Data generation for Personalized Mixture of Gaussian Regressions.

gmreg_gen_data.py

def gen_data(nusers, nsamples, F, K):
    """Generate hyperparameters, parameters, and data for the Personalized
    Mixture of Gaussian Regressions model.

    Args:
        nusers (int): Number of distinct users.
        nsamples (int): Total number of samples to generate.
        F (int): Number of features for feature vectors.
        K (int): Number of clusters.
    Return:
        data, params (tuple of dicts):
            `data` contains X, y, and I.
                X (nsamples x F): the feature vectors for each sample.
                y (nsamples): the target variables for each sample.
                I (nsamples): the user ID for each sample.
            `params` contains pi, Z, beta, and W.
                pi (K): component weights.
                Z (nusers): categorical indicator variables for each user.
                beta (K): precision parameters for each component.
                W (K x F): regression coefficients for each component.
    """

    # Hyperparameters.
    alpha = np.ones(K)
    a0 = 1
    b0 = 1
    mu0 = np.zeros(F)
    coeff_variances = np.ones(F)

    # Parameters.
    pi = stats.dirichlet.rvs(alpha)[0]
    Z = np.random.multinomial(n=1, pvals=pi, size=nusers)
    Z_as_cat = np.nonzero(Z)[1]
    logging.info('assigned clusters: %s' % str(Z_as_cat))

    beta = stats.gamma.rvs(a0, b0, size=K)
    sigma_sq = 1. / beta
    W = stats.multivariate_normal.rvs(
            mean=mu0, cov=np.diag(coeff_variances), size=K)

    # Now generate samples according to which cluster the user belongs to.
    I = np.ndarray((nsamples, 1), dtype=np.int32)
    y = np.ndarray((nsamples,))

    # Randomly generate features, uniform [0, 10] + standard gaussian noise
    X = (np.random.uniform(1, 10, size=(nsamples, F))
            + np.random.randn(nsamples, F))

    # Randomly select user to sample observation for, for all samples.
    pids = np.arange(nusers)
    I[:nusers, 0] = pids  # make sure each user gets at least one observation
    rem = nsamples - nusers

    I[nusers:, 0] = np.random.choice(pids, replace=True, size=rem)
    Z_idx = Z_as_cat[I[:, 0]]
    Ws = W[Z_idx]
    y[:] = (X * Ws).sum(1)

    data = {
        'X': X,
        'y': y,
        'I': I
    }

    params = {
        'pi': pi,
        'Z': Z_as_cat,
        'beta': beta,
        'W': W
    }

    return data, params