Feature building from the lernia library

*lernia library*

We collect weather data from darksky api

*darksky weather api*

And census data from eurostat

*eurostat census data*

For each feature is important to undestand statistical properties such as:

- distribution of variance (normal, Poisson, multimodal…)
- error/loss function

- periodicity
- transform function

- autocorrelation (entropy, information)
- noise kind
- decomposition (find relevant sub-components)

*statistical properties of a time series*

We should evaluate the distribution of each variable, this view is confusing

*no norm*

An important operation for model convergence and performances is to normalize data. We can than see in one view all variances and skweness

*minmax norm*

Outliers can completly skew the distribution of variables and make learning difficult, we therefore remove the extreme percentiles

*norm 5-95*

We remove percentiles and normalize to one

*norm 1-99*

Correlation between features is important to exclude features which are derivable

*feature correlation*

Outlier removal is not changing the correlation between features

*feature correlation*

Some features have too many outliers, we decide to put a threshold and transform the feature into a logistic variable

*norm cat*

Apart from boxplot is important to visualize data density and spot the multimodal distributions

*norm joyplot*

We than sort the features and exclude highly skewed variables

*norm logistic features*

Looking at the 2d cross correlation we understand a lot about interaction between features

*selected features*

And we can have a preliminary understanding about how features interacts

*feature 2d correlation*

We know that apparent temperature is dependent from temperature, humidity, windSpeed, windBearing, cloudCover but we might not know why. Apparent temperature can be an important predictor so basically we can reduce the other components with a PCA

*pca on derivate feature*

Interestingly the first component explains most of the feature set but doesn’t explain the apparent temperature which is describes in the second component

*components importance*

For the same components we can investigate other metrics

*feature pair metrics*

Working with python doesn’t leave many options, contrary to R almost any library return errors. We therfore interpolate or drop lines.

*replacing nans with interpolation*

The main issue with interpolation is at the boundary, special cases should be treated

If we have a lot of time series per location, or multiple signal superimposing we look at the chi square distribution to understand where outlier sequence windows are off

*chi square distribution*

We than replace the off windows with a neighboring cluster

*replace volatile sequences*

Feature importance is a function that simple models return. Since models don’t agree on the same feature importance and production model will even come to much different conclusions.

*feature importance no norm*

Normalization stabilize agreement between models

*feature importance norm*

We can apply as well a feature regularisation checking against a Lasso or a Ridge regression which features are relevant for the predicting variable

*regularisation of features, mismatch in results depending on the regressor*

We than iterate model trainings removing one feature per time and calculate performaces. We can than understand how much is every feature important for the training

*feature knock out*

Strangely removing ozone and pressure the rain prediction suffers. We than analyze time series a realize a big gap in historical data and realize the few data where misleading for the model

*feature time series*

The meaning of building features is to achieve good predictability, if we want to predict rain we have differences in performace between models

*predictability, no norm*

Cleaning features all the models perform basically the same

*predictability, normed*

Same if we train on spatial feature on a binned prediction variable

*predictability, no norm*

After feature cleaning we have better agreement between models

*predictability, normed*

Detailed information can be compressed fitting curves

*simplify complexity*

For a many day time series we can distinguish periods from trends

*simplify complexity*

Time series can be transformed in pictures

*time series in pictures*

Which is important to induce correlation between days and use more sofisticated methods

*reference prediction*

We can interpolate data to have more precise information and induce correlation between neighbors

*interpolate population density*

If we want to know how dense is an area with a particular geo feature

*spot building distance*

We can reduce the density of feature fitting the radial histogram and returning the convexity of the parabola

*spatial degeneracy, parabola convexity*

If we apply boosting the distribution will change and therefore we can train another model to predict the residuals

*residual distribution*

Encoder options

- One hot encoder: each element is represented buy it’s matrix position - few elements
- nominal: groups
- cluster: clusterize the data and compute cluster distance
- hashing: one hot minus collisions
- binary: 1-0
- ordinal: group with oder
- interval
- constrast encoder: difference from stems
- Bayesian encoder: information from dependent variable

Weekdays are categorical but they are intercorrelated, it is convinient to group workdays and weekend and stretch the time: {weekday:1,weekend:2} -> {weekday:1,weekend:0.5}