Logistic regression#

class equadratures.logistic_poly.LogisticPoly(n=2, M_init=None, tol=1e-07, cauchy_tol=1e-05, cauchy_length=3, verbosity=2, order=2, C=1.0, max_M_iters=10, restarts=1)[source]#

Class for defining a logistic subspace polynomial, used for classification tasks.

Parameters

  • n (optional, int) – Dimension of subspace (should be smaller than ambient input dimension d). Defaults to 2.

  • M_init (optional, numpy array of dimensions (d, n)) – Initial guess for subspace matrix. Defaults to a random projection.

  • tol (optional, float) – Optimisation terminates when cost function on training data falls below tol. Defaults to 1e-7.

  • cauchy_tol (optional, float) – Optimisation terminates when the difference between the average of the last cauchy_length cost function evaluations and the current cost is below cauchy_tol times the current evaluation. Defaults to 1e-5.

  • cauchy_length (optional, int) – Length of comparison history for Cauchy convergence. Defaults to 3.

  • verbosity (optional, one of (0, 1, 2)) – Print debug messages during optimisation. 0 for no messages, 1 for printing final residual every restart, 2 for printing residuals at every iteration. Defaults to 0.

  • order (optional, int) – Maximum order of subspace polynomial used. Defaults to 2.

  • C (optional, float) – L2 penalty on coefficients. Defaults to 1.0.

  • max_M_iters (optional, int) – Maximum optimisation iterations per restart. Defaults to 10.

  • restarts (optional, int) – Number of times to restart optimisation. The result with lowest training error is taken at the end. Defaults to 1.

Examples

Fitting and testing a logistic polynomial on a dataset.
>>> log_quad = eq.LogisticPoly(n=1, cauchy_tol=1e-5, verbosity=0, order=p_order, max_M_iters=100, C=0.001)
>>> log_quad.fit(X_train, y_train)
>>> prediction = log_quad.predict(X_test)
>>> error_rate = np.sum(np.abs(np.round(prediction) - y_test)) / y_test.shape[0]
>>> print(error_rate)
fit(X_train, f_train)[source]#

Method to fit logistic polynomial.

Parameters

  • X_train (numpy array, shape (N, d)) – Training input points.

  • f_train (numpy array, shape (N)) – Training output targets.

predict(X)[source]#

Method to predict from input test points.

Parameters

X (numpy array, shape (N, d)) – Test input points.

Returns

Predictions at specified test points.

Return type

numpy array, shape (N)