AI News, Machine Learning for Intraday Stock Price Prediction 1: Linear Models

Machine Learning for Intraday Stock Price Prediction 1: Linear Models

This is the first of a series of posts on the task of applying machine learning for intraday stock price/return prediction.

Let’s look at the individual points in the above graph - there are more than 200,000 datapoints there, but we will just look at the first few to understand what it is that we want to predict.

Please note that it’s typically better to predict returns rather than price difference because models/techniques designed to predict returns can scale across various securities relatively better.

$0.13 price difference for a $154 stock is not much compared to $0.13 price difference for a $20 stock - $0.13 has a different meaning for a $20 stock.

In this post though, we will only use the features derived from the market data to predict the next 1 min price change.

(We will explore news/text data effects in a separate post in future.) The feature set can be broadly classified into two categories: Features describing current market snapshot and Features describing recent history

However, please note that these features try to capture the current market conditions as well as the recent past.

While the price of AAPL could range from 153 to 155 in a day, the volume over last 5 min could range from 100 to 1000000.

However, the model outputing 0 is of absolutely no value - we want opinionated models that can be useful for trading or execution.

Therefore, comparing the standard deviation of the predicted value h(x) with the standard deviation of y is necessary.

Adding a weight penalty to the error term is a simple way to regularize the model - this helps stabilize the training and the model is often better at generalization.

The following results were obtained using a 2-layer feed forward neural network with hidden_size1=100 and hidden_size2=50.

Build, Develop and Deploy a Machine Learning Model to predict cars price using Gradient Boosting.

Now we came to the main task in all this process, which is Data Modeling, for this purpose I will use 4 Machine Learning models dedicated for Regression problems, at the end I will do a Benchmarking table to compare each model r2_score and select the best one.

In literature there are two famous ways of categorical variable transformations, the first one is label encoding, and the second one is the one hot encoding, for this use case we will use the one hot position and the reason why I choose this kind of data labeling is because I will not need any kind of data normalization later, and also this has the benefit of not weighting a value improperly but does have the downside of adding more columns to the data set.

So boosting is an ensemble technique in which learners are learned sequentially with early learners fitting simple models to the data and then analyzing the data for errors, those errors identify problems or particular instances of the data that are difficult or hard to fit, as a consequence later models focus primarily on those examples trying to get them right.

At the end, all the models contribute with weights and the set is combined into some overall predictors, so boosting is a method of converting a sequence of weak learners into a very complex predictor, it’s a way of increasing the complexity of a particular model initial learners tend to be very simple and then the weighted combination can grow more and more complex as learners are added.

A simple deep learning model for stock price prediction using TensorFlow

For a recent hackathon that we did at STATWORX, some of our team members scraped minutely S&P 500 data from the Google Finance API.

Having this data at hand, the idea of developing a deep learning model for predicting the S&P 500 index based on the 500 constituents prices one minute ago came immediately on my mind.

Playing around with the data and building the deep learning model with TensorFlow was fun and so I decided to write my first story: a little TensorFlow tutorial on predicting S&P 500 stock prices.

The dataset contains n = 41266 minutes of data ranging from April to August 2017 on 500 stocks as well as the total S&P 500 index price.

The data was already cleaned and prepared, meaning missing stock and index prices were LOCF’ed (last observation carried forward), so that the file did not contain any missing values.

There are a lot of different approaches to time series cross validation, such as rolling forecasts with and without refitting or more elaborate concepts such as time series bootstrap resampling.

The latter involves repeated samples from the remainder of the seasonal decomposition of the time series in order to simulate samples that follow the same seasonal pattern as the original time series but are not exact copies of its values.

Because most common activation functions of the network’s neurons such as tanh or sigmoid are defined on the [-1, 1] or [0, 1] interval respectively.

Nowadays, rectified linear unit (ReLU) activations are commonly used activations which are unbounded on the axis of possible activation values.

Since neural networks are actually graphs of data and mathematical operations, TensorFlow is just perfect for neural networks and deep learning.

Check out this simple example (stolen from our deep learning introduction from our blog): In the figure above, two numbers are supposed to be added.

The following code implements the toy example from above in TensorFlow: After having imported the TensorFlow library, two placeholders are defined using tf.placeholder().

We need two placeholders in order to fit our model: X contains the network's inputs (the stock prices of all S&P 500 constituents at time T = t) and Y the network's outputs (the index value of the S&P 500 at time T = t + 1).

The None argument indicates that at this point we do not yet know the number of observations that flow through the neural net graph in each batch, so we keep if flexible.

While placeholders are used to store input and target data in the graph, variables are used as flexible containers within the graph that are allowed to change during graph execution.

As a rule of thumb in multilayer perceptrons (MLPs, the type of networks used here), the second dimension of the previous layer is the first dimension in the current layer for weight matrices.

The biases dimension equals the second dimension of the current layer’s weight matrix, which corresponds the number of neurons in this layer.

The cost function of the network is used to generate a measure of deviation between the network’s predictions and the actual observed training targets.

The optimizer takes care of the necessary computations that are used to adapt the network’s weight and bias variables during training.

Those computations invoke the calculation of so called gradients, that indicate the direction in which the weights and biases have to be changed during training in order to minimize the network’s cost function.

Since neural networks are trained using numerical optimization techniques, the starting point of the optimization problem is one the key factors to find good solutions to the underlying problem.

During minibatch training random data samples of n = batch_size are drawn from the training data and fed into the network.

The training of the network stops once the maximum number of epochs is reached or another stopping criterion defined by the user applies.

During the training, we evaluate the networks predictions on the test set — the data which is not learned, but set aside — for every 5th batch and visualize it.

The model quickly learns the shape and location of the time series in the test data and is able to produce an accurate prediction after some epochs.

Please note that there are tons of ways of further improving this result: design of layers and neurons, choosing different initialization and activation schemes, introduction of dropout layers of neurons, early stopping and so on.

Machine Learning Fundamentals: Predicting Airbnb Prices

But understanding machine learning can be difficult — you either use pre-built packages that act like 'black boxes' where you pass in data and magic comes out the other end, or you have to deal with high level maths and linear algebra.

This tutorial is designed to introduce you to the fundamental concepts of machine learning — you'll build your very first model from scratch to make predictions, while understanding exactly how your model works.

An important distinction is that a machine learning model is not a rules-based system, where a series of 'if/then' statements are used to make predictions (eg 'If a students misses more than 50% of classes then automatically fail them').

Similar Houses can help you decide on the price to sell your house for Once you have found a number of similar houses, you could then look at the price that they sold for, and take an average of that for your house listing.

In this example, the 'model' you built was trained on data from other houses in your area — or past observations — and then used to make a recommendation for the price of your house, which is new data the model has not previously seen.

This post presumes you are familiar with Python's pandas library — if you need to brush up on pandas, we recommend our two-part pandas tutorial blog posts or our interactive Python and Pandas course.

The company itself has grown rapidly from its founding in 2008 to a 30 billion dollar valuation in 2016 and is currently worth more than any hotel chain in the world.

The K-nearest neighbors (knn) algorithm is very similar to the three step process we outlined earlier to compare our listing to similar listings and take the average price.

For the purposes of this tutorial we're going to use a fixed k value of 5, but once you become familiar with the workflow around the algorithm you can experiment with this value to see if you get better results with lower or higher k values.

Here's the general formula for Euclidean distance: \(d = \sqrt{(q_1-p_1)^2 + (q_2-p_2)^2 + \cdots + (q_n-p_n)^2}\) where \( q_1 \) to \( q_n \) represent the feature values for one observation and \( p_1 \) to \( p_n \) represent the feature values for the other observation.

\(d = \sqrt{(q_1 - p_1)^2} \) The square root and the squared power cancel and the formula simplifies to: \(d = |

This method is usually used to select a random fraction of the dataframe, but we'll tell it to randomly select 100%, which will randomly shuffle the rows for us.

Before we can take the average of our prices, you'll notice that our price column has the object type, due to the fact that the prices have dollar signs and commas (our sample above doesn't show the commas because all the values are less than $1000).

We've now made our first prediction --- our simple knn model told us that when we're using just the accommodates feature to make predictions of our listing that accommodates three people, we should list our apartment for $88.00.

Here's the formula for RMSE: \( RMSE = \sqrt {\dfrac{ (actual_1-predicted_1)^2 + (actual_2-predicted_2)^2 + \cdots + (actual_n-predicted_n)^2 }{ n }}\) where n represents the number of rows in the test set.

You can see that the best model of the four that we trained is the one using the accomodates column, however the error rates we're getting are quite high relative to the range of prices of the listing in our data set.

Let's remind ourselves what the original Euclidean distance equation looked like again: \(d = \sqrt{(q_1-p_1)^2 + (q_2-p_2)^2 + \cdots + (q_n-p_n)^2}\) We're going to start by building a model that uses the accommodates and bathrooms attributes.

For this case, our Euclidean equation would look like: \(d = \sqrt{(accommodates_1-accommodates_2)^2 + (bathrooms_1-bathrooms_2)^2 }\) To find the distance between two living spaces, we need to calculate the squared difference between both accommodates values, the squared difference between both bathrooms values, add them together, and then take the square root of the resulting sum.

The scikit-learn workflow consists of four main steps: Each model in scikit-learn is implemented as a separate class and the first step is to identify the class we want to create an instance of.

If you refer to the documentation, you'll notice that by default: Let's set the algorithm parameter to brute and leave the n_neighbors value as 5, which matches the manual implementation we built.

If you recall from earlier, all of the following are acceptable list-like objects: You can select the target column from the Dataframe and use that as the second parameter to the fit method: When the fit() method is called, scikit-learn stores the training data we specified within the KNearestNeighbors instance (knn).

The predict method has only one required parameter: The number of feature columns you use during both training and testing need to match or scikit-learn will return an error: The predict() method returns a NumPy array containing the predicted price values for the test set.

Once you become familiar with the different machine learning concepts, unifying your workflow using scikit-learn helps save you a lot of time and helps you avoid mistakes.

You'll notice that our RMSE is a little different from our manually implemented algorithm --- this is likely due to both differences in the randomization and slight differences in implementation between our 'manual' KNN algorithm and the scikit-learn version.

This is an important thing to be aware of - more features does not necessarily make an accurate model, since adding a feature that is not an accurate predictor of your target variable adds 'noise' to your model.

Using Machine Learning to Predict Value of Homes On Airbnb

For example, personalized search ranking enables guests to more easily discover homes, and smart pricing allows hosts to set more competitive prices according to supply and demand.

In this post, I will describe how these tools worked together to expedite the modeling process and hence lower the overall development costs for a specific use case of LTV modeling — predicting the value of homes on Airbnb.

At marketplace companies like Airbnb, knowing users’ LTVs enable us to allocate budget across different marketing channels more efficiently, calculate more precise bidding prices for online marketing based on keywords, and create better listing segments.

While one can use past data to calculate the historical value of existing listings, we took one step further to predict LTV of new listings using machine learning.

The remainder of this post is organized into four topics, along with the tools we used to tackle each task: One of the first steps of any supervised machine learning project is to define relevant features that are correlated with the chosen outcome variable, a process called feature engineering.

However, this work is tedious and time consuming as it requires specific domain knowledge and business logic, which means the feature pipelines are often not easily sharable or even reusable.

The crowdsourced nature of this internal tool allows data scientists to use a wide variety of high quality, vetted features that others have prepared for past projects.

If a desired feature is not available, a user can create her own feature with a feature configuration file like the following: When multiple features are required for the construction of a training set, Zipline will automatically perform intelligent key joins and backfill the training dataset behind the scenes.

As in the example training dataset above, we often need to perform additional data processing before we can fit a model: In this step, we don’t quite know what is the best set of features to use, so writing code that allows us to rapidly iterate is essential.

To make it more concrete, below is a code snippet from our LTV model pipeline: At a high level, we use pipelines to specify data transformations for different types of features, depending on whether those features are of type binary, categorical, or numeric.

Collectively, these transforms ensure that data will be transformed consistently across training and scoring, which solves a common problem of data transformation inconsistency when translating a prototype into production.

For example, we learned that eXtreme gradient boosted trees (XGBoost) significantly outperformed benchmark models such as mean response models, ridge regression models, and single decision trees.

As a result, this framework significantly lowers the cost of model development for data scientists, as if there was a dedicated data engineer working alongside the data scientists to take the model into production!

Boston Home Prices Prediction and Evaluation

It is difficult to measure the quality of a given model without quantifying its performance over training and testing.

This is typically done using some type of performance metric, whether it is through calculating some type of error, the goodness of fit, or some other useful measurement.

The values for R2 range from 0 to 1, which captures the percentage of squared correlation between the predicted and actual values of the target variable.

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