learning-curves 0.1.0

Python module allowing to easily calculate and plot the learning curve of a machine learning model and find the maximum expected accuracy

learning-curves

Learning-curves is a Python module that will help you visualizing the learning curve of your models.

Learning curves give an opportunity to diagnose bias and variance in supervised learning models, but also to visualize how training set size influence the performance of the models (more informations here).

Such plots help you answer the following questions:

• Do I have enough data?
• What would be the best accuracy I would have if I had more data?
• Can I train my model with less data?
• Is my training set biased?

Learning-curves will also help you fitting the learning curve to extrapolate and find the saturation value of the curve.

Installation

$ pip install git+https://github.com/H4dr1en/learning-curves.git

To create learning curve plots, first import the module with import learning_curves.

Usage

It is as simple as:

lc = LearningCurve()
lc.get_lc(estimator, X, Y)

Where estimator implements fit(X,Y) and predict(X,Y).

Output:

On this example the green curve suggests that adding more data to the training set is likely to improve a bit the model accuracy. The green curve also shows a saturation near 0.95. We can easily fit a function to this curve:

lc.plot(predictor="best")

Output:

Here we used a predefined function, pow_2, to fit the green curve. The R2 score is very close to 1, meaning that the fit is optimal. We can therefore use this curve to extrapolate the evolution of the accuracy with the training set size.

This also tells us how many data we should use to train our model to maximize performances and accuracy.

Add custom functions to fit the learning curve

Such function are called Predictor. You can create a Predictor like this:

predictor = Predictor("myPredictor", lambda x,a,b : a*x + b, [1,0])

Here we created a Predictor called "myPredictor" with the function y(x) = a*x + b. Because internally SciPy optimize.curve_fit is called, a first guess of the parameters a and b are required. Here we gave them respective value 1 and 0. You can then add the Predictor to the LearningCurve object in two different ways:

• Pass the Predictor to the LearningCurve constructor:

lc = LearningCurve([predictor])

• Register the Predictor inside the predictors of the LearningCurve object:

lc.predictors.append(predictor)

By default, six Predictors are instantiated:

self.predictors = [
    Predictor("pow",        lambda x,a,b,c    : a - b*x**c,                  [1, 1.7,-.5]),
    Predictor("pow_2",      lambda x,a,b,c,d  : a - (b*x+d)**c,              [1, 1.7,-.5, 1e-3]),
    Predictor("pow_log",    lambda x,a,b,c,m,n: a - b*x**c + m*np.log(x**n), [1.3, 1.7,-.5,1e-3,2]),
    Predictor("pow_log_2",  lambda x,a,b,c    : a / (1 + (x/np.exp(b))**c),  [1, 1.7,-.5]),
    Predictor("log_lin",    lambda x,a,b      : np.log(a*np.log(x)+b),       [1, 1.7]),
    Predictor("log",        lambda x,a,b      : a - b/np.log(x),             [1.6, 1.1])
]

Some predictors perform better (R2 score is closer to 1) than others, depending on the dataset, the model and the value to be preditected.

Find the best Predictor

To find the Predictor that will fit best your learning curve, we provide a best_predictor function:

lc.best_predictor()

Output:

('exp_log', 0.999147437907635, <learning_curve.Predictor at 0x7feb9f2a4ac8>)

Plot the Predictors

You can plot any Predictors fitted function with the plot function:

lc.plot(predictor="best")

Ouput:

Note that this is the exact same output as calling get_lc because internally this function just calls train to compute the data points of the learning curve and then call plot(predictor="best").

You can also plot all of the Predictor curves:

lc.plot(predictor="all")

Output:

Save and load LearningCurve instances

Because Predictor contains lambda functions, you can not simply save a LearningCurve instance. One possibility is to only save the data points of the curve inside lc.recorder["data"] and retrieve then later on. But then the custom predictors are not saved. Therefore it is recommended to use the save and load methods:

lc.save("path/to/save.pkl")
lc = LearningCurve.load("path/to/save.pkl")

This internally uses the dill library to save the LearningCurve instance with all the Predictors.

Documentation

Function/Class	Parameters	Type	Default	Description
Predictor.__init__				Instantiate a Predictor object.
	name	str	Required	Name of the Predictor
	func	Lambda	Required	Lambda function used for fitting of the learning curve
	guess	List	Required	Starting parameters used for fitting the curve
LC.__init__				Instantiate a LearningCurve object.
	predictors	List	empty	Predictors to add to the LearningCurve object
	scoring	Callable	r2_score	Scoring function used to evaluate the fits of the learning curve
LC.get_lc	estimator	Object	Required	Model (any object implementing fit(X,Y) and predict(X,Y) methods)
	X	array	Required	X numpy array used for prediction
	Y	array	Required	Y numpy array used for prediction
	train_sizes	List	Predefined	List of training size used for calculating the learning curve. Can be a list of floats between 0 and 1 (assumed to be percentages) or a list of integers (assumed to be number of values)
	test_size	int/float	0.2	percentage / value of the test set size
	n_splits	int	3	Number of splits used for cross validation
	verbose	int	1	The higher, the more verbose
	n_jobs	int	-1	Number of workers. -1 sets to maximum possible. See sklearn.
LC.train				Compute the learning curve of an estimator over a dataset. Returns an object that can then be passed to plot_lc function
				Same as get_lc
LC.get_predictor				Get the first predictor with matching {name}. Returns None if no predictor matches.
	name	str	Required	Name of the predictor
LC.fit_all				Fit a curve with all the Predictors and retrieve score if y_pred is finite. Returns an array of predictors with the updated params and score.
	x	Array	Required	1D array (list) representing the training sizes
	y	Array	Required	1D array (list) representing the scores
LC.fit				Fit a curve with a predictor and retrieve score (default:R2) if y_pred is finite. Returns the predictor with the updated params and score.
	predictor	Predictor	Required	The predictor to use for fitting the learning curve
	x	Array	Required	1D array (list) representing the training sizes
	y	Array	Required	1D array (list) representing the scores
LC.best_predictor				Returns the best predictor of the LearningCurve data for the test score learning curve
LC.best_predictor_cust				Find the best predictor for a custom learning curve
	x	Array	Required	1D array (list) representing the training sizes
	y	Array	Required	1D array (list) representing the scores
LC.plot				Plot the training and test learning curve of the LearningCurve data, and optionally a fitted function
	predictor	str	None	Name of the Predictor to use for plotting the fitted curve. Can also be "all" and "best".
	kwargs	dict	None	See LC.plot_cust for optional parameters
LC.plot_cust				Plot any training and test learning curve, and optionally a fitted function.
	train_sizes	array	Required	Data points of the learning curve. The output of LC.train can be used as parameters of this function
	train_scores_mean	array	Required	See train_sizes parameter
	train_scores_std	array	Required	See train_sizes parameter
	test_scores_mean	array	Required	See train_sizes parameter
	test_scores_std	array	Required	See train_sizes parameter
	predictor	array	Required	See LC.plot
	ylim	2-uple	None	Limits of the y axis of the plot
	figsize	2-uple	None	Size of the figure
	title	str	None	Title of the plot
	scores	Bool	True	if predictor parameter is not None, then if scores is True then the score of the fitted Predictor(s) are shown on the plot.
	kwargs	dict	None	Ignored
LC.plot_fitted_curve				Add to a matplotlib figure a fitted curve
	ax	axe	Required	Figure where the curve will be printed
	P	Predictor	Required	Predictor to use for the computing of the curve
	x	array	Required	1D array (list) representing the training sizes
LC.save				Save the LearningCurve object in disk using dill
	path	Path/str	lc_data.pkl	Path to the file where the save will be done
LC.load				Load a LearningCurve object from disk.
	path	Path/str	lc_data.pkl	Path to the file where the save is located