From df99654ef1bd9416cfe6bc2a4da7049fe80ccb69 Mon Sep 17 00:00:00 2001 From: Dmitri Soshnikov Date: Tue, 17 Aug 2021 00:25:12 +0300 Subject: [PATCH] More work on intro to statistics --- .../04-stats-and-probability/README.md | 10 +- .../04-stats-and-probability/notebook.ipynb | 250 ++++++++++++++++++ 2 files changed, 259 insertions(+), 1 deletion(-) diff --git a/1-Introduction/04-stats-and-probability/README.md b/1-Introduction/04-stats-and-probability/README.md index 4ea65986..9f673ecc 100644 --- a/1-Introduction/04-stats-and-probability/README.md +++ b/1-Introduction/04-stats-and-probability/README.md @@ -34,7 +34,7 @@ Another important distribution is **normal distribution**, which we will talk ab ## Mean, Variance and Standard Deviation -Suppose we draw a sequence of n samples of a random variable X: x1, x2, ..., xn. We can define **mean** (or **arithmetic average**) value of the sequence in the traditional way as (x1+x2+xn)/n. As we grow the size of the sample (i.e. take the limit with n→∞), we will obtain the mean (also called **expectation**) of the distribution. +Suppose we draw a sequence of n samples of a random variable X: x1, x2, ..., xn. We can define **mean** (or **arithmetic average**) value of the sequence in the traditional way as (x1+x2+xn)/n. As we grow the size of the sample (i.e. take the limit with n→∞), we will obtain the mean (also called **expectation**) of the distribution. We will denote expectation by **E**(x). > It can be demonstrated that for any discrete distribution with values {x1, x2, ..., xN} and corresponding probabilities p1, p2, ..., pN, the expectation would equal to E(X)=x1p1+x2p2+...+xNpN. @@ -80,7 +80,15 @@ One of the reasons why normal distribution is so important is so-called **centra From central limit theorem it also follows that, when N→∞, the probability of the sample mean to be equal to μ becomes 1. This is known as **the law of large numbers**. +## Covariance and Correlation +One of the things Data Science does is finding relations between data. We say that two sequences **correlate** when they exhibit the similar behavior at the same time, i.e. they either rise/fall simultaneously, or one sequence rises when another one falls and vice versa. In other words, there seems to be some relation between two sequences. + +> Correlation does not necessarily indicate causal relationship between two sequences; sometimes both variables can depend on some external cause, or it can be purely by chance the two sequences correlate. However, strong mathematical correlation is a good indication that two variables are somehow connected. + + Mathematically, the main concept that show the relation between two random variables is **covariance**, that is computed like this: Cov(X,Y) = **E**\[(X-**E**(X))(Y-**E**(Y))\]. We compute the deviation of both variables from their mean values, and then product of those deviations. If both variables deviate together, the product would always be a positive value, that would add up to positive covariance. If both variables deviate out-of-sync (i.e. one falls below average when another one rises above average), we will always get negative numbers, that will add up to negative covariance. If the deviations are not dependent, they will add up to roughly zero. + +The absolute value of covariance does not tell us much on how large the correlation is, because it depends on the magnitude of actual values. To normalize it, we can divide covariance by standard deviation of both variables, to get **correlation**. The good thing is that correlation is always in the range of [-1,1], where 1 indicates strong positive correlation between values, -1 - strong negative correlation, and 0 - no correlation at all (variables are independent). ## 🚀 Challenge diff --git a/1-Introduction/04-stats-and-probability/notebook.ipynb b/1-Introduction/04-stats-and-probability/notebook.ipynb index ad4cd849..7a3580ae 100644 --- a/1-Introduction/04-stats-and-probability/notebook.ipynb +++ b/1-Introduction/04-stats-and-probability/notebook.ipynb @@ -504,6 +504,256 @@ ], "metadata": {} }, + { + "cell_type": "markdown", + "source": [ + "## Correlation and Evil Baseball Corp\r\n", + "\r\n", + "Correlation allows us to find inner connection between data sequences. In our toy example, let's pretend there is an evil baseball corporation that pays it's players according to their height - the taller the player is, the more money he/she gets. Suppose there is a base salary of $1000, and an additional bonus from $0 to $100, depending on height. We will take the real players from MLB, and compute their imaginary salaries:" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 99, + "source": [ + "heights = df['Height']\r\n", + "salaries = 1000+(heights-heights.min())/(heights.max()-heights.mean())*100\r\n", + "print(list(zip(heights,salaries))[:10])" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "[(74, 1075.2469071629068), (74, 1075.2469071629068), (72, 1053.7477908306478), (72, 1053.7477908306478), (73, 1064.4973489967772), (69, 1021.4991163322591), (69, 1021.4991163322591), (71, 1042.9982326645181), (76, 1096.746023495166), (71, 1042.9982326645181)]\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Let's now compute covariance and correlation of those sequences. `np.cov` will give us so-called **covariance matrix**, which is an extension of covariance to multiple variables. The element $M_{ij}$ of the covariance matrix $M$ is a correlation between input variables $X_i$ and $X_j$, and diagonal values $M_{ii}$ is the variance of $X_{i}$. Similarly, `np.corrcoef` will give us **correlation matrix**." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 100, + "source": [ + "print(f\"Covariance matrix:\\n{np.cov(heights,salaries)}\")\r\n", + "print(f\"Covariance = {np.cov(heights,salaries)[0,1]}\")\r\n", + "print(f\"Correlation = {np.corrcoef(heights,salaries)[0,1]}\")" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Covariance matrix:\n", + "[[ 5.31679808 57.15323023]\n", + " [ 57.15323023 614.37197275]]\n", + "Covariance = 57.15323023054467\n", + "Correlation = 1.0\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Correlation equal to 1 means that there is a strong **linear relation** between two variables. We can visually see the linear relation by plotting one value against the other:" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 101, + "source": [ + "plt.scatter(heights,salaries)\r\n", + "plt.show()" + ], + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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+ }, + "metadata": {} + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Let's see what happens if the relation is not linear. Suppose that our corporation decided to hide the obvious linear dependency between heights and salaries, and introduced some non-linearity into the formula, such as `sin`:" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 91, + "source": [ + "salaries = 1000+np.sin((heights-heights.min())/(heights.max()-heights.mean()))*100\r\n", + "print(f\"Correlation = {np.corrcoef(heights,salaries)[0,1]}\")" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Correlation = 0.9835304456670811\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "In this case, the correlation is slightly smaller, but it is still quite high. Now, to make the relation even less obvious, we might want to add some extra randomness by adding some random variable to the salary. Let's see what happens:" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 102, + "source": [ + "salaries = 1000+np.sin((heights-heights.min())/(heights.max()-heights.mean()))*100+np.random.random(size=len(heights))*20-10\r\n", + "print(f\"Correlation = {np.corrcoef(heights,salaries)[0,1]}\")" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Correlation = 0.9384710733057905\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 104, + "source": [ + "plt.scatter(heights, salaries)\r\n", + "plt.show()" + ], + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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" + }, + "metadata": {} + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "> Can you guess why the dots line up into vertical lines like this?\r\n", + "\r\n", + "We have observed the correlation between artificially engineered concept like salary and the observed variable *height*. Let's also see if the two observed variables, such as height and weight, also correlate:" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 111, + "source": [ + "np.corrcoef(df['Height'],df['Weight'])" + ], + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[ 1., nan],\n", + " [nan, nan]])" + ] + }, + "metadata": {}, + "execution_count": 111 + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Unfortunately, we did not get any results - only some strange `nan` values. This is due to the fact that some of the values in our series are undefined, represented as `nan`, which causes the result of the operation to be undefined as well. By looking at the matrix we can see that `Weight` is problematic column, because self-correlation between `Height` values has been computed.\r\n", + "\r\n", + "> This example shows the importance of **data preparation** and **cleaning**. Without proper data we cannot compute anything.\r\n", + "\r\n", + "Let's use `fillna` method to fill the missing values, and compute the correlation: " + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 114, + "source": [ + "np.corrcoef(df['Height'],df['Weight'].fillna(method='pad'))" + ], + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([[1. , 0.52959196],\n", + " [0.52959196, 1. ]])" + ] + }, + "metadata": {}, + "execution_count": 114 + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "The is indeed a correlation, but not such a strong one as in our artificial example. Indeed, if we look at the scatter plot of one value against the other, the relation would be much less obvious:" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 115, + "source": [ + "plt.scatter(df['Height'],df['Weight'])\r\n", + "plt.show()" + ], + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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" 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