Math assignment and kaggle challenge

assMath/ass2a/shorya/.ipynb_checkpoints/Q3-checkpoint.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "456148e3",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Enter the number of datapoints: 1000000\n",
+      "Enter the mean: 2.56\n",
+      "Enter the standard deviation: 1.2\n",
+      "The parameters from MLE for the normal are: 2.5590225411793885 and 1.4417001920006909\n"
+     ]
+    }
+   ],
+   "source": [
+    "#The derivation is given in the handwritten solutions\n",
+    "import numpy as np\n",
+    "n=int(input(\"Enter the number of datapoints: \"))\n",
+    "mu=float(input(\"Enter the mean: \"))\n",
+    "sigma=float(input(\"Enter the standard deviation: \"))\n",
+    "data=[]\n",
+    "data=np.random.normal(mu, sigma, n)\n",
+    "mean_mle=sum(data)/n\n",
+    "variance_mle=0\n",
+    "for i in range(n):\n",
+    "    variance_mle+=(data[i]-mean_mle)**2\n",
+    "variance_mle/=n\n",
+    "print(\"The parameters from MLE for the normal are:\",mean_mle,\"and\",variance_mle)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b2fb48fb",
+   "metadata": {},
+   "source": [
+    "I have provided the explanation in the handwritten solutions"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

assMath/ass2a/shorya/.ipynb_checkpoints/Q4-checkpoint.ipynb

@@ -0,0 +1,109 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "e5d9ca83",
+   "metadata": {},
+   "source": [
+    "I have provided the explanantion in the handwritten solutions \n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "id": "05e00952",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0.00444714 0.25404008]\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import math\n",
+    "\n",
+    "# Define the negative log-posterior function\n",
+    "def negative_log_posterior(theta, X, y, prior_mean, prior_cov):\n",
+    "    # Compute the log-likelihood\n",
+    "    logits = np.dot(X, theta)\n",
+    "    likelihood = np.sum(y*logits - np.log(1 + np.exp(logits)))\n",
+    "\n",
+    "    # Compute the log-prior\n",
+    "    prior = -0.5 * np.dot((theta - prior_mean).T, np.linalg.inv(prior_cov)).dot(theta - prior_mean)\n",
+    "\n",
+    "    # Compute the negative log-posterior\n",
+    "    neg_log_posterior = - (likelihood + prior)\n",
+    "\n",
+    "    return neg_log_posterior\n",
+    "\n",
+    "def sig(w,x):\n",
+    "        return (1/(1 + np.exp(-np.dot(w,x))))\n",
+    "    \n",
+    "def grad_descent_map(X,y,prior_mean,prior_cov,lr):\n",
+    "    \n",
+    "    X = np.concatenate((np.ones((X.shape[0], 1)), X), axis=1)\n",
+    "    weights=np.random.normal(0, 1/math.sqrt(X.shape[0]), X.shape[1])\n",
+    "    update=[1e9]*X[0].size\n",
+    "    while(np.max(np.array(update))>2*1e-5):\n",
+    "        update=0\n",
+    "        for i in range(X.shape[0]):\n",
+    "            update+=(y[i]-sig(weights,X[i]))*X[i]\n",
+    "        update/=X.shape[0]\n",
+    "        update-=np.dot((weights-prior_mean),np.linalg.inv(prior_cov))\n",
+    "        update*=lr\n",
+    "        weights+=update\n",
+    "    return weights\n",
+    "\n",
+    "#Data for a model which gives 1 for +ve/zero and -1 for -ve numbers    \n",
+    "X=[]\n",
+    "y=[]\n",
+    "for x in range(-50,50,1):\n",
+    "    X.append([x])\n",
+    "    if(x>=0):y.append(1)\n",
+    "    else:y.append(0)\n",
+    "X=np.array(X)\n",
+    "y=np.array(y)\n",
+    "\n",
+    "#Assuming prior to be standard gaussian\n",
+    "prior_mean = np.zeros(X.shape[1]+1)  \n",
+    "prior_cov = np.eye(X.shape[1]+1)  \n",
+    "\n",
+    "result=grad_descent_map(X,y,prior_mean,prior_cov,0.05)\n",
+    "print(result)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0ca293b1",
+   "metadata": {},
+   "source": [
+    "Here the first weight is b and second weight is a in ax+b"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

assMath/ass2a/shorya/Q3.ipynb

@@ -0,0 +1,66 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "456148e3",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Enter the number of datapoints: 1000000\n",
+      "Enter the mean: 2.56\n",
+      "Enter the standard deviation: 1.2\n",
+      "The parameters from MLE for the normal are: 2.5590225411793885 and 1.4417001920006909\n"
+     ]
+    }
+   ],
+   "source": [
+    "#The derivation is given in the handwritten solutions\n",
+    "import numpy as np\n",
+    "n=int(input(\"Enter the number of datapoints: \"))\n",
+    "mu=float(input(\"Enter the mean: \"))\n",
+    "sigma=float(input(\"Enter the standard deviation: \"))\n",
+    "data=[]\n",
+    "data=np.random.normal(mu, sigma, n)\n",
+    "mean_mle=sum(data)/n\n",
+    "variance_mle=0\n",
+    "for i in range(n):\n",
+    "    variance_mle+=(data[i]-mean_mle)**2\n",
+    "variance_mle/=n\n",
+    "print(\"The parameters from MLE for the normal are:\",mean_mle,\"and\",variance_mle)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b2fb48fb",
+   "metadata": {},
+   "source": [
+    "I have provided the explanation in the handwritten solutions"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

assMath/ass2a/shorya/Q4.ipynb

@@ -0,0 +1,109 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "e5d9ca83",
+   "metadata": {},
+   "source": [
+    "I have provided the explanantion in the handwritten solutions \n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "id": "05e00952",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0.00444714 0.25404008]\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import math\n",
+    "\n",
+    "# Define the negative log-posterior function\n",
+    "def negative_log_posterior(theta, X, y, prior_mean, prior_cov):\n",
+    "    # Compute the log-likelihood\n",
+    "    logits = np.dot(X, theta)\n",
+    "    likelihood = np.sum(y*logits - np.log(1 + np.exp(logits)))\n",
+    "\n",
+    "    # Compute the log-prior\n",
+    "    prior = -0.5 * np.dot((theta - prior_mean).T, np.linalg.inv(prior_cov)).dot(theta - prior_mean)\n",
+    "\n",
+    "    # Compute the negative log-posterior\n",
+    "    neg_log_posterior = - (likelihood + prior)\n",
+    "\n",
+    "    return neg_log_posterior\n",
+    "\n",
+    "def sig(w,x):\n",
+    "        return (1/(1 + np.exp(-np.dot(w,x))))\n",
+    "    \n",
+    "def grad_descent_map(X,y,prior_mean,prior_cov,lr):\n",
+    "    \n",
+    "    X = np.concatenate((np.ones((X.shape[0], 1)), X), axis=1)\n",
+    "    weights=np.random.normal(0, 1/math.sqrt(X.shape[0]), X.shape[1])\n",
+    "    update=[1e9]*X[0].size\n",
+    "    while(np.max(np.array(update))>2*1e-5):\n",
+    "        update=0\n",
+    "        for i in range(X.shape[0]):\n",
+    "            update+=(y[i]-sig(weights,X[i]))*X[i]\n",
+    "        update/=X.shape[0]\n",
+    "        update-=np.dot((weights-prior_mean),np.linalg.inv(prior_cov))\n",
+    "        update*=lr\n",
+    "        weights+=update\n",
+    "    return weights\n",
+    "\n",
+    "#Data for a model which gives 1 for +ve/zero and -1 for -ve numbers    \n",
+    "X=[]\n",
+    "y=[]\n",
+    "for x in range(-50,50,1):\n",
+    "    X.append([x])\n",
+    "    if(x>=0):y.append(1)\n",
+    "    else:y.append(0)\n",
+    "X=np.array(X)\n",
+    "y=np.array(y)\n",
+    "\n",
+    "#Assuming prior to be standard gaussian\n",
+    "prior_mean = np.zeros(X.shape[1]+1)  \n",
+    "prior_cov = np.eye(X.shape[1]+1)  \n",
+    "\n",
+    "result=grad_descent_map(X,y,prior_mean,prior_cov,0.05)\n",
+    "print(result)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0ca293b1",
+   "metadata": {},
+   "source": [
+    "Here the first weight is b and second weight is a in ax+b"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}