Cocalc 05 Test Ipynb

This notebook is part of Bite Size Bayes, an introduction to probability and Bayesian statistics using Python. License: Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) The following cell downloads utils.py, which contains some utility function we'll need. If everything we need is installed, the following cell should run with no error messages. In the previous notebook I presented Theorem 4, which is a way to compute the probability of a disjunction (or operation) using the probability of a conjunction (and operation). 193.75 is the relaxed solution, but we can't rent 193.75 apartments.

Let's check 193 and 194 to see which yields a larger profit. Bottom line: rent 194 apartments for profit $220,312. There appear to be local maxima around x=−3x=-3x=−3 and x=1x=1x=1 while there appear to be local minima around x=−0.5x=-0.5x=−0.5 and x=3.5x = 3.5x=3.5. Note - there is a strange quirk here in the scipy.optimize.minimize. When we optimize without bounds result.fun is a number, but when we optimize with bounds result.fun is a list with one number so we have to refer to result.fun[0] to get the number. How many iterations does it take to reliably find the global minimum with dim = 3?

With dim = 4? Use the multi-start strategy. We have seen how a time series can have a unit root that creates a stochastic trend and makes the time series highly persistent. When we use such an integrated time series in their original, rather than in differenced, form as a feature in a linear regression model, its relationship with the outcome will often appear statistically significant,... This phenomenon is called spurious regression (for details, see Chapter 18 in Wooldridge, 2008). Therefore, the recommended solution is to difference the time series so they become stationary before using them in a model.

However, there is an exception when there are cointegration relationships between the outcome and one or more input variables. To understand the concept of cointegration, let's first remember that the residuals of a regression model are a linear combination of the inputs and the output series. Usually, the residuals of the regression of one integrated time series on one or more such series yields non-stationary residuals that are also integrated, and thus behave like a random walk. However, for some time series, this is not the case: the regression produces coefficients that yield a linear combination of the time series in the form of the residuals that are stationary, even though... Such time series are cointegrated. A non-technical example is that of a drunken man on a random walk accompanied by his dog (on a leash).

Both trajectories are non-stationary but cointegrated because the dog will occasionally revert to his owner. In the trading context, arbitrage constraints imply cointegration between spot and futures prices. In other words, a linear combination of two or more cointegrated series has a stable mean to which this linear combination reverts. This also applies when the individual series are integrated of a higher order and the linear combination reduces the overall order of integration. After completing this lab you will be able to: An important step in testing your model is to split your data into training and testing data.

We will place the target data price in a separate dataframe y_data: Now, we randomly split our data into training and testing data using the function train_test_split. x_data: features or independent variables x_train, y_train: parts of available data as training set if statement inside a if statement or if-elif or if-else are called as nested if statements. In the above example, i iterates over the 0,1,2,3,4.

Every time it takes each value and executes the algorithm inside the loop. It is also possible to iterate over a nested list illustrated below. A use case of a nested for loop in this case would be, As the name says. It is used to break out of a loop when a condition becomes true when executing the loop. This continues the rest of the loop.

Sometimes when a condition is satisfied there are chances of the loop getting terminated. This can be avoided using continue statement. 📚 The CoCalc Library - books, templates and other resources This notebook contains an excerpt from the Python Data Science Handbook by Jake VanderPlas; the content is available on GitHub. The text is released under the CC-BY-NC-ND license, and code is released under the MIT license. If you find this content useful, please consider supporting the work by buying the book!

< Feature Engineering | Contents | In Depth: Linear Regression > The previous four sections have given a general overview of the concepts of machine learning. In this section and the ones that follow, we will be taking a closer look at several specific algorithms for supervised and unsupervised learning, starting here with naive Bayes classification. The techniques in the last chapter are very powerful, but they only work with one variable or dimension. Gaussians represent a mean and variance that are scalars - real numbers. They provide no way to represent multidimensional data, such as the position of a dog in a field.

You may retort that you could use two Kalman filters from the last chapter. One would track the x coordinate and the other the y coordinate. That does work, but suppose we want to track position, velocity, acceleration, and attitude. These values are related to each other, and as we learned in the g-h chapter we should never throw away information. Through one key insight we will achieve markedly better filter performance than was possible with the equations from the last chapter. In this chapter I will introduce you to multivariate Gaussians - Gaussians for more than one variable, and the key insight I mention above.

Then, in the next chapter we will use the math from this chapter to write a complete filter in just a few lines of code. In the last two chapters we used Gaussians for a scalar (one dimensional) variable, expressed as N(μ,σ2)\mathcal{N}(\mu, \sigma^2)N(μ,σ2). A more formal term for this is univariate normal, where univariate means 'one variable'. The probability distribution of the Gaussian is known as the univariate normal distribution What might a multivariate normal distribution be? Multivariate means multiple variables.

Our goal is to be able to represent a normal distribution across multiple dimensions. I don't necessarily mean spatial dimensions - it could be position, velocity, and acceleration. Consider a two dimensional case. Let's say we believe that x=2x = 2x=2 and y=17y = 17y=17. This might be the x and y coordinates for the position of our dog, it might be the position and velocity of our dog on the x-axis, or the temperature and wind speed at... It doesn't really matter.

We can see that for NNN dimensions, we need NNN means, which we will arrange in a column matrix (vector) like so: Therefore for this example we would have

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