categorical interactions such as concatenation of building_id and meter
串联building_id和meter产生新的categorical featurebuilding_id_meter
count frequency of feautures
计算特征的数量
Smoothed and 1st, 2nd-order differentiation temperature features using Savitzky-Golay filter.
Cyclic encoding of periodic features; e.g., hour gets mapped to hour_x = cos(2pihour/24) and hour_y = sin(2pihour/24)
这个很骚，就是对于循环特征的编码，用cos和sin进行编码
Bayesian target encoding
这个是作者自己写的一种target编码，下面会详细讲一下
3rd 的思路：作者因为缺乏时间，仅仅消除了一些异常值。使用的是当同一时间同一地区都出现0的时候，消除他们，然后消除了一些最大的异常值。
温度的滞后，多个高分作者都提到过。

2.4.1 Savitzky-Golay filter

Savitzky-Golay卷积平滑算法是移动平滑算法的改进。
Savitzky-Golay卷积平滑关键在于矩阵算子的求解。

总结：先计算出B，然后计算预测Y，这个需要利用矩阵的运算。应该不难。回头复现的时候上代码
下面回到比赛上来看他们的处理结果
第一个图蓝色线是原数据
第一个图黄色线是用G-S平滑后的数据
第二个图蓝色线是G-S平滑后的数据的一阶导数
第二个图黄色线是G-S平滑后的数据的二阶导数

2.4.2 Bayesian target encoding(python实现)

import gc
import numpy as np
import pandas as pd 
from sklearn.linear_model import RidgeCV
from sklearn.metrics import mean_squared_error

PRIOR_PRECISION = 10
class GaussianTargetEncoder():
        
    def __init__(self, group_cols, target_col="target", prior_cols=None):
        self.group_cols = group_cols
        self.target_col = target_col
        self.prior_cols = prior_cols

    def _get_prior(self, df):
        if self.prior_cols is None:
            prior = np.full(len(df), df[self.target_col].mean())
        else:
            prior = df[self.prior_cols].mean(1)
        return prior
                    
    def fit(self, df):
        self.stats = df.assign(mu_prior=self._get_prior(df), y=df[self.target_col])
        self.stats = self.stats.groupby(self.group_cols).agg(
            n        = ("y", "count"),
            mu_mle   = ("y", np.mean),
            sig2_mle = ("y", np.var),
            mu_prior = ("mu_prior", np.mean),
        )        
    
    def transform(self, df, prior_precision=1000, stat_type="mean"):
        
        precision = prior_precision + self.stats.n/self.stats.sig2_mle
        
        if stat_type == "mean":
            numer = prior_precision*self.stats.mu_prior\
                    + self.stats.n/self.stats.sig2_mle*self.stats.mu_mle
            denom = precision
        elif stat_type == "var":
            numer = 1.0
            denom = precision
        elif stat_type == "precision":
            numer = precision
            denom = 1.0
        else: 
            raise ValueError(f"stat_type={stat_type} not recognized.")
        
        mapper = dict(zip(self.stats.index, numer / denom))
        if isinstance(self.group_cols, str):
            keys = df[self.group_cols].values.tolist()
        elif len(self.group_cols) == 1:
            keys = df[self.group_cols[0]].values.tolist()
        else:
            keys = zip(*[df[x] for x in self.group_cols])
        
        values = np.array([mapper.get(k) for k in keys]).astype(float)
        
        prior = self._get_prior(df)
        values[~np.isfinite(values)] = prior[~np.isfinite(values)]
        
        return values
    
    def fit_transform(self, df, *args, **kwargs):
        self.fit(df)
        return self.transform(df, *args, **kwargs)

# load data
train = pd.read_csv("/kaggle/input/ashrae-energy-prediction/train.csv")
test  = pd.read_csv("/kaggle/input/ashrae-energy-prediction/test.csv")

# create target
train["target"] = np.log1p(train.meter_reading)
test["target"] = train.target.mean()

# create time features
def add_time_features(df):
    df.timestamp = pd.to_datetime(df.timestamp)    
    df["hour"]    = df.timestamp.dt.hour
    df["weekday"] = df.timestamp.dt.weekday
    df["month"]   = df.timestamp.dt.month

add_time_features(train)
add_time_features(test)

# define groupings and corresponding priors
groups_and_priors = {
    
    # singe encodings
    ("hour",):        None,
    ("weekday",):     None,
    ("month",):       None,
    ("building_id",): None,
    ("meter",):       None,
    
    # second-order interactions
    ("meter", "hour"):        ["gte_meter", "gte_hour"],
    ("meter", "weekday"):     ["gte_meter", "gte_weekday"],
    ("meter", "month"):       ["gte_meter", "gte_month"],
    ("meter", "building_id"): ["gte_meter", "gte_building_id"],
        
    # higher-order interactions
    ("meter", "building_id", "hour"):    ["gte_meter_building_id", "gte_meter_hour"],
    ("meter", "building_id", "weekday"): ["gte_meter_building_id", "gte_meter_weekday"],
    ("meter", "building_id", "month"):   ["gte_meter_building_id", "gte_meter_month"],
}

features = []
for group_cols, prior_cols in groups_and_priors.items():
    features.append(f"gte_{'_'.join(group_cols)}")
    gte = GaussianTargetEncoder(list(group_cols), "target", prior_cols)    
    train[features[-1]] = gte.fit_transform(train, PRIOR_PRECISION)
    test[features[-1]]  = gte.transform(test,  PRIOR_PRECISION)

train_preds = np.zeros(len(train))
test_preds = np.zeros(len(test))

for m in range(4):
    
    print(f"Meter {m}", end="") 
    
    # instantiate model
    model = RidgeCV(
        alphas=np.logspace(-10, 1, 25), 
        normalize=True,
    )    
    
    # fit model
    model.fit(
        X=train.loc[train.meter==m, features].values, 
        y=train.loc[train.meter==m, "target"].values
    )

    # make predictions 
    train_preds[train.meter==m] = model.predict(train.loc[train.meter==m, features].values)
    test_preds[test.meter==m]   = model.predict(test.loc[test.meter==m, features].values)
    
    # transform predictions
    train_preds[train_preds < 0] = 0
    train_preds[train.meter==m] = np.expm1(train_preds[train.meter==m])
    
    test_preds[test_preds < 0] = 0 
    test_preds[test.meter==m] = np.expm1(test_preds[test.meter==m])
    
    # evaluate model
    meter_rmsle = rmsle(
        train_preds[train.meter==m],
        train.loc[train.meter==m, "meter_reading"].values
    )
    
    print(f", rmsle={meter_rmsle:0.5f}")

print(f"Overall rmsle={rmsle(train_preds, train.meter_reading.values):0.5f}")
del train, train_preds, test
gc.collect()

2.5 models ensemble

2nd的思想：Due to the size of the dataset and difficulty in setting up a robust validation framework, we did not focus much on feature engineering, fearing it might not extrapolate cleanly to the test data. Instead we chose to ensemble as many different models as possible to capture more information and help the predictions to be stable across years.
因为数据集的规模巨大，以及难以建立验证框架的困难，他们担心特征工程可能不发清晰的推断到测试数据上，因此并未过多的关注特征工程。相反，整合尽可能多的不同模型来捕获更多的信息，并帮助预测集的平稳。
根据他们过去的经验，在没有可靠的验证框架的情况下，构建好的特征是非常棘手的
2nd的思想：We bagged a bunch of boosting models XGB, LGBM, CB at various levels of data: Models for every site+meter, models for every building+meter, models for every building-type+meter and models using entire train data. It was very useful to build a separate model for each site so that the model could capture site-specific patterns and each site could be fitted with a different parameter set suitable for it. It also automatically solved for issues like timestamp alignment and feature measurement scale being different across sites so we didn’t have to solve for them separately.
为每一个建立单独的model，作者大概为这次比赛总共建立了超过5000个models进行融合
3nd的思想：Given diverse experiments with different CV schemes I did over the period of the competition, I decided to simply combine all the results (over 30), I got into a single submission using a simple average after selection by pearson correlation (6th on private LB).
作者因为时间不充裕，所以简单的融合了所有的结果，超过30个的结果。作者简单的使用平均的方法。然后使用peason correlation皮尔逊相关系数来选择平均那几个结果。
不得不说，就算lightGBM的性能高于XGB和Catboost，但是这三个都是要用在比赛中的，可能是能提取不同的信息。有的人还会使用CNN和FFNN

2.5.1 pearson correlation(+python 实现)

Pearson相关系数（Pearson CorrelationCoefficient）是用来衡量两个数据集合是否在一条线上面，它用来衡量定距变量间的线性关系。

#如何使用
from scipy.stats.stats import pearsonr
pearsonr(x, y)

#具体文档查看
from pydoc import help
from scipy.stats.stats import pearsonr
help(pearsonr)

>>>
Help on function pearsonr in module scipy.stats.stats:

pearsonr(x, y)
 Calculates a Pearson correlation coefficient and the p-value for testing
 non-correlation.

 The Pearson correlation coefficient measures the linear relationship
 between two datasets. Strictly speaking, Pearson's correlation requires
 that each dataset be normally distributed. Like other correlation
 coefficients, this one varies between -1 and +1 with 0 implying no
 correlation. Correlations of -1 or +1 imply an exact linear
 relationship. Positive correlations imply that as x increases, so does
 y. Negative correlations imply that as x increases, y decreases.

 The p-value roughly indicates the probability of an uncorrelated system
 producing datasets that have a Pearson correlation at least as extreme
 as the one computed from these datasets. The p-values are not entirely
 reliable but are probably reasonable for datasets larger than 500 or so.

 Parameters
 ----------
 x : 1D array
 y : 1D array the same length as x

 Returns
 -------
 (Pearson's correlation coefficient,
  2-tailed p-value)

 References
 ----------
 http://www.statsoft.com/textbook/glosp.html#Pearson%20Correlation