def test_map(self):
g = Gaussian(mean=Gaussian(np.zeros(2), np.ones(2)), var=np.ones(2))
g.map(np.array([[1., 0.], [0., 1.], [-1., 0.], [0., -1.]]))
self.assertTrue((g.mean == 0).all())
g1 = Gaussian(mean=Gaussian(np.zeros(2), np.ones(2)), var=np.ones(2))
g1.bayes(np.array([[1., 0.], [0., 1.], [-1., 0.], [0., -1.]]))
self.assertTrue((g.mean == g1.mean.mean).all())
def __init__(self, initial_proba, transition_proba, means, covs):
"""
construct hidden markov model with Gaussian emission model 用高斯模型构建HMM
Parameters
----------
initial_proba : (n_hidden,) np.ndarray or None
probability of initial states 初始状态概率
transition_proba : (n_hidden, n_hidden) np.ndarray or None
transition probability matrix 转移概率矩阵， 是隐状态之间的转换
(i, j) component denotes the transition probability from i-th to j-th hidden state
means : (n_hidden, ndim) np.ndarray
mean of each gaussian component 每一部分的系数（概率）？或者每一高斯部分的均值
covs : (n_hidden, ndim, ndim) np.ndarray
covariance matrix of each gaussian component 每一高斯部分的方差矩阵
Attributes
----------
ndim : int
dimensionality of observation space 观测空间的维数
n_hidden : int
number of hidden states 隐藏状态的数量
"""
assert initial_proba.size == transition_proba.shape[
0] == transition_proba.shape[1] == means.shape[0] == covs.shape[0]
assert means.shape[1] == covs.shape[1] == covs.shape[2]
super().__init__(initial_proba, transition_proba)
self.ndim = means.shape[1]
self.means = means
self.covs = covs
self.precisions = np.linalg.inv(self.covs)
self.gaussians = [Gaussian(m, cov) for m, cov in zip(means, covs)]
def test_init(self):
g = Gaussian(mean=np.ones(2))
self.assertTrue((g.mean == 1).all())
self.assertTrue(g.var is None)
g = Gaussian(mean=np.ones(3), var=np.ones(3) * 2)
self.assertTrue(np.allclose(g.precision, np.ones(3) * 0.5))
def test_draw(self):
g = Gaussian(mean=np.ones((2, 4)), var=np.ones((2, 4)) * 2)
sample = g.draw(10000)
self.assertTrue(np.allclose(np.mean(sample, 0), g.mean, 1e-1, 1e-1))
self.assertTrue(np.allclose(np.var(sample, 0), g.var, 1e-1, 1e-1))
def test_pdf(self):
g = Gaussian(mean=np.zeros(1), var=np.ones(1))
self.assertEqual(g.pdf(np.zeros((1, 1))), (2 * np.pi)**-0.5)
self.assertEqual(g.pdf(np.ones((1, 1))),
(2 * np.pi)**-0.5 * np.exp(-0.5))
def test_bayes(self):
g = Gaussian(mean=Gaussian(np.zeros(2), np.ones(2)), var=np.ones(2))
g.bayes(np.array([[1., 0.], [0., 1.], [-1., 0.], [0., -1.]]))
self.assertTrue((g.mean.var == np.ones(2) * 0.2).all())
def test_ml(self):
g = Gaussian()
g.ml(np.array([[1., 0.], [0., 1.], [-1., 0.], [0., -1.]]))
self.assertTrue((g.mean == 0).all())
self.assertTrue((g.var == 0.5 * np.ones(2)).all())
def test_var(self):
g = Gaussian(mean=np.ones((2, 3)), var=np.ones((2, 3)) * 2)
self.assertTrue((g.var == np.ones((2, 3)) * 2).all())
def test_mean(self):
g = Gaussian(mean=np.ones(3))
self.assertTrue((g.mean == 1).all())
def test_repr(self):
g = Gaussian(mean=np.ones(2), var=np.ones(2) * 2)
self.assertEqual(repr(g),
"Gaussian(\nmean=\n[ 1. 1.],\nvar=\n[ 2. 2.]\n)")
def test_draw(self):
g = Gaussian(mean=np.ones(2), var=np.eye(2) * 2)
sample = g.draw(10000)
self.assertTrue(np.allclose(np.mean(sample, 0), g.mean, 1e-1, 1e-1))
self.assertTrue(np.allclose(np.cov(sample.T), g.var, 1e-1, 1e-1))