# Machine Learning

## PyTorch

### Get Historical Data

Get some historical market data to train and test the model. For example, to get data for the SPY ETF during 2020 and 2021, run:

qb = QuantBook() symbol = qb.AddEquity("SPY", Resolution.Daily).Symbol history = qb.History(symbol, datetime(2020, 1, 1), datetime(2022, 1, 1)).loc[symbol]

### Prepare Data

You need some historical data to prepare the data for the model. If you have historical data, manipulate it to train and test the model. In this example, use the following features and labels:

Data Category | Description |
---|---|

Features | The last 5 closing prices |

Labels | The following day's closing price |

The following image shows the time difference between the features and labels:

Follow these steps to prepare the data:

- Perform fractional differencing on the historical data.
- Loop through the
`df`

DataFrame and collect the features and labels. - Convert the lists of features and labels into
`numpy`

arrays. - Standardize the features and labels
- Split the data into training and testing periods.

df = (history['close'] * 0.5 + history['close'].diff() * 0.5)[1:]

Fractional differencing helps make the data stationary yet retains the variance information.

n_steps = 5 features = [] labels = [] for i in range(len(df)-n_steps): features.append(df.iloc[i:i+n_steps].values) labels.append(df.iloc[i+n_steps])

features = np.array(features) labels = np.array(labels)

X = (features - features.mean()) / features.std() y = (labels - labels.mean()) / labels.std()

X_train, X_test, y_train, y_test = train_test_split(X, y)

### Train Models

You need to prepare the historical data for training before you train the model. If you have prepared the data, build and train the model. In this example, create a deep neural network with 2 hidden layers. Follow these steps to create the model:

- Define a subclass of
`nn.Module`

to be the model. - Create an instance of the model and set its configuration to train on the GPU if it's available.
- Set the loss and optimization functions.
- Train the model.

In this example, use the ReLU activation function for each layer.

class NeuralNetwork(nn.Module): # Model Structure def __init__(self): super(NeuralNetwork, self).__init__() self.flatten = nn.Flatten() self.linear_relu_stack = nn.Sequential( nn.Linear(5, 5), # input size, output size of the layer nn.ReLU(), # Relu non-linear transformation nn.Linear(5, 5), nn.ReLU(), nn.Linear(5, 1), # Output size = 1 for regression ) # Feed-forward training/prediction def forward(self, x): x = torch.from_numpy(x).float() # Convert to tensor in type float result = self.linear_relu_stack(x) return result

device = 'cuda' if torch.cuda.is_available() else 'cpu' model = NeuralNetwork().to(device)

In this example, use the mean squared error as the loss function and stochastic gradient descent as the optimizer.

loss_fn = nn.MSELoss() learning_rate = 0.001 optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)

In this example, train the model through 5 epochs.

epochs = 5 for t in range(epochs): print(f"Epoch {t+1}\n-------------------------------") # Since we're using SGD, we'll be using the size of data as batch number. for batch, (X, y) in enumerate(zip(X_train, y_train)): # Compute prediction and loss pred = model(X) real = torch.from_numpy(np.array(y).flatten()).float() loss = loss_fn(pred, real) # Backpropagation optimizer.zero_grad() loss.backward() optimizer.step() if batch % 100 == 0: loss, current = loss.item(), batch print(f"loss: {loss:.5f} [{current:5d}/{len(X_train):5d}]")

### Test Models

You need to build and train the model before you test its performance. If you have trained the model, test it on the out-of-sample data. Follow these steps to test the model:

- Predict with the testing data.
- Plot the actual and predicted values of the testing period.
- Calculate the R-square value.

predict = model(X_test) y_predict = predict.detach().numpy() # Convert tensor to numpy ndarray

df = pd.DataFrame({'Real': y_test.flatten(), 'Predicted': y_predict.flatten()}) df.plot(title='Model Performance: predicted vs actual standardized fractional return', figsize=(15, 10)) plt.show()

r2 = 1 - np.sum(np.square(y_test.flatten() - y_predict.flatten())) / np.sum(np.square(y_test.flatten() - y_test.mean())) print(f"The explained variance by the model (r-square): {r2*100:.2f}%")

### Store Models

You can save and load `PyTorch`

models using the ObjectStore.

#### Save Models

Don't use the `torch.save`

method to save models because the tensor data will be lost and corrupt the save. Follow these steps to save models in the ObjectStore:

- Set the key name of the model to be stored in the ObjectStore.
- Call the
`GetFilePath`

method with the key. - Call the
`dump`

method with the model and file path. - Call the
`Save`

method with the key.

model_key = "model"

file_name = qb.ObjectStore.GetFilePath(model_key)

This method returns the file path where the model will be stored.

joblib.dump(model, file_name)

If you dump the model using the `joblib`

module before you save the model, you don't need to retrain the model.

qb.ObjectStore.Save(model_key)

#### Load Models

You must save a model into the ObjectStore before you can load it from the ObjectStore. If you saved a model, follow these steps to load it:

- Call the
`ContainsKey`

method. - Call the
`GetFilePath`

method with the key. - Call the
`load`

method with the file path.

qb.ObjectStore.ContainsKey(model_key)

This method returns a boolean that represents if the `model_key`

is in the ObjectStore. If the ObjectStore does not contain the `model_key`

, save the model using the `model_key`

before you proceed.

file_name = qb.ObjectStore.GetFilePath(model_key)

This method returns the path where the model is stored.

loaded_model = joblib.load(file_name)

This method returns the saved model.