# Custom Models¶

## Defining a Model¶

The ModelBase class in albatross uses the Curiously Recurring Template Pattern (CRTP) which makes defining them slightly different from the standard inheritence pattern in C++.

In general an albatross model requires defining _fit_impl, _predict_impl and a struct Fit<MyModel> which is in charge of storing any coefficients.

## Fit Method¶

To get model.fit(dataset) to work you need to add a _fit_impl method to your class, this fit implementation needs to take a vector of features and corresponding targets (often measurements) and needs to return a Fit<ModelType> object holding any information required to make predictions.

class ModelType : public ModelBase<ModelType> {

Fit<ModelType> _fit_impl(const std::vector<FeatureType> &features,
const MarginalDistribution &targets) const;

}


The FeatureType here can be which ever type your problem requires and you can have multiple _fit_impl methods for different types in the same model. Templated _fit_impl methods also work.

## Predict Method¶

To get model.predict(features) to work you need to add a _predict_impl method to your class, this predict implementation needs to take a vector of features and a Fit<ModelType> and needs to return either an Eigen::VectorXd (mean only), MarginalDistribution (mean and variance) or JointDistribution (mean and covariance).

class ModelType : public ModelBase<ModelType> {

JointDistribution _predict_impl(const std::vector<FeatureType> &features,
const Fit<ModelType> &fit,
PredictTypeIdentity<JointDistribution>) const;

}


In this case above we’ve implemented predict to return a JointDistribution which holds the mean prediction as well as a full covariance. A JointDistribution can be converted into a MarginalDistribution by taking the diagonal of the covariance matrix and a MarginalDistribution can be converted into a mean only prediction (Eigen::VectorXd) by simply taking the mean of the distribution. As a result, by implementing predict for a JointDistribution you will be able to call all of the following.

const auto prediction model.fit(dataset).predict(features);
JointDistribution joint_pred =prediction.joint();
MarginalDistribution marginal_pred = prediction.marginal();
Eigen::VectorXd mean_pred = prediction.mean();


If you define _predict_impl with a MarginalDistribution instead, then you’ll find that you can call,

MarginalDistribution marginal_pred = prediction.marginal();
Eigen::VectorXd mean_pred = prediction.mean();


but calling prediction.joint(); would result in a compile time error. Similarly if you just define the mean only version then asking for anything other than prediction.mean() will result in a compile time error.

We saw above that you could implement the JointDistribution version and have access to all the predict types, but that is often inefficient. Instead you may want to impelement specialized version for each of the predict types. This is what is done in for the Gaussian processes (see gp.hpp). The desire to have specialized predict types is what led to the mysterious PredictTypeIdentity<> argument, which is required to allow overridable _predict_impl methods with different return types.

## Fit Type¶

The fit type needs to be a specialization of the Fit<> struct. The idea is that by forcing the output of _fit_impl to be a custom type we can subsequently make model types constant, which gives us peace of mind that there isn’t accidentally some state that get’s stored in a model which would cause two calls to fit to produce different results.

Once you’ve defined the Fit<> you shouldn’t ever need to actually inspect that type, that should be left to the internals of albatross. Instead you are encouraged to use auto,

const auto fit_model = model.fit(dataset);


or write everything as one liners.

const Eigen::VectorXd mean = model.fit(dataset).predict(features).mean();


Here’s an illustration of the actual types that would result from a typical model workflow:

const ModelType model = make_my_model();
const FitModel<ModelType, Fit<ModelType>> fit_model = model.fit(dataset);
const Prediction<ModelType, FeatureType, Fit<ModelType>> prediction = fit_model.predict(features);
const JointDistribution joint_prediction = prediction.joint();


Again, thanks to auto type declarations you shouldn’t need to actually know these types but it may be helpful to get a glimpse of what’s happening under the hood. This chain of types is what allows albatross to keep track of how exactly you’re using a model and decide (at compile time) the most efficient methods to use.

## Example¶

Here’s an example of a model which always returns the mean of the training data.

struct Fit<MeanModel> {
double mean;
}

class MeanModel : public albatross::ModelBase<MeanModel> {
public:

using FitType = Fit<MeanModel>;

std::string get_name() const { return "mean"; }

template <typename FeatureType>
FitType _fit_impl(const std::vector<FeatureType> &features,
const MarginalDistribution &targets) const {
FitType model_fit = {targets.mean.mean()};
return model_fit;
}

template <typename FeatureType>
Eigen::VectorXd _predict_impl(const std::vector<FeatureType> &features,
const FitType &fit,
PredictTypeIdentity<Eigen::VectorXd>) const {
Eigen::VectorXd output(features.size());
output.fill(fit.mean);
return output;
}
}


While defining your own model isn’t as simple as standard inheritence , the benefits are large. Once you’ve defined a model using the ModelBase class you can immediately start using all the tools built around it, things such as cross validation, outlier detection using RANSAC, and tuning tuning.