#!/usr/bin/env python
# coding: utf-8

# # Time Series Regression
# 
# Time Series Regression (TSR) involves training a model from a collection of time
# series (real valued, ordered, data) in order to predict a continuous target variable.
# 
# There are two types of TSR.
# 
# 1) Time Series Forecasting Regression (TSFR) relates to forecasting reduced to regression
# through a sliding window. This is the more familiar type to most people.
# 
# 2) Time Series *Extrinsic* Regression (TSER) was formally specified in Tan et al. [1] as a
# related, but distinct, type of time series regression problem. Rather than being derived from a
# forecasting problem, TSER involves a predictive model built on time series to predict a real-valued
# variable distinct from the training input series.
# 
# This notebook focuses on the `aeon` regression module, which consists of algorithms 
# used for TSER, but also applicable to TSFR.
# 
# <img src="img/tser.png" width="600" alt="time series regression">
# 
# An example TSER problem is shown in the below image of soil spectrograms which can be used to estimate
# the potassium concentration. Ground truth is found through expensive
# lab based experiments that take some time. Spectrograms (ordered data series we treat as time series)
# are cheap to obtain and the data can be collected in any environment. An accurate regressor from spectrogram
# to concentration would make land and crop management more efficient.
# 
# <img src="img/spectra.png" width="600" alt="spectrograph example">

# ## Data Storage and Problem Types
# 
# Regressors take time series input as either 3D numpy of shape`(n_cases, n_channels, n_timepoints)` for
# equal length series or as a list of 2D numpy of length `[n_cases]`. All regressors work with equal
# length problems. Regression functionality for unequal length is currently limited.
# 
# `aeon` ships two example regression problems in the `datasets` module:

# In[9]:


import warnings

import matplotlib.pyplot as plt
import numpy as np

from aeon.datasets import load_cardano_sentiment, load_covid_3month

warnings.filterwarnings("ignore")

covid_train, covid_train_y = load_covid_3month(split="train")
covid_test, covid_test_y = load_covid_3month(split="test")
cardano_train, cardano_train_y = load_cardano_sentiment(split="train")
cardano_test, cardano_test_y = load_cardano_sentiment(split="test")
covid_train.shape


# Covid3Month is from the [monash tser archive](http://tseregression.org/) who in turn got
# the data from [WHO's COVID-19 database](https://covid19.who.int/). The goal of this dataset is to predict
# COVID-19's death rate on 1st April 2020 for each country using daily confirmed cases for the last three months.
# 
# This dataset contains 201 time series (140 train, 61 test), where each time series is
# the daily confirmed cases for a country. The data is univariate, each series length 84.

# In[10]:


plt.title("First three cases for Covid3Month")
plt.plot(covid_train[0][0])
plt.plot(covid_train[1][0])
plt.plot(covid_train[2][0])


# In[11]:


cardano_train.shape


# The CardanoSentiment dataset was created By combining historical sentiment data for
# Cardano cryptocurrency, extracted from EODHistoricalData and made available on
# Kaggle, with historical price data for the same cryptocurrency extracted from
# CryptoDataDownload. The predictors are hourly close price (in USD) and traded
# volume during a day, resulting in 2-dimensional time series of length 24. The
# response variable is the normalized sentiment score on the day spanned by the timepoints.

# In[12]:


plt.title("First three cases for CardanoSentiment")
plt.plot(cardano_train[0][0])
plt.plot(cardano_train[1][0])
plt.plot(cardano_train[2][0])


# 

# # Time Series Regressors in aeon
# 
# All regressors inherit from the `BaseRegressor` class. Like classification and
# clustering, regressors have methods `fit` and `predict` to train and use the model.
# The list of regressors available can be found with `all_estimators`.

# In[13]:


from aeon.utils.discovery import all_estimators

all_estimators("regressor")


# Currently we have 18 regressors, including deep learning, feature based, convolution
# based, interval based and distance based regressors, in addition to the utility
# regressors such as Dummy and Pipeline.

# In[14]:


from aeon.regression.distance_based import KNeighborsTimeSeriesRegressor

knn = KNeighborsTimeSeriesRegressor()
knn.fit(covid_train, covid_train_y)
p = knn.predict(covid_test)
sse = np.sum((covid_test_y - p) * (covid_test_y - p))
sse


# ## Multivariate Regression
# Nearly all of the regressors can handle multivariate data

# In[15]:


all_estimators("regressor", tag_filter={"capability:multivariate": True})


# In[16]:


from aeon.regression import DummyRegressor

fp = KNeighborsTimeSeriesRegressor()
dummy = DummyRegressor()
dummy.fit(cardano_train, cardano_train_y)
knn.fit(cardano_train, cardano_train_y)
pred = knn.predict(cardano_test)
res_knn = cardano_test_y - pred
res_dummy = cardano_test_y - dummy.predict(cardano_test)
plt.title("Raw residuals")
plt.plot(res_knn)
plt.plot(res_dummy)


# ## References
# 
# [1] Tan et al. "Time series extrinsic regression", Data Mining and Knowledge
# Discovery, 35(3), 2021
# [2] Guijo-Rubio et al. "Unsupervised Feature Based Algorithms for Time Series
# Extrinsic Regression", ArXiv, 2023