1.0 / len(Y) * (X.T * (X * theta - Y)) \n", "\n", "# Batch gradient descent (BGD)\n", - "def BGD(X, Y, theta, cost_function = mean_squared_error, alpha=0.1, eps=10**-5, max_steps = 10000000000):\n", + "def BGD(X, Y, theta, cost_function = mean_squared_error, learning_rate=0.1, eps=10**-5, max_steps = 10000000000):\n", " cost = cost_function(theta, X, Y)\n", " logs = [[cost, theta]]\n", " \n", " for i in range(max_steps):\n", - " theta = theta - alpha * gradient(theta, X, Y)\n", + " theta = theta - learning_rate * gradient(theta, X, Y)\n", " next_cost = cost_function(theta, X, Y)\n", " logs.append([next_cost, theta])\n", " if abs(cost - next_cost) <= eps:\n", @@ -138,22 +168,21 @@ " cost = next_cost\n", " return theta, logs\n", "\n", - "# Batch gradient descent (BGD)\n", - "def steepest_descent(X, Y, theta, cost_function = mean_squared_error, eps=10**-5, max_steps = 10000000000):\n", + "# BGD z momentum\n", + "def momentum(X, Y, theta, cost_function = mean_squared_error, learning_rate=0.1, momentum = 0.9, epochs=30):\n", " cost = cost_function(theta, X, Y)\n", " logs = [[cost, theta]]\n", - " \n", - " for i in range(max_steps):\n", - " theta = theta - alpha * gradient(theta, X, Y)\n", + " delta_history = [np.matrix([0]*(degree+1)).T]\n", + " for i in range(epochs):\n", + " delta_history.append(momentum * delta_history[-1] + learning_rate * gradient(theta, X, Y))\n", + " theta = theta - delta_history[-1]\n", " next_cost = cost_function(theta, X, Y)\n", " logs.append([next_cost, theta])\n", - " if abs(cost - next_cost) <= eps:\n", - " break\n", " cost = next_cost\n", " return theta, logs\n", "\n", "# Mini-batch gradient descent (MBGD)\n", - "def MBGD(X, Y, theta, cost_function = mean_squared_error, alpha=0.1, epochs=5, batch_size=16):\n", + "def MBGD(X, Y, theta, cost_function = mean_squared_error, learning_rate=0.1, epochs=5, batch_size=16):\n", " cost = cost_function(theta, X, Y)\n", " logs = [[cost, theta]]\n", " start, end = 0, batch_size\n", @@ -167,7 +196,7 @@ " Y_shuffled = np.concatenate(Y_shuffled, axis=0) \n", " for j in range(int(steps)):\n", " batch = X_shuffled[start:end,:], Y_shuffled[start:end,:]\n", - " theta = theta - alpha * gradient(theta, batch[0], batch[1])\n", + " theta = theta - learning_rate * gradient(theta, batch[0], batch[1])\n", " cost = cost_function(theta, X, Y)\n", " logs.append([cost, theta])\n", "\n", @@ -179,14 +208,28 @@ " return theta, logs\n", "\n", "# Stochastic gradient descent (SGD)\n", - "def SGD(X, Y, theta, cost_function = mean_squared_error, alpha=0.1, epochs=5, batch_size=16):\n", - " return MBGD(X, Y, theta, gradient, cost_function, alpha, epochs, 1)\n", + "def SGD(X, Y, theta, cost_function = mean_squared_error, learning_rate=0.1, epochs=5):\n", + " return MBGD(X, Y, theta, cost_function, learning_rate, epochs, 1)\n", "\n", - "#print(mean_squared_error([1,2,1,1],[1,2,43,1]))\n", - "#mean_squared_error(polynomial_regression(initial_theta, X), Y)\n", - "#final_theta, logs_1 = BGD(X, Y, initial_theta)\n", - "final_theta, logs_2 = MBGD(X, Y, initial_theta, epochs = 30, batch_size = 16)\n", - "#final_theta, logs_2 = SGD(X, Y, initial_theta, epochs = 30)" + "final_theta_BGD, logs_1 = BGD(X, Y, initial_theta)\n", + "print(\"BGD:\")\n", + "print_theta(final_theta_BGD)\n", + "print(f\"{len(logs_1)} updates\\n\")\n", + "\n", + "final_theta_MBGD, logs_2 = MBGD(X, Y, initial_theta, epochs = 60)\n", + "print(\"MBGD:\")\n", + "print_theta(final_theta_MBGD)\n", + "print(f\"{len(logs_2)} updates\\n\")\n", + "\n", + "final_theta_SGD, logs_3 = SGD(X, Y, initial_theta, epochs = 60)\n", + "print(\"SGD:\")\n", + "print_theta(final_theta_SGD)\n", + "print(f\"{len(logs_3)} updates\\n\")\n", + "\n", + "final_theta_momentum, logs_4 = momentum(X, Y, initial_theta, epochs = 60)\n", + "print(\"momentum:\")\n", + "print_theta(final_theta_momentum)\n", + "print(f\"{len(logs_4)} updates\\n\")" ] }, { @@ -216,9 +259,73 @@ "scrolled": true }, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "BGD:\n" + ] + }, { "data": { - "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", "text/plain": [ "
" ] @@ -238,40 +345,27 @@ " chart.plot(X_plot, Y_plot, color=\"red\", lw=2, label=f\"degree {len(theta)}\")\n", " plt.ylim([0,250])\n", " plt.show()\n", - " \n", - "#plot_polynomial_regression(initial_theta)\n", - "plot_polynomial_regression(final_theta)" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "-33.70007165990287x^0 + 36.22536357022561x^1 + 77.13438753083798x^2 + 97.31645980974973x^3 + 103.01308458334519x^4 + " - ] - } - ], - "source": [ - "for i,x in enumerate(final_theta.tolist()):\n", - " x = x[0]\n", - " print(f\"{x}x^{i}\", end=\" + \")" + "\n", + "print(\"BGD:\")\n", + "plot_polynomial_regression(final_theta_BGD)\n", + "print(\"MBGD:\")\n", + "plot_polynomial_regression(final_theta_MBGD)\n", + "print(\"SGD:\")\n", + "plot_polynomial_regression(final_theta_SGD)\n", + "print(\"Momentum:\")\n", + "plot_polynomial_regression(final_theta_momentum)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## 4. Regresja wielomianowa z wykorzystaniem gotowej biblioteki" + "## 4. Regresja wielomianowa z wykorzystaniem gotowych bibliotek" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -282,7 +376,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -292,7 +386,7 @@ " ('linearregression', LinearRegression())])" ] }, - "execution_count": 8, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -305,7 +399,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -314,7 +408,7 @@ "4" ] }, - "execution_count": 9, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, @@ -342,6 +436,29 @@ "plt.xlim([0,100])\n", "degree" ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "polyfit_theta = np.polyfit(data[\"Height\"]/data[\"Height\"].max(), Y, degree)\n", + "plot_polynomial_regression(polyfit_theta)" + ] } ], "metadata": {