> ## Documentation Index > Fetch the complete documentation index at: https://nixtlaverse.nixtla.io/llms.txt > Use this file to discover all available pages before exploring further. # Temporal Classification A logistic regression analyzes the relationship between a binary target variable and its predictor variables to estimate the probability of the dependent variable taking the value 1. In the presence of temporal data where observations along time aren’t independent, the errors of the model will be correlated through time and incorporating autoregressive features or lags can capture temporal dependencies and enhance the predictive power of logistic regression.
NHITS’s inputs are static exogenous $\mathbf{x}^{(s)}$, historic exogenous $\mathbf{x}^{(h)}_{[:t]}$, exogenous available at the time of the prediction $\mathbf{x}^{(f)}_{[:t+H]}$ and autoregressive features $\mathbf{y}_{[:t]}$, each of these inputs is further decomposed into categorical and continuous. The network uses a multi-quantile regression to model the following conditional probability:$\mathbb{P}(\mathbf{y}_{[t+1:t+H]}|\;\mathbf{y}_{[:t]},\; \mathbf{x}^{(h)}_{[:t]},\; \mathbf{x}^{(f)}_{[:t+H]},\; \mathbf{x}^{(s)})$ In this notebook we show how to fit NeuralForecast methods for binary sequences regression. We will: - Installing NeuralForecast. - Loading binary sequence data. - Fit and predict temporal classifiers. - Plot and evaluate predictions. You can run these experiments using GPU with Google Colab. Open In Colab ## 1. Installing NeuralForecast ```python theme={null} %%capture !pip install neuralforecast ``` ```python theme={null} import numpy as np import pandas as pd from sklearn import datasets import matplotlib.pyplot as plt from neuralforecast import NeuralForecast from neuralforecast.models import MLP, NHITS, LSTM from neuralforecast.losses.pytorch import DistributionLoss, Accuracy ``` ## 2. Loading Binary Sequence Data The `core.NeuralForecast` class contains shared, `fit`, `predict` and other methods that take as inputs pandas DataFrames with columns `['unique_id', 'ds', 'y']`, where `unique_id` identifies individual time series from the dataset, `ds` is the date, and `y` is the target binary variable. In this motivation example we convert 8x8 digits images into 64-length sequences and define a classification problem, to identify when the pixels surpass certain threshold. We declare a pandas dataframe in long format, to match NeuralForecast’s inputs. ```python theme={null} digits = datasets.load_digits() images = digits.images[:100] plt.imshow(images[0,:,:], cmap=plt.cm.gray, vmax=16, interpolation="nearest") pixels = np.reshape(images, (len(images), 64)) ytarget = (pixels > 10) * 1 fig, ax1 = plt.subplots() ax2 = ax1.twinx() ax1.plot(pixels[10]) ax2.plot(ytarget[10], color='purple') ax1.set_xlabel('Pixel index') ax1.set_ylabel('Pixel value') ax2.set_ylabel('Pixel threshold', color='purple') plt.grid() plt.show() ``` ```python theme={null} # We flat the images and create an input dataframe # with 'unique_id' series identifier and 'ds' time stamp identifier. Y_df = pd.DataFrame.from_dict({ 'unique_id': np.repeat(np.arange(100), 64), 'ds': np.tile(np.arange(64)+1910, 100), 'y': ytarget.flatten(), 'pixels': pixels.flatten()}) Y_df ``` | | unique\_id | ds | y | pixels | | ---- | ---------- | ---- | --- | ------ | | 0 | 0 | 1910 | 0 | 0.0 | | 1 | 0 | 1911 | 0 | 0.0 | | 2 | 0 | 1912 | 0 | 5.0 | | 3 | 0 | 1913 | 1 | 13.0 | | 4 | 0 | 1914 | 0 | 9.0 | | ... | ... | ... | ... | ... | | 6395 | 99 | 1969 | 1 | 14.0 | | 6396 | 99 | 1970 | 1 | 16.0 | | 6397 | 99 | 1971 | 0 | 3.0 | | 6398 | 99 | 1972 | 0 | 0.0 | | 6399 | 99 | 1973 | 0 | 0.0 | ## 3. Fit and predict temporal classifiers ### Fit the models Using the `NeuralForecast.fit` method you can train a set of models to your dataset. You can define the forecasting `horizon` (12 in this example), and modify the hyperparameters of the model. For example, for the `NHITS` we changed the default hidden size for both encoder and decoders. See the `NHITS` and `MLP` [model documentation](https://nixtlaverse.nixtla.io/neuralforecast/models.mlp.html). > **Warning** > > For the moment Recurrent-based model family is not available to > operate with Bernoulli distribution output. This affects the following > methods `LSTM`, `GRU`, `DilatedRNN`, and `TCN`. This feature is work > in progress. ```python theme={null} # %%capture horizon = 12 # Try different hyperparmeters to improve accuracy. models = [MLP(h=horizon, # Forecast horizon input_size=2 * horizon, # Length of input sequence loss=DistributionLoss('Bernoulli'), # Binary classification loss valid_loss=Accuracy(), # Accuracy validation signal max_steps=500, # Number of steps to train scaler_type='standard', # Type of scaler to normalize data hidden_size=64, # Defines the size of the hidden state of the LSTM #early_stop_patience_steps=2, # Early stopping regularization patience val_check_steps=10, # Frequency of validation signal (affects early stopping) ), NHITS(h=horizon, # Forecast horizon input_size=2 * horizon, # Length of input sequence loss=DistributionLoss('Bernoulli'), # Binary classification loss valid_loss=Accuracy(), # Accuracy validation signal max_steps=500, # Number of steps to train n_freq_downsample=[2, 1, 1], # Downsampling factors for each stack output #early_stop_patience_steps=2, # Early stopping regularization patience val_check_steps=10, # Frequency of validation signal (affects early stopping) interpolation_mode="nearest", ) ] nf = NeuralForecast(models=models, freq=1) Y_hat_df = nf.cross_validation(df=Y_df, n_windows=1) ``` ```python theme={null} # By default NeuralForecast produces forecast intervals # In this case the lo-x and high-x levels represent the # low and high bounds of the prediction accumulating x% probability Y_hat_df ``` | | unique\_id | ds | cutoff | MLP | MLP-median | MLP-lo-90 | MLP-lo-80 | MLP-hi-80 | MLP-hi-90 | NHITS | NHITS-median | NHITS-lo-90 | NHITS-lo-80 | NHITS-hi-80 | NHITS-hi-90 | y | | ---- | ---------- | ---- | ------ | ----- | ---------- | --------- | --------- | --------- | --------- | ----- | ------------ | ----------- | ----------- | ----------- | ----------- | --- | | 0 | 0 | 1962 | 1961 | 0.173 | 0.0 | 0.0 | 0.0 | 1.0 | 1.0 | 0.761 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | 0 | | 1 | 0 | 1963 | 1961 | 0.784 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | 0.571 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | 1 | | 2 | 0 | 1964 | 1961 | 0.042 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.009 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0 | | 3 | 0 | 1965 | 1961 | 0.072 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.054 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0 | | 4 | 0 | 1966 | 1961 | 0.059 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.000 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0 | | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | | 1195 | 99 | 1969 | 1961 | 0.551 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | 0.697 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | 1 | | 1196 | 99 | 1970 | 1961 | 0.662 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | 0.465 | 0.0 | 0.0 | 0.0 | 1.0 | 1.0 | 1 | | 1197 | 99 | 1971 | 1961 | 0.369 | 0.0 | 0.0 | 0.0 | 1.0 | 1.0 | 0.382 | 0.0 | 0.0 | 0.0 | 1.0 | 1.0 | 0 | | 1198 | 99 | 1972 | 1961 | 0.056 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.000 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0 | | 1199 | 99 | 1973 | 1961 | 0.000 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.000 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0 | ```python theme={null} # Define classification threshold for final predictions # If (prob > threshold) -> 1 Y_hat_df['NHITS'] = (Y_hat_df['NHITS'] > 0.5) * 1 Y_hat_df['MLP'] = (Y_hat_df['MLP'] > 0.5) * 1 Y_hat_df ``` | | unique\_id | ds | cutoff | MLP | MLP-median | MLP-lo-90 | MLP-lo-80 | MLP-hi-80 | MLP-hi-90 | NHITS | NHITS-median | NHITS-lo-90 | NHITS-lo-80 | NHITS-hi-80 | NHITS-hi-90 | y | | ---- | ---------- | ---- | ------ | --- | ---------- | --------- | --------- | --------- | --------- | ----- | ------------ | ----------- | ----------- | ----------- | ----------- | --- | | 0 | 0 | 1962 | 1961 | 0 | 0.0 | 0.0 | 0.0 | 1.0 | 1.0 | 1 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | 0 | | 1 | 0 | 1963 | 1961 | 1 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | 1 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | 1 | | 2 | 0 | 1964 | 1961 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0 | | 3 | 0 | 1965 | 1961 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0 | | 4 | 0 | 1966 | 1961 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0 | | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | | 1195 | 99 | 1969 | 1961 | 1 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | 1 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | 1 | | 1196 | 99 | 1970 | 1961 | 1 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | 0 | 0.0 | 0.0 | 0.0 | 1.0 | 1.0 | 1 | | 1197 | 99 | 1971 | 1961 | 0 | 0.0 | 0.0 | 0.0 | 1.0 | 1.0 | 0 | 0.0 | 0.0 | 0.0 | 1.0 | 1.0 | 0 | | 1198 | 99 | 1972 | 1961 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0 | | 1199 | 99 | 1973 | 1961 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0 | ## 4. Plot and Evaluate Predictions Finally, we plot the forecasts of both models against the real values. And evaluate the accuracy of the `MLP` and `NHITS` temporal classifiers. ```python theme={null} plot_df = Y_hat_df[Y_hat_df.unique_id==10] fig, ax = plt.subplots(1, 1, figsize = (20, 7)) plt.plot(plot_df.ds, plot_df.y, label='target signal') plt.plot(plot_df.ds, plot_df['MLP'] * 1.1, label='MLP prediction') plt.plot(plot_df.ds, plot_df['NHITS'] * .9, label='NHITS prediction') ax.set_title('Binary Sequence Forecast', fontsize=22) ax.set_ylabel('Pixel Threshold and Prediction', fontsize=20) ax.set_xlabel('Timestamp [t]', fontsize=20) ax.legend(prop={'size': 15}) ax.grid() ``` ```python theme={null} def accuracy(y, y_hat): return np.mean(y==y_hat) mlp_acc = accuracy(y=Y_hat_df['y'], y_hat=Y_hat_df['MLP']) nhits_acc = accuracy(y=Y_hat_df['y'], y_hat=Y_hat_df['NHITS']) print(f'MLP Accuracy: {mlp_acc:.1%}') print(f'NHITS Accuracy: {nhits_acc:.1%}') ``` ```text theme={null} MLP Accuracy: 77.8% NHITS Accuracy: 74.5% ``` ## References * [Cox D. R. (1958). “The Regression Analysis of Binary Sequences.” Journal of the Royal Statistical Society B, 20(2), 215–242.](https://arxiv.org/abs/2201.12886) * [Cristian Challu, Kin G. Olivares, Boris N. Oreshkin, Federico Garza, Max Mergenthaler-Canseco, Artur Dubrawski (2023). NHITS: Neural Hierarchical Interpolation for Time Series Forecasting. Accepted at AAAI 2023.](https://arxiv.org/abs/2201.12886)