1)Linear_Regression+GD.ipynb

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    "# 1) Linear Regression\n",
    "\n",
    "- Attempts to model the relationship between two variables by fitting a linear equation to the observed data.\n",
    "\n",
    "- One variable is considered to be an explanatory variable(independent variable x) and other is considered to be a dependend variable(y)\n",
    "\n",
    "- But first we must understand if there is a relationship between the variables of interest: this does not necessarily mean one causes another but there is some significant association between the two variables.\n",
    "\n",
    "- Scatterplot can be used to determine the strength of the relationship between the two variables:\n",
    "    \n",
    "            * If there is no relationship between the exploratory and dependent variable, then there is no point in fitting a linear model\n",
    "            \n",
    "            * Scatter plot does not indicate any increasing or decreasing trends.\n",
    "            \n",
    "- A valuable numerical association between two variables is the correlation coefficient which is a value between [-1,1] indicating the strength of association of the observed data for two variables.\n",
    "\n",
    "\n",
    "\n",
    "- A linear regression line has an equation of the form:\n",
    "\n",
    "$$y = a\\times x + b $$\n",
    "\n",
    "- Here x = independet or exploratory variable and y = dependent variable.\n",
    "\n",
    "- a = intercept , b = slope of the line\n",
    "\n",
    "\n",
    "- Say dataset is $X = \\left \\{ x_{i1},x_{i2}.....x_{ip} \\right \\}_{i=1}^{n}$ of n features.\n",
    "\n",
    "\n",
    "- Let the dependent variable be $y = \\left \\{ y_{1},y_{2},y_{3}......y_{n} \\right \\}$\n",
    "\n",
    "\n",
    "- Assuming there is a linear dependency between $x$ and $y$, the model prediction can be given as :\n",
    "\n",
    "$$y_{i} = w_{0}+w_{1}x_{i1}+w_{2}x_{i2}+......+w_{p}x_{ip}$$ $$ i = 1.....n$$\n",
    "\n",
    "$w_{1},w_{2}.....w_{p}$ = model weights\n",
    "\n",
    "\n",
    "- Using vector notation, we can write this as : \n",
    "\n",
    "    - $Y = \\begin{bmatrix}y_{1}\\\\ .\\\\ .\\\\y_{n}\\\\\\end{bmatrix}$   $W = \\begin{bmatrix}w_{0}\\\\.\\\\.\\\\w_{p}\\end{bmatrix}$  $ X =  \\begin{bmatrix}x_{1}^{T}\\\\ .\\\\.\\\\x_{n}^{T} \\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Now, we can write the prediction matrix $\\bar{Y}$ as : \n",
    "\n",
    "$$\\bar{Y} = W^{T}X$$\n",
    "\n",
    "\n",
    "- $w_{0}$ = Intercept term\n",
    "\n",
    "- $w_{1},w_{2}.......w_{p}$ = Model parameters\n",
    "\n",
    "- $W$ = Parameter Vector\n",
    "\n",
    "\n",
    "\n",
    "### 1.1) Linear Regression Assumptions \n",
    "\n",
    "- **Linearity :** The relationshio between $X$ and $Y$ must be linear. We can check this using Scatter Plots.\n",
    "\n",
    "\n",
    "- **Normality :** For any value of $X$ and $Y$, it should be normally distributed. We can check this using (Q-Q) plot. Normality can be checked with a goodness of fit test(K-S) test. When data is not normally distributed, we can use non-linear transformation(eg: log-transformation) to solve the issue.\n",
    "\n",
    "\n",
    "\n",
    "- **Homoscedasticity :** The variance of residuals is same for any value of $X$.\n",
    "\n",
    "\n",
    "- **No or Little Multicollinearity :** This happens when independent variables are too highly correlated with each other.\n",
    "\n",
    "\n",
    "#### 1.1.1) Test for multicollinearity:\n",
    "  \n",
    "  1)<u> Correlation Matrix </u>:\n",
    "      Compute Pearson's Bivariate Correlation amoung all independent variables and coorelation coefficient must be smaller than 1.\n",
    "      \n",
    "  2)<u> Tolerence </u>:\n",
    "      Measures the influence of one independent variable on all the independent variables.\n",
    "      $$Tolerence(T) = 1-R^{2}$$\n",
    "      \n",
    "   **<u>Calculating Tolerence</u>**\n",
    "   \n",
    "   1) Regress each independent variable on all other independent value.\n",
    "       \n",
    "   2) Substract each $R^{2}$ value from 1. If $T<1$ => Might be multicollinearity. If $T<0.01$ => Multicollinearity.\n",
    "   \n",
    "  \n",
    "  3)<u>Variance Inflation Factor</u>:\n",
    "  \n",
    "  $VIF = \\frac{1}{T}$\n",
    "  \n",
    "  VIF = 1 => Not Multicollinearity\n",
    "  \n",
    "  VIF Between 1 - 5 => Moderately Multicollinear\n",
    "  \n",
    "  VIF >10 => High multicollinearity\n",
    "  \n",
    "  \n",
    "  - Mean Centering could help solve the problem of Multicollinearity.\n",
    "  \n",
    "  - Remove independent variables with high VIF values.\n",
    "       \n",
    "       \n",
    "       \n",
    "**Anscombe's quartet**\n",
    "\n",
    "- This comprises of 4 datasets that have nearly identical simple descriptive statistics(ie nearly identical means, standard deviations, and correlations) yet have different distributions and appear very differently when graphed.\n",
    "\n",
    "\n",
    "- The following diagram illustrates the pitfalls of relying solely on a fitted model to understand the relationship between variables:\n",
    "\n",
    "<img src=\"images/anscomb.png\" width=\"700\" height=\"700\">\n",
    "\n",
    "\n",
    "- They were created to demonstrate the importance of graphing data before analyzing it and the effect of outliers and other influential observations on Statistical properties.\n",
    "\n",
    "\n",
    "**Generalized Linear Models(GLM)**\n",
    "\n",
    "- GLM's are a framework for modelling response variables that are continuous(bounded) or discrete.\n",
    "\n",
    "- They can be used:\n",
    "    \n",
    "    - When modelling positive quantiles(prices of polulation) that vay over large scale. They can be described using a skewed distribution such as log-normal or Poisson.\n",
    "    \n",
    "    - Modelling Categorical data where there are fixed number of choices that cannot be meaningfully ordered. They can be modelled with a) Bernaulli/binomial distribution(Binary Choices) or b) Categorical/Multinomial Choices(multi-class)\n",
    "\n",
    "- A GLM is made up of a linear predictor\n",
    "\n",
    "$$y = w_{0} + w_{1}x_{1i}+.....w_{p}x_{pi}$$ $$i = 1...n$$\n",
    "\n",
    "- A link function 'g' that relates the mean of the response variable(s) to the predictors:\n",
    "\n",
    "\n",
    "$$g(\\mu )  = y$$\n",
    "\n",
    "\n",
    "$$g(\\mu ) = W^{T}X$$\n",
    "\n",
    "\n",
    "$$\\mu = g^{-1}(W^{T}X)$$\n",
    "\n",
    "\n",
    "- The link function is often related to the distribution of response, and in particular it typically has the effect of response, and in particular it typically has the effect of transforming $\\left ( -\\infty,+ \\infty \\right )$ range of the linear predictor and the range of response variable.\n",
    "\n",
    "\n",
    "- eg: When modelling Binomial data, 'g' must map from (0,1) -> $\\left ( -\\infty,+ \\infty \\right )$. So a common choice would be to choose:\n",
    "\n",
    "$$g\\left ( \\mu_{i}  \\right ) = logit(\\mu_{i}) = log\\left ( \\frac{\\mu_{i}}{1 - \\mu_{i}} \\right )$$\n",
    "\n",
    "- For more on GLM's refer : https://statmath.wu.ac.at/courses/heather_turner/glmCourse_001.pdf"
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    "### 1.2) Training Linear Regression  \n",
    "\n",
    " $$y = W^{T}X$$\n",
    "\n",
    "- We need to measure the goodness of fit or how well the model fits the data.\n",
    "\n",
    "\n",
    "<img src=\"images/lr-intuition.png\" width=\"300\" height=\"300\">\n",
    "\n",
    "- In linear regression, the observations (red) are assumed to be the result of random deviations (green) from an underlying relationship (blue) between a dependent variable (y) and an independent variable (x).\n",
    "\n",
    "\n",
    "- In LR., we try to minimize the deviations. How to measure this deviation.\n",
    "\n",
    "\n",
    "- One Common metric for that is the Mean(Mean Square Error)\n",
    "\n",
    "\n",
    "- To train a Linear Regression model, you need to find the value $W$ that minimizes the MSE.\n",
    "\n",
    "\n",
    " $$ L(W) = MSE(X,y) = \\frac{1}{n}\\sum_{i=1}^{n}\\left ( W^{T}x^{\\left ( i \\right )} - y^{(i)} \\right ) $$\n",
    "\n",
    "\n",
    "- There is an Analytical Solution to find the $W$ that minimizes this loss/cost function also called Normal Equation.\n",
    "\n",
    "\n",
    "$$\\hat{W} = \\left ( X^{T}X \\right )^{-1}X^{T}y$$\n",
    "\n",
    "- Proof : https://en.wikipedia.org/wiki/Linear_regression\n",
    "\n",
    "\n",
    "- $\\hat{W}$ = Value of W that minimizes the loss function.\n",
    "\n",
    "\n",
    "- $y$ = Vector of target values containing $y^{1}.....y^{m}$\n",
    "\n",
    "\n",
    "- However computing the inverse of $(X^{T}X)^{-1}$ for an $n \\times n$ matrix is about $O(n^{2.4}) \\approx O(n^{3})$ depending on the implementation.\n",
    "\n",
    "\n",
    "- Hence this is a very slow process. However for extremely large datasets that might not fit into RAM, this method cannot be applied.\n",
    "\n",
    "\n",
    "- But Predictions are extremely fast $\\approx O(m)$ where m = number of features\n",
    "\n",
    "\n"
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    "### 1.3) Gradient Descent"
   ]
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    "- This is a generic optimization technique capable of finding optimal solutions to a wide range of problems.\n",
    "\n",
    "\n",
    "- Thee Genral idea is to tweak the parameters iteratively to minimize a loss/cost function.\n",
    "\n",
    "\n",
    "- For a GD to work, the loss function must be differentiable. This method is also called the steepest descent method.\n",
    "\n",
    "\n",
    "<img src=\"images/gd-1.jpg\" width=\"400\" height=\"400\">\n",
    "\n",
    "\n",
    "- If Learning Rate = too small => GD. takes too much time to converge.\n",
    "\n",
    "\n",
    "- If Learning Rate = Large => May not converge as it misses the minimum.\n",
    "\n",
    "\n",
    "<img src=\"images/gd-lr.png\" width=\"700\" height=\"700\">\n",
    "\n",
    "\n",
    "- What if the functions don't look like convex functions\n",
    "\n",
    "\n",
    "<img src=\"images/gd-localmin.png\" width=\"400\" height=\"400\">\n",
    "\n",
    "\n",
    "- In this case we can reset the initial value and do again.\n",
    "\n",
    "\n",
    "- The Loss function for Linear Regression(MSE) is a convex function ie if we pick any two points in the curve, the line segment joining them never crosses the line. This means that there are no local minima but a single global minimum and also it is a continuous function.\n",
    "\n",
    "\n",
    "- G.D. is guaranteed to approach arbitrarily close to the global minimum.\n",
    "\n",
    "\n",
    "- Train a Model => Search for a combination of model parameters that minimizes the Loss function. \n"
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    "$$L(W) = \\frac{1}{n}\\sum_{i=1}^{n}\\left ( W^{T}x^{(i)} - y^{i}  \\right )^{2}$$\n",
    "\n",
    "\n",
    "- We need to find a direction where function decreases and we need to take a step in this direction.\n",
    "\n",
    "- Optimization Problem: $\\underset{W}{min}L(W)$\n",
    "\n",
    "\n",
    "- Let Initial weights = $w^{0}$\n",
    "\n",
    "\n",
    "- The gradient vector :\n",
    "\n",
    "$$\\bigtriangledown L(w^{0}) = \\left ( \\frac{\\delta L(w^{0})}{\\delta w_{1}} + \\frac{\\delta L(w^{0})}{\\delta w_{2}} + .......+ \\frac{\\delta L(w^{0})}{\\delta w_{n}} \\right )$$\n",
    "\n",
    "\n",
    "- This Gradient Vector points in the direction of Steepest Ascent at $w^{0}$.\n",
    "\n",
    "\n",
    "- This function has a fast decreasing rate in the direction of negative gradient.\n",
    "\n",
    "\n",
    "$$\\frac{\\delta L(w)}{\\delta w_{j}} = \\frac{2}{m}\\sum_{i=1}^{m}\\left ( w^{T}x^{(i)} - y^{(i)} \\right )\\left ( x_{j}^{(i)} \\right )$$\n",
    "\n",
    "\n",
    "$$\\bigtriangledown _{w}L(w) = \\begin{bmatrix}\\frac{\\delta L(w)}{\\delta w_{1}}\\\\ \\frac{\\delta L(w)}{\\delta w_{2}}\\\\.\\\\.\\\\\\frac{\\delta L(w)}{\\delta w_{n}} \\end{bmatrix} = \\frac{2}{m}X^{T}\\left ( X.w - y \\right )$$\n",
    "\n",
    "\n",
    "\n",
    "- **Gradient Descent Step :**\n",
    "\n",
    "$$w^{t} = w^{t-1} - \\eta \\bigtriangledown _{w}L(w^{t-1})$$\n",
    "\n",
    "- Where $\\eta$ = Learning Rate\n",
    "\n",
    "\n",
    "- When $\\eta$ = too small => The Algorithm eventually reach the optimal solution, but it will take too much time.\n",
    "\n",
    "\n",
    "- When $\\eta$ = too large => The Algorithm diverges jumping all over the place and actually getting further and further away from the solution at every step.\n",
    "\n",
    "\n",
    "- We can use GridSearch to find a good Learning Rate.\n",
    "\n",
    "\n",
    "- We can set the number of iterations to be large but to interruprt the algorithm when the gradient vector becomes tiny, we can calculate the norm of the Gradient vector at every step and if it is less than a tiny value $(\\epsilon)$, Gradient Descent has reached minimum so we must halt the Gradient Descent.\n",
    "\n",
    "\n",
    "- Gradient Descent works even in spaces of any number of dimensions even in infinite dimension ones.\n",
    "\n",
    "<img src=\"images/gd-pc.png\" width=\"400\" height=\"400\">\n"
   ]
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    "### 1.3.1) Stochastic Gradient Descent"
   ]
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    "- Batch Gradient Descent or Gradient Descent requires the whole training set in memory to compute the gradients at every step. This makes it slow when train set is huge. Also if the training dataset doesn't fit the memory we might not be able to use GD.\n",
    "\n",
    "\n",
    "- In SGD, we just pick a random instance in the training set at each step and then compute the gradients based only on that single instance.\n",
    "\n",
    "\n",
    "- This makes the algorithm fast since it has very little data to manipulate at every iteration. It also makes possible to train huge datasets that does not fit into memory.\n",
    "\n",
    "\n",
    "- Due to it's Stochastic(random) nature, the algorithm is much less regular than G.D. instead of decreasing untill it reaches the minimum, the Loss function will bounce up and down, decreasing only on average ie Noisy updates.\n",
    "\n",
    "\n",
    "- Over the time it will end up closer to minimum, but once it gets there it will continue to bounce around, never settling down. Once Algorithm stops final parameters are good but not optimal.\n",
    "\n",
    "\n",
    "<img src=\"images/sgd-gd.png\" width=\"700\" height=\"700\">\n",
    "\n",
    "\n",
    "- One advantage of having such updates is that, when there is an irregular function, then this can help the algorithm jump out of local minima, So SGD has better chance of finding global minimim than GD.\n",
    "\n",
    "\n",
    "- This Randomness can halp to avoid local minima, but what if the algorithm never settle at a minimum?\n",
    "    \n",
    "    - > Gradually reduce the learning rate\n",
    "    \n",
    "    - > The algorithm starts with large Learning Rate and then slowly reduce the learning rate and it becomes smaller and smaller allowing the algorithm to settle at Global minimum. This is called **simulated annealing**.\n",
    "    \n",
    "    - > The function that determines the Learning Rate at each iteration is called **learning rate scheduler**\n",
    "    \n",
    "    - > If Learning Rate is reduced too quickly, then the algorithm may get stuck in Local minima or Frozen halfway\n",
    "    \n",
    "    - > If Learning Rate is reduced too slowly, then we might jump around the minimum for a long time and end up in suboptimal solution.\n",
    "    \n",
    "    \n",
    "<img src=\"sgd-pc.png\" width=\"400\" height=\"400\">\n",
    "    "
   ]
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    "### 1.3.2) Mini-Batch Stochastic Gradient Descent"
   ]
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    "- Here, instead of computing gradients based on full training set (or) just a single instance, mini-batch GD computes the gradients on small random sets of instances called **mini-batches**.\n",
    "\n",
    "- The main advantage of mini-batch GD over SGD is that we can get performance boost from hardware optimization of matrix operations especially with a GPU.\n",
    "\n",
    "- Both Mini-SGD as well as SGD tends to walk around minimum but GD will converge to minimum, however GD takes more time to take each step\n",
    "\n",
    "-  Both SGD and mini-batch SGD would also reach minimum if good learning rate is chosen.\n",
    "\n",
    "<img src=\"images/mini-sgd.png\" width=\"700\" height=\"700\">\n",
    "\n",
    "\n",
    "<img src=\"images/msgd-pc.png\" width=\"400\" height=\"400\">\n"
   ]
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    "### 1.4) Polynomial Regression"
   ]
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    "- What if the data is more complex than simple straight line and cannot be fit with simple Linear Regression.\n",
    "\n",
    "\n",
    "- Polynomial Regreession is a regression analysis in which the relationship betwen an independent variable($X$) and dependent variable($y$) is modelled as an $n^{th}$ degree polynomial in $X$.\n",
    "\n",
    "\n",
    "- Fits non-linear relationship between the value $x$ and corresponding conditional mean of $y$ denoted as : $E(y | x)$\n",
    "\n",
    "\n",
    "- Although polynomial regression fits a non-linear model to the data, as a statistical estimation problem, it is linear, in the sense that the regression function $E(y|x)$ is linear in the unknown parameters that are estimated from the data.\n",
    "\n",
    "\n",
    "- Polynomial regression is considered as special case of multiple linear regression.\n",
    "\n",
    "\n",
    "- The goal of Polynomial Regression is to model the expected value of dependent variable $y$ in terms of independent variable(or vector of independent variables) $x$.\n",
    "\n",
    "\n",
    "- In simple Linear Regression, the model prediction is given as :\n",
    "\n",
    "$$y = w_{0}+w_{1}x$$\n",
    "\n",
    "- In many settings, such a linear relationship may not hold. For example: A quadratic model of the form will be like:\n",
    "\n",
    "$$y = w_{0} + w_{1}x + w_{2}x^{2}$$\n",
    "\n",
    "\n",
    "- In general, we can model an expected value of $y$ as an $n^{th}$ degree polynomial, yielding the general polynomial regression model:\n",
    "\n",
    "$$y = w_{0} + w_{1}x + w_{2}x^{2} + .....+w_{n}x^{n}$$\n",
    "\n",
    "\n",
    "- The models are all linear from the point of view of estimation, since the regression function is linear in terms of the unknown parameters $w_{0} , w_{1}...$\n",
    "\n",
    "\n",
    "- So for Least Squares analysis, the computational and Inferential problem of polynomial regression can be completely addressed using the techniques of multiple regression. This is done by treating $x,x^{2}....$ as being distinct independent variables in a multiple regression model.\n"
   ]
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    "#### 1.4.1) Matrix form and Calculation of estimates\n",
    "\n",
    "\n",
    "$$y_{i} = w_{0} + w_{1}x_{i} + w_{2}x_{i}^{2} + ...... + w_{m}x_{i}^{m}$$$$(i = 1,2,.....,n)$$\n",
    "\n",
    "\n",
    "- This can be expressed in matrix form as : \n",
    "\n",
    "$$\\begin{bmatrix}y_{1}\\\\ y_{2}\\\\.\\\\.\\\\.\\\\y_{n} \\end{bmatrix} = \\begin{bmatrix}1 &x_{1}  &x_{1}^{2}  &.&.&.&.x_{1}^{m} \\\\ 1 &x_{2}  &x_{2}^{2}  &.&.&.&.x_{2}^{m} \\\\. &.  &.  &.&.&.&. \\\\. &.  &.  &.&.&.&. \\\\. &.  &.  &.&.&.&. \\\\1 &x_{n}  &x_{n}^{2}  &.&.&.&.x_{n}^{m}  \\end{bmatrix}\\begin{bmatrix}w_{0}\\\\ w_{1}\\\\ .\\\\ .\\\\ .\\\\ w_{m}\\end{bmatrix}$$\n",
    "\n",
    "\n",
    "- In pure Matrix Notation, this can be written as :\n",
    "\n",
    "$$ {y} = XW $$\n",
    "\n",
    "\n",
    "$$ \\tilde{W} = (X^{T}X)^{-1}(X^{T}{y}) $$\n",
    "\n",
    "\n",
    "- We can solve this using Gradient Descent as well."
   ]
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    "### 1.5) Regularized Linear Models\n",
    "\n",
    "#### 1.5.1.1) Overfitting :\n",
    "\n",
    "- This occurs when a statisticsl model/ ML algorithm captures the noise of the data or intitively it happens when model (or) algorithm fits data too well.\n",
    "\n",
    "\n",
    "- Specifically Overfitting Occurs if the model (or) Algorithm shows low bias but high Variance. Overfitting models perform well on training data but generalizes poorly according to Cross-Validation metrics.\n",
    "\n",
    "\n",
    "**How to prevent it**\n",
    "- > Cross-Validation\n",
    "- > Train with more data\n",
    "- > Feature Selection\n",
    "- > Early Stopping\n",
    "- > Regularization\n",
    "- > Ensembling"
   ]
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    "#### 1.5.1.2) Underfitting :\n",
    "\n",
    "- Occurs when a statistical model/ML algorithm cannot capture the underlying trend in the data or intuitively it happens when the model/Algorithm does not fit the data well enough.\n",
    "\n",
    "\n",
    "- Specifically, underfitting occurs if model (or) Algorithm shows low variance but high bias. This is a result of excessively simple model.\n",
    "\n",
    "\n",
    "- Underfitted models perform poorly in both train and validation data set.\n",
    "\n",
    "\n",
    "**How to prefent it**\n",
    "- > Increase the number of Parameters in ML models\n",
    "- > Increase complxity (or) type of model\n",
    "- > Increasing the training time untill cost function in ML model is minimized."
   ]
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    "#### 1.5.1.3) Generalization Error :\n",
    "\n",
    "- Generalization error can be classified into 3 types. They are : \n",
    "\n",
    "1) **Bias** : This is due to wrong assumptions such as like data is linear when it is actually quadratic. When a model has high bias then it indicates that the model is an underfit model.\n",
    "\n",
    "2) **Variance** : This is due to model's excessive sensitivity to small variations in the training data. A model with high degrees of freedom(higher degree polynomial) is likely to have high variance and thus overfit the training data.\n",
    "\n",
    "3) **Irreducible Error** : This is due to noisiness in the data, this can be reduced by cleaning the data properly.\n",
    "\n",
    "\n",
    "**Bias-Variance tradeoff**\n",
    "\n",
    "- Increase in model's complexity will typically increase it's Variance and reduce it's bias.\n",
    "\n",
    "- Reducing a model's complexity will typically increase it's bias and reduce it's variance.\n",
    "\n",
    "- This is why it is called as Bias-Variance Tradeoff\n"
   ]
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    "#### 1.5.2) Ridge Regression :\n",
    "\n",
    "- A good way to reduce overfitting is to regularize the model. The fewer degrees of freedom it has the harder it will be for the model to overfit the data. eg: A simple way to regularize a polynomial model is to reduce the number of polynomial degrees.\n",
    "\n",
    "\n",
    "- Ridge regression is a regularized version of Linear Regression with regularization term $\\alpha \\sum_{i=1}^{n}w_{i}^{2}$ is added to the Loss function.\n",
    "\n",
    "\n",
    "- This forces the Learning Algorithm to not only fit the data, but also keep the model weights as small as possible.\n",
    "\n",
    "\n",
    "- Regularization term must be added to the loss function only during training. Once the model is trained, we evaluate the model using unregularized performance measure.\n",
    "\n",
    "\n",
    "- The hyperparameter $\\alpha$ controls how much we want to regularize the models:\n",
    "- > If $\\alpha = 0$, Then Ridge Regression becomes Linear Regression.\n",
    "- > If $\\alpha = V.large$, then all weights end up close to zero and results in a flat line going through the mean of data.\n",
    "- > <img src=\"images/ridge-alpha.png\" width=\"700\" height=\"700\">\n",
    "- > From the above image it can be clearly seen that as alpha increases the line gets flatter and flatter\n",
    "\n",
    "- $$L_{reg}(w) = L(w) + \\alpha \\sum_{i=1}^{n}w_{i}^{2}$$\n",
    "\n",
    "- The bias term $w_{0}$ is not regularized\n",
    "\n",
    "\n",
    "- If **w** is the weight vector, then the regularization term is simply equal to $\\left \\| w \\right \\|_{2}^{2}$ where $\\left \\| . \\right \\|$ is the $L_{2}$ norm of the weight vector.\n",
    "\n",
    "\n",
    "- We can solve Ridge Regression using either SGD or Closed-form equation.\n",
    "\n",
    "\n",
    "$$\\hat{w} = (X^{T}X + \\alpha A)^{-1}X^{T}y$$\n",
    "\n",
    "- Where **A** is an $n\\times n$ identity matrix except with 0 in top-left which corresponds to the bias term."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5.3) Lasso Regression :\n",
    "\n",
    "- Lasso(Least Absolute Shrinkage & Selection Operator Regression) is a Regularized version of Linear Regression.\n",
    "\n",
    "- Adds a regularization term to the Loss function. It uses $L_{1}$ norm of weight vector instead of $L_{2}$ norm.\n",
    "\n",
    "$$L_{reg}(w) = L(w) + \\alpha\\sum_{i=1}^{n}\\left | w_{i} \\right |$$\n",
    "\n",
    "- An important characteristic of $L_{1}$ regularization is that it completely eliminates the weights of least importance(ie set them to 0).\n",
    "\n",
    "\n",
    "- Lasso Regression automatically performs feature selection and outputs a sparse model. Lasso function is not differentiable at $w_{i} = 0$ (for $i = 1,2,3...n$). But GD. still works fine if we use a subgradient vector instead when any $w_{i} = 0$.\n",
    "\n",
    "$$\\bigtriangledown _{w}MSE(w) = \\begin{bmatrix}sign(w_{1})\\\\ sign(w_{2})\\\\.\\\\.\\\\sign(w_{n}) \\end{bmatrix}$$\n",
    "\n",
    "$$sign(w_{i}) = \\left\\{\\begin{matrix}-1 & w_{i}<0\\\\ 0& w_{i}=0\\\\ +1&w_{i}>0 \\end{matrix}\\right.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5.4) Elastic Net :\n",
    "\n",
    "- It is in between Ridge and Lasso Regression. The regularization term is a simple mix of both Ridge and Lasso Regression terms and we can control the mix ratio(r)\n",
    "\n",
    "- If $r = 0$ = > E.N $\\approx$ Ridge Regression\n",
    "\n",
    "- If $r = 1$ = > E.N $\\approx$ Lasso Regression\n",
    "\n",
    "$$L_{EN}(w) = L(w) + r\\alpha\\sum_{i=1}^{n}\\left | w_{i} \\right | + \\frac{1-r}{2}\\alpha\\sum_{i=1}^{n}w_{i}^2$$\n",
    "\n",
    "\n",
    "- **Now when to choose EN. over plain L.R ?**\n",
    "- > It is always preferable to have atleast a bit of regularization, so generally you should avoid plain LR.\n",
    "- > Ridge is good, but if we need to apply feature selection also, then go for Lasso or EN. since they tend to reduce the weights of useless features down to zero.\n",
    "- > Elastic Net is preferred over Lasso since Lasso may behave erratically when the number of Features is greater than the number of training instances (or) when several features are strongly correlated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.6) Extentions to Gradient Descent\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.6.1) Momentum Approach:\n",
    "\n",
    "- Stochastic gradient descent with momentum remembers the update $Δ w$ at each iteration, and determines the next update as a linear combination of the gradient and the previous update.\n",
    "\n",
    "\n",
    "- Here an additional vector $(h)$ is maintained at every iteration.\n",
    "\n",
    "\n",
    "$$h_{t} = \\alpha h_{t-1} + \\eta_{t}g_{t}$$\n",
    "\n",
    "\n",
    "$$w^{t} = w^{t-1} - h_{t}$$\n",
    "\n",
    "\n",
    "- $h_{t} = $ Weighted sum of gradients from all the previous iteration and from this iteration also.\n",
    "\n",
    "\n",
    "- Tends to move in the same direction as of previous steps. $h_{t}$ cancels some coordinates that lead to oscillation of gradients and help to achieve better convergence.\n",
    "\n",
    "\n",
    "- ie  The momentum term increases for dimensions whose gradients point in the same directions and reduces updates for dimensions whose gradients change directions. As a result, we gain faster convergence and reduced oscillation.\n",
    "\n",
    "\n",
    "- when using momentum, we push a ball down a hill. The ball accumulates momentum as it rolls downhill, becoming faster and faster on the way (until it reaches its terminal velocity if there is air resistance, i.e. $\\alpha < 1$\n",
    "\n",
    "\n",
    "- $h_{t}$ accumulates values along dimensions where the gradients have same sign.\n",
    "\n",
    "\n",
    "- Usually $\\alpha$ = 0.9\n",
    "\n",
    "\n",
    "<img src=\"images/sgd-mom.png\" width=\"700\" height=\"700\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.6.2) Nestrov Accelerated Momentum Approach:\n",
    "\n",
    "- A ball that rolls down a hill, blindly following the slope, is highly unsatisfactory. We'd like to have a smarter ball, a ball that has a notion of where it is going so that it knows to slow down before the hill slopes up again.\n",
    "\n",
    "\n",
    "$$h_{t} = \\alpha h_{t-1} + \\eta_{t}\\bigtriangledown_{L}(w^{t-1} - \\alpha h_{t-1})$$\n",
    "\n",
    "$$w^{t} = w^{t-1} - h_{t}$$\n",
    " \n",
    "\n",
    "<img src=\"images/sgd-nag.png\" width=\"700\" height=\"700\">\n",
    "\n",
    "\n",
    "- Here we first step in the direction of $h_{t}$ to get some new approximation of parameter vector and then calculate gradient at the new point.\n",
    "\n",
    "\n",
    "- Both NAG as well as Momentum approach is sensitive to learning rate$(\\eta)$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.6.3) AdaGrad :\n",
    "\n",
    "- Adagrad is a modified SGD with per-parameter learning rate.\n",
    "\n",
    "\n",
    "- This increases the learning rate for sparser parameters and decreases the learning rate for ones that are less sparse.\n",
    "\n",
    "\n",
    "- Improves convergence performance over standard stochastic gradient descent in settings where data is sparse and sparse parameters are more informative. Examples of such applications include natural language processing and image recognition.\n",
    "\n",
    "\n",
    "$$G_{j}^{t} = G_{j}^{t} - g_{t,j}^{2}$$\n",
    "\n",
    "$$w_{j}^{t} = w_{j}^{t-1} - \\frac{\\eta _t}{\\sqrt{G_{j}^{t}+\\epsilon }}g_{t,j}$$\n",
    "\n",
    "\n",
    "- $g_{t,j} = $ Gradient at iteration t with respect to parameter j.\n",
    "\n",
    "\n",
    "- Here base learning rate can be fixed : $\\eta _t = 0.01$\n",
    "\n",
    "\n",
    "- $G = $ Sum of squares of gradients from all previous iterations\n",
    "\n",
    "\n",
    "- $G_{j}^{t}$ always increases which leads to early stopping which is a bit of problem too because sometimes $G$ becomes to large that it results in stopping before it reaches the minimum.\n",
    "\n",
    "\n",
    "- AdaGrad can be applied to non-convex optimization problems also.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.6.4) RMSProp :\n",
    "\n",
    "- RMSProp (for Root Mean Square Propagation) is also a method in which the learning rate is adapted for each of the parameters. \n",
    "\n",
    "\n",
    "- RMSprop divides the learning rate by an exponentially decaying average of squared gradients. \n",
    "\n",
    "\n",
    "$$G_{j}^{t} = \\alpha G_{j}^{t-1} + (1-\\alpha)g_{t,j}^{2}$$\n",
    "\n",
    "$$w_{j}^{t} = w_{j}^{t-1} - \\frac{\\eta _t}{\\sqrt{G_{j}^{t}+\\epsilon }}g_{t,j}$$\n",
    "\n",
    "- RMSProp has shown excellent adaptation of learning rate in different applications. \n",
    "\n",
    "\n",
    "- RMSProp can work with mini-batches as well.\n",
    "\n",
    "\n",
    "- Typically $\\alpha = 0.9$ and default value of learning rate is set to $\\eta = 0.001$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.6.5) Adam :\n",
    "\n",
    "-  Adaptive Moment Estimation(Adam) is an update to the RMSProp optimizer ie it computes the learning rates for each parameters adaptively.\n",
    "\n",
    "\n",
    "- In addition to storing an exponentially decaying average of past squared gradients like Adadelta and RMSprop, Adam also keeps an exponentially decaying average of past gradients, similar to momentum.\n",
    "\n",
    "\n",
    "- Momentum can be seen as a ball running down a slope, Adam behaves like a heavy ball with friction, which thus prefers flat minima in the error surface.\n",
    "\n",
    "\n",
    "$$V_{j}^{t} = \\frac{\\beta _{2}V_{j}^{t-1} + (1-\\beta_{2})}{1-\\beta_{2}^{t}}g_{t,j}^{2}$$\n",
    "\n",
    "$$w_{j}^{t} = w_{j}^{t-1} - \\frac{\\eta_{t}}{\\sqrt{V_{j}^{t}}+\\epsilon}g_{t,j}$$\n",
    "\n",
    "\n",
    "- The approximation $V$ has bias towards $0$ especially at initial steps cos we initialize $\\beta_{2}$ with $0$. So iorder to get rid of this bias, we divide by $1-\\beta_{2}^{t}$. This normalization allows to get rid of the bias."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.7 Linear Regression with SGD implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython impsort display\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Create random set of Examples : \n",
    "X = np.random.rand(1000,4)\n",
    "y = 3 * X[:, 0] + 10 * X[:, 1] + -2 * X[:, 2] + -3 * X[:, 3]  # True Weights = [3,10,-2,-3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot scatter plot of variables wrt. the targer variable.\n",
    "for i in range(X.shape[1]):\n",
    "    plt.scatter(X[:, i], y, s=20)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- From the above plots we can clearly see that the 2nd feature with more weight is a very important feature here.\n",
    "\n",
    "- Now we know how to find the solution using Analytical solution which is :\n",
    "\n",
    "$$\\hat{W} = \\left ( X^{T}X \\right )^{-1}X^{T}y$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal weights =  [ 3. 10. -2. -3.]\n"
     ]
    }
   ],
   "source": [
    "dot_prd = np.dot(X.T,X)\n",
    "inv = np.linalg.inv(dot_prd) \n",
    "w_opt = np.dot(np.dot(inv,X.T),y)\n",
    "print('Optimal weights = ',w_opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- This is same as our true weights."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Now we will use SGD to solve the problem\n",
    "\n",
    "\n",
    "- Gradient of loss function : $\\frac{2}{m}X^{T}\\left ( X.w - y \\right )$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mse_loss(X,w,y):\n",
    "    pred = np.dot(X,w)\n",
    "    mse = (np.square(y-pred)).mean()\n",
    "    return mse\n",
    "    \n",
    "def get_grads(X,w,y):\n",
    "    m = X.shape[0]\n",
    "    return (2/m)*np.dot(X.T,np.dot(X,w)-y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Simple SGD\n",
    "np.random.seed(42)\n",
    "w = np.array([0,0,0,0]) #Initial Weights\n",
    "eta= 0.1 # learning rate\n",
    "n_iter = 1000 # Number of Iterations\n",
    "batch_size = 128\n",
    "loss = np.zeros(n_iter)\n",
    "\n",
    "es = 0.0001 #For early stopping \n",
    "\n",
    "for i in range(n_iter):\n",
    "    ind = np.random.choice(X.shape[0], batch_size)\n",
    "    loss[i] = mse_loss(X[ind, :], w, y[ind])\n",
    "    w = w - eta*get_grads(X[ind, :], w, y[ind])\n",
    "    if(i%10==0):\n",
    "        plt.plot(loss[:i])\n",
    "        plt.grid()\n",
    "        ymin, ymax = plt.ylim()\n",
    "        plt.ylim(0, ymax)\n",
    "        plt.xlabel('Iterations')\n",
    "        plt.ylabel('Loss')\n",
    "        display.clear_output(wait=True)\n",
    "        plt.show()\n",
    "    \n",
    "    if(loss[i]<es):\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mini-batch SGD Converged in :  322\n",
      "FInal Weights [ 3.00125892  9.96801032 -1.98367596 -2.98748938]\n"
     ]
    }
   ],
   "source": [
    "print(\"mini-batch SGD Converged in : \",i)\n",
    "print(\"FInal Weights\",w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- This is very close to our true weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0001236901054422838"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we will calculate the predictions with the predicted weight and calcumate the mse\n",
    "mse_loss(X,w,y) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The error is also very less"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### SGD With Momentum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "w = np.array([0,0,0,0]) #Initial Weights\n",
    "\n",
    "eta = 0.05 # learning rate\n",
    "alpha = 0.9 # momentum\n",
    "\n",
    "h = np.zeros_like(w)  #This is the additional vector\n",
    "\n",
    "es = 0.0001 #For early stopping \n",
    "\n",
    "\n",
    "n_iter = 1000\n",
    "batch_size = 128\n",
    "loss = np.zeros(n_iter)\n",
    "\n",
    "\n",
    "for i in range(n_iter):\n",
    "    ind = np.random.choice(X.shape[0], batch_size)\n",
    "    loss[i] = mse_loss(X[ind, :], w, y[ind])\n",
    "    \n",
    "    h = alpha*h + eta*get_grads(X[ind, :], w, y[ind])\n",
    "    \n",
    "    w = w-h\n",
    "    \n",
    "    if(i%10==0):\n",
    "        plt.plot(loss[:i])\n",
    "        plt.grid()\n",
    "        ymin, ymax = plt.ylim()\n",
    "        plt.ylim(0, ymax)\n",
    "        plt.xlabel('Iterations')\n",
    "        plt.ylabel('Loss')\n",
    "        display.clear_output(wait=True)\n",
    "        plt.show()\n",
    "        \n",
    "        \n",
    "    if(loss[i]<es):\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mini-batch SGD Converged in :  99\n",
      "FInal Weights [ 3.0110051   9.98150995 -1.98861845 -2.98908499]\n",
      "MSE Loss =  0.00012119072244298674\n"
     ]
    }
   ],
   "source": [
    "print(\"mini-batch SGD Converged in : \",i)\n",
    "print(\"FInal Weights\",w)\n",
    "print('MSE Loss = ',mse_loss(X,w,y) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Normal min-batch SGD took around 300 iterations to converge wheras Momentum took only 99 iterations, it is very fast."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### SGD With Nestrov accelerated momentum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "w = np.array([0,0,0,0]) #Initial Weights\n",
    "\n",
    "eta = 0.05 # learning rate\n",
    "alpha = 0.9 # momentum\n",
    "\n",
    "h = np.zeros_like(w)  #This is the additional vector\n",
    "\n",
    "es = 0.0001 #For early stopping \n",
    "\n",
    "\n",
    "n_iter = 1000\n",
    "batch_size = 128\n",
    "loss = np.zeros(n_iter)\n",
    "\n",
    "\n",
    "for i in range(n_iter):\n",
    "    ind = np.random.choice(X.shape[0], batch_size)\n",
    "    loss[i] = mse_loss(X[ind, :], w, y[ind])\n",
    "    \n",
    "    h = alpha*h + eta*get_grads(X[ind, :], w-alpha*h, y[ind])  #Only change is here\n",
    "    \n",
    "    w = w-h\n",
    "    \n",
    "    if(i%10==0):\n",
    "        plt.plot(loss[:i])\n",
    "        plt.grid()\n",
    "        ymin, ymax = plt.ylim()\n",
    "        plt.ylim(0, ymax)\n",
    "        plt.xlabel('Iterations')\n",
    "        plt.ylabel('Loss')\n",
    "        display.clear_output(wait=True)\n",
    "        plt.show()\n",
    "        \n",
    "        \n",
    "    if(loss[i]<es):\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mini-batch SGD Converged in :  68\n",
      "FInal Weights [ 2.97210585 10.00265989 -1.99139759 -2.97989916]\n",
      "MSE Loss =  0.00010935911636362774\n"
     ]
    }
   ],
   "source": [
    "print(\"mini-batch SGD Converged in : \",i)\n",
    "print(\"FInal Weights\",w)\n",
    "print('MSE Loss = ',mse_loss(X,w,y) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Faster Convergence and better results than previous methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### RMSProp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "w = np.array([0,0,0,0]) #Initial Weights\n",
    "\n",
    "eta = 0.05 # learning rate\n",
    "alpha = 0.9 # momentum\n",
    "gt = None\n",
    "eps = 1e-8\n",
    "es = 0.0001 #For early stopping \n",
    "\n",
    "\n",
    "n_iter = 1000\n",
    "batch_size = 128\n",
    "loss = np.zeros(n_iter)\n",
    "\n",
    "for i in range(n_iter):\n",
    "    ind = np.random.choice(X.shape[0], batch_size)\n",
    "    loss[i] = mse_loss(X[ind, :], w, y[ind])\n",
    "    \n",
    "    gt = get_grads(X[ind, :], w, y[ind])**2\n",
    "    gt = alpha*gt +(1-alpha)*gt\n",
    "    \n",
    "    w = w-(eta*get_grads(X[ind, :], w, y[ind]))/np.sqrt(gt+eps)\n",
    "    \n",
    "    if(i%10==0):\n",
    "        plt.plot(loss[:i])\n",
    "        plt.grid()\n",
    "        ymin, ymax = plt.ylim()\n",
    "        plt.ylim(0, ymax)\n",
    "        plt.xlabel('Iterations')\n",
    "        plt.ylabel('Loss')\n",
    "        display.clear_output(wait=True)\n",
    "        plt.show()\n",
    "        \n",
    "    if(loss[i]<es):\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mini-batch SGD Converged in :  1000\n",
      "FInal Weights [ 3.10050876  9.80013145 -2.00028514 -2.99902859]\n",
      "MSE Loss =  0.006143874058183476\n"
     ]
    }
   ],
   "source": [
    "print(\"mini-batch SGD Converged in : \",i+1)\n",
    "print(\"FInal Weights\",w)\n",
    "print('MSE Loss = ',mse_loss(X,w,y) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Adam"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "w = np.array([0,0,0,0]) #Initial Weights\n",
    "\n",
    "eta = 0.05 # learning rate\n",
    "alpha = 0.9 # momentum\n",
    "gt = None\n",
    "vt = 0\n",
    "beta = 0.0005\n",
    "\n",
    "eps = 1e-8\n",
    "es = 0.0001 #For early stopping \n",
    "\n",
    "\n",
    "n_iter = 1000\n",
    "batch_size = 128\n",
    "loss = np.zeros(n_iter)\n",
    "\n",
    "for i in range(n_iter):\n",
    "    ind = np.random.choice(X.shape[0], batch_size)\n",
    "    loss[i] = mse_loss(X[ind, :], w, y[ind])\n",
    "    \n",
    "    gt = get_grads(X[ind, :], w, y[ind])**2\n",
    "    \n",
    "    vt = (beta*vt) + (1-beta)*gt \n",
    "    \n",
    "    w = w-(eta*get_grads(X[ind, :], w, y[ind]))/np.sqrt(vt)+eps\n",
    "    \n",
    "    if(i%10==0):\n",
    "        plt.plot(loss[:i])\n",
    "        plt.grid()\n",
    "        ymin, ymax = plt.ylim()\n",
    "        plt.ylim(0, ymax)\n",
    "        plt.xlabel('Iterations')\n",
    "        plt.ylabel('Loss')\n",
    "        display.clear_output(wait=True)\n",
    "        plt.show()\n",
    "        \n",
    "    if(loss[i]<es):\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mini-batch SGD Converged in :  1000\n",
      "FInal Weights [ 3.0615056   9.91395114 -1.97206378 -2.90447283]\n",
      "MSE Loss =  0.004484283193169871\n"
     ]
    }
   ],
   "source": [
    "print(\"mini-batch SGD Converged in : \",i+1)\n",
    "print(\"FInal Weights\",w)\n",
    "print('MSE Loss = ',mse_loss(X,w,y) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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