def initialize(deep_map, X,num_pseudo_params):
smart_map = {}
for layer,layer_map in deep_map.iteritems():
smart_map[layer] = {}
for unit,gp_map in layer_map.iteritems():
smart_map[layer][unit] = {}
cov_params = gp_map['cov_params']
lengthscales = cov_params[1:]
if layer == 0:
pairs = itertools.combinations(X, 2)
dists = np.array([np.abs(p1-p2) for p1,p2 in pairs])
smart_lengthscales = np.array([np.log(np.median(dists[:,i])) for i in xrange(len(lengthscales))])
kmeans = KMeans(n_clusters = num_pseudo_params, init = 'k-means++')
fit = kmeans.fit(X)
smart_x0 = fit.cluster_centers_
#inds = npr.choice(len(X), num_pseudo_params, replace = False)
#smart_x0 = np.array(X)[inds,:]
smart_y0 = np.ndarray.flatten(smart_x0)
#smart_y0 = np.array(y)[inds]
smart_noise_scale = np.log(np.var(smart_y0))
else:
smart_x0 = gp_map['x0']
smart_y0 = np.ndarray.flatten(smart_x0[:,0])
smart_lengthscales = np.array([np.log(1) for i in xrange(len(lengthscales))])
smart_noise_scale = np.log(np.var(smart_y0))
gp_map['cov_params'] = np.append(cov_params[0],smart_lengthscales)
gp_map['x0'] = smart_x0
gp_map['y0'] = smart_y0
#gp_map['noise_scale'] = smart_noise_scale
smart_map[layer][unit] = gp_map
smart_params = pack_deep_params(smart_map)
return smart_params
def fitMulticlass(self,X,y):
self.X = np.array(X) #converting X to np array
self.y = np.array(y) #converting y to np array
self.X = np.append(np.ones((self.X.shape[0],1)),self.X,axis=1)
self.totalFeatures = self.X.shape[1]
self.theta= np.zeros((self.totalFeatures,y.shape[1]))
for i in range(self.maxIterations):
softP = self.softmax(self.X, self.theta)
for j in range(self.y.shape[1]):
val = np.exp(self.X.dot(self.theta[:,j]))/softP
error = -(self.y[:,j]-val)
self.theta[:,j] = self.theta[:,j]- (self.learningRate * error.dot(self.X))/self.X.shape[0]
return self.theta
def predict(self, X):
"""
predicts according to the trained model
X: samples
return prediction
"""
self.X = X
bias = np.ones((self.X.shape[0], 1))
self.X = np.append(bias, self.X, axis=1)
self.X = np.array(self.X)
Z = 1 / (1 + np.exp(-(self.X.dot(self.coef_))))
Y = np.round(Z)
return Y
def step(self, action):
#Y = self.obs(self.x)
self.counter += 1
self.x, self.P, K = self.EKF(self.x, self.P, action)
self.L = np.linalg.cholesky(self.P)
ind_tril = np.tril_indices(self.L.shape[0])
done = self.terminal_state(self.x)
reward = self.reward_func(action)
self.state = np.append(self.x, self.L[ind_tril])
if self.counter > 256:
done = True
return self.state, reward, done, {}
def fparams(self):
"""
full parameter values
Appends xi to params if the kernel uses xi
Returns:
np.array(float) - params.append(xi)
"""
if self.kernel.use_xi:
return np.append(self.params, self.kernel.xi)
else:
return self.params
def dump_state(self, xk):
'''
callback to save the state to disk during optimization
'''
filename = 'state.txt'
if not os.path.exists(filename):
past = np.zeros((0, xk.shape[0]))
else:
past = np.loadtxt(filename)
if past.ndim < 2:
past = past.reshape(1, -1)
np.savetxt(filename, np.append(past, xk.reshape(1, -1), axis=0))
def predict_multi(self, X):
"""
predict multiclass output
X: samples
"""
bias = np.ones((X.shape[0], 1))
X = np.append(bias, X, axis=1)
X = np.array(X)
Z = 1 / (1 + np.exp(-(X.dot(self.coef_))))
Y = []
for i in Z:
Y.append(np.argmax(i))
return Y
def __init__(self):
self.counter = 0
self.targetUpdatefreq = 100 # Not being used
self.max_action = 0.01
self.world_box = np.array([[5.0, 5.0], [-5.0, -5.0]])
#self.min_position = np.array([-5.0, -5.0])
self.xlow = np.append(self.world_box[1], [0., -1., -1.])
self.xhigh = np.append(self.world_box[0], [2*pi, 1., 1.])
self.low_state = np.append(self.xlow, -10*np.ones(15)) #
self.high_state = np.append(self.xhigh, 10*np.ones(15)) #
self.action_space = spaces.Box(-np.ones(2), np.ones(2))
self.observation_space = spaces.Box(self.low_state, self.high_state)
self.viewer = None
#self.state = self.observation_space.sample()
self.noise = np.array([0.01]*5 + [0.2]*2) #std
dt = 0.1
self.Q = np.eye(5) * (0.01**2)
self.R = np.eye(2) * (0.2**2)
self.P = np.eye(5) * (0.0001**2)
self.Id = np.eye(5)
# initialize state
pos = random.uniform(self.world_box[0], self.world_box[1])
ang = math.atan2(pos[1], pos[1]) -pi + random.uniform(-pi/8, pi/8)
ang %= 2*pi
self.x = np.append(pos, [ang, 0., 0.])
self.L = np.linalg.cholesky(self.P)
self.goal_position = np.array([0., 0.])
self.A = jacobian(self.dynamics)
self.H = jacobian(self.obs)
self.seed()
self.reset()
def sdot(
self, S, t, params, Cin
): # X is population vector, t is time, R is intrinsic growth rate vector, C is the rate limiting nutrient vector, A is interaction matrix
'''
Calculates and returns derivatives for the numerical solver odeint
Parameters:
S: current state
t: current time
Cin: array of the concentrations of the auxotrophic nutrients and the
common carbon source
params: list parameters for all the equations
num_species: the number of bacterial populations
Returns:
dsol: array of the derivatives for all state variables
'''
# extract variables
# autograd gives t as an array_box, need to convert to int
if str(
type(t)
) == '<class \'autograd.numpy.numpy_boxes.ArrayBox\'>': # sort this out
t = t._value
t = int(t)
else:
t = int(t)
t = min(Cin.shape[0] - 1,
t) # to prevent solver from going past the max time
C0in = Cin[t]
#C0in = Cin
N = S[0]
C0 = S[1]
# extract parameters
q = self.ode_params[0]
y, Rmax = params[0:2]
Km = self.ode_params[3]
R = self.monod(C0, Rmax, Km)
# calculate derivatives
dN = N * (R.astype(float) - q) # q term takes account of the dilution
dC0 = q * (C0in - C0) - 1 / y * R * N
# consstruct derivative vector for odeint
dC0 = np.array([dC0])
dsol = np.append(dN, dC0)
return tuple(dsol)
def reward_func(self, action):
R = np.eye(4) * 1.25
P_reduced = np.delete(self.P, 2, 0)
P_reduced = np.delete(P_reduced, 2, 1)
#P_reduced = P_reduced + np.eye(4)*1e-4
P_ = inv(P_reduced)
S_ = inv(R) + P_
S = inv(S_)
mu = np.append(self.x[:2], self.x[3:])
a = -0.5 * np.dot(mu.T.dot(P_ - np.dot(P_.dot(S), P_)), mu)
reward = np.exp(a) * np.sqrt(np.linalg.det(S)/np.linalg.det(P_reduced)) #- np.sum(mu[:2]**2)
#reward -= 1.
reward -= -0.1*action[0]**2 + 1*action[1]**2 + 1.
return reward
def gradient(self, params):
# use the gradient if the model provides it.
# if not, compute it using autograd.
if not hasattr(self.mean, 'gradient'):
_grad = lambda mean, argnum, params: jacobian(mean, argnum)(*params)
else:
_grad = lambda mean, argnum, params: mean.gradient(*params)[argnum]
n_params = len(np.atleast_1d(params))
grad_likelihood = np.array([])
for i in range(n_params):
grad = _grad(self.mean, i, params)
grad_likelihood = np.append(grad_likelihood,
np.nansum(grad * (1 - self.data / self.mean(*params))))
return grad_likelihood
def __init__(self, breakpoints, *args, **kwargs):
breakpoints = np.sort(breakpoints)
if not (breakpoints[-1] < np.inf):
raise ValueError("Do not add inf to the breakpoints.")
if breakpoints[0] < 0:
raise ValueError("First breakpoint must be greater than 0.")
self.breakpoints = np.append(breakpoints, [np.inf])
n_breakpoints = len(self.breakpoints)
self._fitted_parameter_names = ["lambda_%d_" % i for i in range(n_breakpoints)]
super(PiecewiseExponentialFitter, self).__init__(*args, **kwargs)
def __init__(self):
self.counter = 0
self.episode_len = 1000
self.max_action = 1
self.world_box = np.array([[5.0, 5.0], [-5.0, -5.0]])
#self.min_position = np.array([-5.0, -5.0])
#self.xlow = np.append(self.world_box[1], [0., -1., -1.])
#self.xhigh = np.append(self.world_box[0], [2*pi, 1., 1.])
self.xlow = np.array([0., -pi, -1., -1.])
self.xhigh = np.array([8., pi, 1., 1.])
self.low_state = np.append(self.xlow, -5 * np.ones(15)) #
self.high_state = np.append(self.xhigh, 5 * np.ones(15)) #
self.action_space = spaces.Box(-np.ones(2), np.ones(2))
self.observation_space = spaces.Box(self.low_state, self.high_state)
self.viewer = None
#self.state = self.observation_space.sample()
self.noise = np.array([0.01] * 5 + [0.1] * 2) #std
self.dt = 0.1
self.Q = np.eye(5) * (0.01**2)
self.R = np.eye(2) * (0.1**2)
self.P = np.eye(5) * 0.
self.Id = np.eye(5)
self.A = jacobian(self.dynamics)
self.H = jacobian(self.obs)
self.goal_position = np.array([0., 0.])
self.goal_radius = 0.8
self.seed()
self.reset()
def __init__(self, name='', length=1, matrix_size=2, diag_lb=0.0, val=None):
self.name = name
self.__matrix_size = int(matrix_size)
self.__matrix_shape = np.array([ int(matrix_size), int(matrix_size) ])
self.__length = int(length)
self.__shape = np.append(self.__length, self.__matrix_shape)
# vec_size is the size of a single matrix in vector form.
self.__vec_size = int(matrix_size * (matrix_size + 1) / 2)
self.__diag_lb = diag_lb
assert diag_lb >= 0
if val is None:
default_val = np.diag(np.full(self.__matrix_size, diag_lb + 1.0))
self.__val = np.broadcast_to(default_val, self.__shape)
else:
self.set(val)
def l2_difference_minimisation(N, patterns, weights, biases, sc):
'''
minimisation of || lmbd*W @ Z - Z||
'''
Z = deepcopy(patterns).T.reshape(N, -1)
W = np.array([])
for i in range(N):
A = Z.T
b = Z[i, :]
if sc == False:
# add one more constraint to eliminate the diagonals
tmp = np.zeros((1, N))
tmp[0, i] = 1
A = np.vstack([A, tmp])
b = np.append(b, 0)
elif sc == True:
pass
else:
raise AttributeError(
'The \'sc\' parameter can take only boolean values')
w = lsqr(A, b)[0]
W = np.append(W, w)
weights = W.reshape(N, N)
return weights, biases
def gradient_function(self, w):
# separate w and w0
w0 = w[-1]
w = w[:-1]
eta = np.dot(self.x, w.T) + w0
grad_w = np.dot(
np.where(eta > 30, self.y - 1,
self.y - (np.exp(eta) / (1 + np.exp(eta)))), self.x)
grad_w_0 = np.dot(
np.where(eta > 30, self.y - 1,
self.y - (np.exp(eta) / (1 + np.exp(eta)))), 1)
print(grad_w_0)
return np.append(grad_w, grad_w_0)
def grouping(self, solution):
# grouping different groups in solution into one group
if self.number_group > 1:
# solution_help = np.zeros((solution.shape[0], 10))
# for i in range(10):
# solution_help[:, i] = np.sum(solution[:, i * self.number_group:(i+1) * self.number_group], axis=1)
# solution = solution_help
solution_help = []
for i in range(10):
solution_help = np.append(solution_help, np.sum(solution[:, i * self.number_group:(i+1) * self.number_group], axis=1))
solution = np.reshape(solution_help, (10, solution.shape[0])).T
return solution
def __init__(self, breakpoints, alpha=0.05, penalizer=0.0):
super(PiecewiseExponentialRegressionFitter, self).__init__(alpha=alpha)
breakpoints = np.sort(breakpoints)
if len(breakpoints) and not (breakpoints[-1] < np.inf):
raise ValueError("Do not add inf to the breakpoints.")
if len(breakpoints) and breakpoints[0] < 0:
raise ValueError("First breakpoint must be greater than 0.")
self.breakpoints = np.append(breakpoints, [np.inf])
self.n_breakpoints = len(self.breakpoints)
self.penalizer = penalizer
self._fitted_parameter_names = ["lambda_%d_" % i for i in range(self.n_breakpoints)]
def fit_autograd(self, X, y):
self.X = np.array(X) #converting X to np array
self.y = np.array(y) #converting y to np array
self.X = np.append(np.ones((self.X.shape[0],1)),self.X,axis=1) #appending columns of ones
self.theta = np.random.rand(self.X.shape[1])#np.ones(self.X.shape[1])#
agrad = elementwise_grad(self.costFunctionUnregularised)
agrad1 = elementwise_grad(self.costFunctionL1Regularised)
agrad2 = elementwise_grad(self.costFunctionL2Regularised)
for iterationNum in range(self.maxIterations):
if self.regularization == 'l1':
self.theta -= (self.learningRate*(agrad1(self.theta, self.X, self.y))) /(self.X.shape[0])
elif self.regularization == 'l2':
self.theta -= (self.learningRate*(agrad2(self.theta, self.X, self.y))) /(self.X.shape[0])
else:
self.theta -= (self.learningRate*(agrad(self.theta, self.X, self.y))) /(self.X.shape[0])
return self.theta
def chebyshev_centre(A, b, gamma):
rows, cols = A.shape
c = np.zeros(cols + 1)
c[-1] = -1
A_ = np.hstack([A, np.sqrt(np.sum(np.power(A, 2), axis=1)).reshape(-1, 1)])
A_ = np.vstack([A_, -c.reshape(1, -1)])
b_ = np.append(b, 100).reshape(-1, 1)
# l2 norm minimisation of w
P = gamma * np.eye(cols + 1)
P[:, -1] = P[-1, :] = 0
res = solve_qp(P=P, q=c, G=A_, h=b_)
x_c = np.array(res[:-1])
R = np.float(res[-1])
return x_c, R
def run_nn(N, input_size, output_size):
integer_part = int(np.floor(N[0]))
alpha = N[0] - integer_part
# Network parameters
layer_sizes = [input_size]
layer_sizes.extend([output_size for i in range(0, integer_part - 1)])
L2_reg = 1.0
# Training parameters
param_scale = 0.1
# Load and process wines data
N_data, train_images, train_labels, test_images, test_labels = get_wine_data()
batch_size = len(train_images)
# Make neural net functions
N_weights, pred_fun, loss_fun, frac_err = make_nn_funs(layer_sizes, L2_reg)
# Gradient with respect to weights and alpha
loss_grad_P = grad(loss_fun, 0)
# Initialize weights
rs = npr.RandomState(11)
W = rs.randn(N_weights) * param_scale
print(" Train err | Test err | Alpha")
f_out = open(filename, 'w')
f_out.write(" Train err | Test err | Alpha\n")
f_out.close()
def print_perf(params):
f_out = open(filename, 'a')
test_perf = frac_err(params, test_images, test_labels)
train_perf = frac_err(params, train_images, train_labels)
print("{0:15}|{1:15}|{2:15}".format(train_perf, test_perf, params[-1]))
f_out.write("{0:15}|{1:15}|{2:15}\n".format(train_perf, test_perf, params[-1]))
f_out.close()
# Minimize with BFGS
res = optimize.minimize(loss_fun, np.append(W, alpha), jac=loss_grad_P, method='L-BFGS-B', \
args=(train_images, train_labels), options={'disp': True, 'maxiter': 2})
print(res)
final_test_err = frac_err(res.x, train_images, train_labels)
print(N[0], final_test_err)
return final_test_err
def __init__(self, name='', array_shape=(1), matrix_size=2, diag_lb=0.0, val=None):
self.name = name
self.__matrix_size = int(matrix_size)
self.__matrix_shape = np.array([ int(matrix_size), int(matrix_size) ])
self.__array_shape = array_shape
self.__array_ranges = [ range(0, t) for t in self.__array_shape ]
self.__array_length = np.prod(self.__array_shape)
self.__shape = np.append(self.__array_shape, self.__matrix_shape)
# __vec_size is the size of a single matrix in vector form.
self.__vec_size = int(matrix_size * (matrix_size + 1) / 2)
self.__diag_lb = diag_lb
assert diag_lb >= 0
if val is None:
default_val = np.diag(np.full(self.__matrix_size, diag_lb + 1.0))
self.__val = np.broadcast_to(default_val, self.__shape)
else:
self.set(val)
def __init__(self, breakpoints, *args, **kwargs):
if (breakpoints is None) or (not list(breakpoints)):
raise ValueError("Breakpoints must be provided.")
if not (max(breakpoints) < np.inf):
raise ValueError("Do not add inf to the breakpoints.")
if min(breakpoints) <= 0:
raise ValueError("First breakpoint must be greater than 0.")
breakpoints = np.sort(breakpoints)
self.breakpoints = np.append(breakpoints, [np.inf])
n_breakpoints = len(self.breakpoints)
self._fitted_parameter_names = ["lambda_%d_" % i for i in range(n_breakpoints)]
super(PiecewiseExponentialFitter, self).__init__(*args, **kwargs)
def __init__(self, breakpoints, alpha=0.05, penalizer=0.0, fit_intercept=True):
super(PiecewiseExponentialRegressionFitter, self).__init__(alpha=alpha)
breakpoints = np.sort(breakpoints)
if len(breakpoints) and not (breakpoints[-1] < np.inf):
raise ValueError("Do not add inf to the breakpoints.")
if len(breakpoints) and breakpoints[0] < 0:
raise ValueError("First breakpoint must be greater than 0.")
self.breakpoints = np.append(breakpoints, [np.inf])
self.n_breakpoints = len(self.breakpoints)
self._hazard = egrad(self._cumulative_hazard, argnum=1) # pylint: disable=unexpected-keyword-arg
self.penalizer = penalizer
self.fit_intercept = fit_intercept
self._fitted_parameter_names = ["lambda_%d_" % i for i in range(self.n_breakpoints)]
def compute_restricted_hessian_and_dParamsdWeights(self, dims, weights,
comp_dParams_dWeights=True):
'''
Computes the dims.shape[0] by dims.shape[0] Hessian only along the entries
in dims (used when using l_1 regularization)
'''
theta0 = self.params.get_free()
# Objective to differentiate just along the dimensions specified
def lowDimObj(weights, thetaOnDims, thetaOffDims, invPerm):
allDims = np.append(dims, offDims)
thetaFull = np.append(thetaOnDims, thetaOffDims)[invPerm]
return self.weighted_model_objective(weights, thetaFull)
offDims = np.setdiff1d(np.arange(self.params.get_free().shape[0]), dims)
thetaOnDims = theta0[dims]
thetaOffDims = theta0[offDims]
# lowDimObj will concatenate thetaOnDims, thetaOffDims, then needs to
# un-permute them into the original theta.
allDims = np.append(dims, offDims)
invPerm = np.zeros(theta0.shape[0], dtype=np.int32)
for i, idx in enumerate(allDims):
invPerm[idx] = i
evalHess = autograd.hessian(lowDimObj, argnum=1)
array_box_go_away = self.params.get_free().copy()
restricted_hess = evalHess(weights,
thetaOnDims,
thetaOffDims,
invPerm)
self.params.set_free(theta0)
dObj_dParams = autograd.jacobian(lowDimObj, argnum=1)
d2Obj_dParamsdWeights = autograd.jacobian(dObj_dParams, argnum=0)
if comp_dParams_dWeights:
restricted_dParamsdWeights = d2Obj_dParamsdWeights(weights,
thetaOnDims,
thetaOffDims,
invPerm)
return restricted_hess, restricted_dParamsdWeights
else:
return restricted_hess
def predict_cumulative_hazard(self,
df,
times=None,
conditional_after=None) -> pd.DataFrame:
"""
Return the cumulative hazard rate of subjects in X at time points.
Parameters
----------
X: numpy array or DataFrame
a (n,d) covariate numpy array or DataFrame. If a DataFrame, columns
can be in any order. If a numpy array, columns must be in the
same order as the training data.
times: iterable, optional
an iterable of increasing times to predict the cumulative hazard at. Default
is the set of all durations (observed and unobserved). Uses a linear interpolation if
points in time are not in the index.
Returns
-------
cumulative_hazard_ : DataFrame
the cumulative hazard of individuals over the timeline
"""
if isinstance(df, pd.Series):
return self.predict_cumulative_hazard(df.to_frame().T)
if conditional_after is not None:
raise NotImplementedError()
times = np.atleast_1d(
coalesce(times, self.timeline,
np.unique(self.durations))).astype(float)
n = times.shape[0]
times = times.reshape((n, 1))
lambdas_ = self._prep_inputs_for_prediction_and_return_parameters(df)
bp = np.append(self.breakpoints, [np.inf])
M = np.minimum(np.tile(bp, (n, 1)), times)
M = np.hstack([M[:, tuple([0])], np.diff(M, axis=1)])
return pd.DataFrame(np.dot(M, (1 / lambdas_)),
columns=_get_index(df),
index=times[:, 0])
def simple_contour(f, c=0, delta=0.01):
'''Donne les coordonnées demandées sur un cadre de côté unitaire de manière optimisée'''
x = np.array([])
y = np.array([])
def g(x):
return (f(0, x))
if find_seed(g, c) == None:
return x, y
y = np.append(y, np.array([find_seed(g, c)]))
x = np.append(x, np.array([0]))
grad = gradient(f, x[-1], y[-1])
tang = [-grad[1], grad[0]]
print(tang)
if tang[0] < 0:
tang = [grad[1], -grad[0]]
while x[-1] <= 1 and y[-1] <= 1 and x[-1] >= 0 and y[-1] >= 0:
grad = gradient(f, x[-1], y[-1])
tang = [grad[1], -grad[0]]
norme = math.sqrt(tang[0]**2 + tang[1]**2)
x = np.append(x, np.array(x[-1] + (delta * tang[0]) / (norme)))
y = np.append(y, np.array(y[-1] + (delta * tang[1]) / (norme)))
def F(
x, y
): #On définit la fonction F pour les deux derniers points trouvés
return np.array(
[f(x, y) - c, (x - x[-2])**2 + (y - y[-2])**2 - delta**2])
res = newton(
F, np.array([x[-1], y[-1]])
) #On applique Newton: ATTENTION, un problème non résolu apparait lors de l'éxécution de autograd.jacobian
x[-1], y[-1] = res[0], res[1]
else:
tang = [-grad[1], grad[0]]
while x[-1] <= (1) and y[-1] <= (1) and x[-1] >= 0 and y[-1] >= 0:
grad = gradient(f, x[-1], y[-1])
tang = [-grad[1], grad[0]]
norme = math.sqrt(tang[0]**2 + tang[1]**2)
x = np.append(x, np.array(x[-1] + (delta * tang[0]) / (norme)))
y = np.append(y, np.array(y[-1] + (delta * tang[1]) / (norme)))
def F(x, y):
return np.array(
[f(x, y) - c, (x - x[-2])**2 + (y - y[-2])**2 - delta**2])
res = newton(F, np.array([x[-1], y[-1]]))
x[-1], y[-1] = res[0], res[1]
return x, y
def forward(self, model, x_traj, u_traj, k_traj, K_traj, alpha):
x_traj_new = np.array(x_traj)
u_traj_new = np.array(u_traj)
for t in range(len(u_traj)):
control = alpha**t * k_traj[t] + np.matmul(
K_traj[t], (x_traj_new[t] - x_traj[t]))
u_traj_new[t] = np.clip(u_traj[t] + control, -2, 2)
# Create the vector of observations X={x,u}
observations = np.array([np.append(x_traj_new[t], u_traj_new[t])])
# Comment for Task 4
test_predict = x_traj_new[t] + model.predict(observations)
# TODO Task 4: use the dynamics of the system instead of the learned model compute the next state -- DONE
x_traj_new[t + 1] = test_predict
# x_traj_new[t + 1] = self.f(x_traj_new[t], u_traj_new[t])
return x_traj_new, u_traj_new
def cost(S, v):
# Unpack parameters
nu = np.append(v, 0)
logdetS = np.expand_dims(np.linalg.slogdet(S)[1], 1)
y = np.concatenate([samples.T, np.ones((1, N))], axis=0)
# Calculate log_q
y = np.expand_dims(y, 0)
# 'Probability' of y belonging to each cluster
log_q = -0.5 * (np.sum(y * np.linalg.solve(S, y), axis=1) + logdetS)
alpha = np.exp(nu)
alpha = alpha / np.sum(alpha)
alpha = np.expand_dims(alpha, 1)
loglikvec = logsumexp(np.log(alpha) + log_q, axis=0)
return -np.sum(loglikvec)
def init_yields(self, quiet=False):
nf = len(self.KL_amplitude_files)
npar = len(self.param_sets)
total_yields = nf * npar
if not quiet:
print "Making yields for bias study:"
print " # of params : {}".format(npar)
print " # of A(KL)'s : {}".format(nf)
print " # TOTAL yield sets : {}".format(total_yields)
yield_n = 0
if not quiet: print(" Yield gen: {}/{}".format(yield_n, total_yields))
for fi, f in enumerate(self.KL_amplitude_files):
self.generator_model.load_KL_amplitude(f)
for pi, p in enumerate(self.param_sets):
physics_param = p
sys.stdout.write("\033[F") #back to previous line
sys.stdout.write("\033[K") #clear line
yield_n += 1
if not quiet:
print(" Yield gen: {}/{}".format(yield_n, total_yields))
if len(p) == 3:
# single channel setup
avg_yields = self.generator_model.predict_yields(
p, self.N_signal[0]
) # Yields calculated using FullModel.py
elif len(p) == 5:
# two channel channel setup
avg_yields_ch1 = self.generator_model.predict_yields(
p[0:3], self.N_signal[0]
) # Yields calculated using FullModel.py
avg_yields_ch2 = self.generator_model.predict_yields(
[p[0], p[3], p[4]], self.N_signal[1]
) # Yields calculated using FullModel.py
avg_yields = np.append(avg_yields_ch1, avg_yields_ch2)
self.yields["{}_{}".format(fi, pi)] = avg_yields
self.yields_init = True
def fit(self, X, y):
"""
trains the model
X: samples
y: labels
returns trained weights
"""
self.X = X.copy()
bias = np.ones((self.X.shape[0], 1))
self.X = np.append(bias, self.X, axis=1) # Include Bais
self.X = np.array(self.X)
self.y = y
self.nofFeatures = len(self.X[0])
self.samples = len(self.X)
self.coef_ = np.ones(self.nofFeatures) # init features
for i in range(self.epoch):
err = self.sigmoid(self.X.dot(self.coef_)) - y # error
self.coef_ = self.coef_ - self.lr * (err).dot(self.X) # coef
return self.coef_
def yields_chi_square(self, xy_and_Fi, *args):
''' The function to me minimized when fitting x, y, is the chi-square
xy_Fi: a list with elements [{Fi}, xm, ym, xp, yp]
data: The yields to which the fit is being made
'''
data = args[0]
Nplus = sum(data[0:len(data)/2]) # B+
Nminus = sum(data[len(data)/2:]) # B-
xy = xy_and_Fi[0:4]
Fi = xy_and_Fi[4:]
Fi = np.append(Fi, 1-sum(Fi))
predictions = self.predict_yields(xy, Nplus, Nminus, Fi=Fi)
uncertainty_squared = data
for i, u in enumerate(uncertainty_squared):
if u==0: uncertainty_squared[i]=1 # make sure there are no divisions by zero
minLL = np.sum(0.5*(data - predictions)**2/uncertainty_squared) # least squares fit
return minLL
f_out.close()
def print_perf(params):
f_out = open(filename, 'a')
test_perf = frac_err(params, test_images, test_labels)
train_perf = frac_err(params, train_images, train_labels)
print("{0:15}|{1:15}|{2:15}".format(train_perf, test_perf, params[-1]))
f_out.write("{0:15}|{1:15}|{2:15}\n".format(train_perf, test_perf, params[-1]))
f_out.close()
# Minimize with BFGS
num_iterations = []
train_errors = []
test_errors = []
for i in range(0, 100):
optimize.minimize(loss_fun, np.append(W, alpha), jac=loss_grad_P, method='L-BFGS-B', \
args=(train_images, train_labels), options={'disp': True}, callback=print_perf)
training_error = 0.
test_error = 0.
with open(filename, 'r') as input_file:
next(input_file)
curr_iteration = 0
for line in input_file:
data_as_string = line.split('|')
data = map(float, data_as_string)
training_error = data[0]
test_error = data[1]
curr_iteration += 1
num_iterations.append(curr_iteration)
def minConf_SPG(funObj, x, funProj, options=None):
""" This function implements Mark Schmidt's MATLAB implementation of
spectral projected gradient (SPG) to solve for projected quasi-Newton
direction
min funObj(x) s.t. x in C
Parameters
----------
funObj: function that returns objective function value and the gradient
x: initial parameter value
funProj: fcuntion that returns projection of x onto C
options:
verbose: level of verbosity (0: no output, 1: final, 2: iter (default), 3:
debug)
optTol: tolerance used to check for optimality (default: 1e-5)
progTol: tolerance used to check for lack of progress (default: 1e-9)
maxIter: maximum number of calls to funObj (default: 500)
numDiff: compute derivatives numerically (0: use user-supplied
derivatives (default), 1: use finite differences, 2: use complex
differentials)
suffDec: sufficient decrease parameter in Armijo condition (default
: 1e-4)
interp: type of interpolation (0: step-size halving, 1: quadratic,
2: cubic)
memory: number of steps to look back in non-monotone Armijo
condition
useSpectral: use spectral scaling of gradient direction (default:
1)
curvilinear: backtrack along projection Arc (default: 0)
testOpt: test optimality condition (default: 1)
feasibleInit: if 1, then the initial point is assumed to be
feasible
bbType: type of Barzilai Borwein step (default: 1)
Notes:
- if the projection is expensive to compute, you can reduce the
number of projections by setting testOpt to 0
"""
nVars = x.shape[0]
options_default = {'verbose':2, 'numDiff':0, 'optTol':1e-5, 'progTol':1e-9,\
'maxIter':500, 'suffDec':1e-4, 'interp':2, 'memory':10,\
'useSpectral':1,'curvilinear':0,'feasibleInit':0,'testOpt':1,\
'bbType':1}
options = setDefaultOptions(options, options_default)
if options['verbose'] >= 2:
if options['testOpt'] == 1:
print '{:10s}'.format('Iteration') + \
'{:10s}'.format('FunEvals') + \
'{:10s}'.format('Projections') + \
'{:15s}'.format('StepLength') + \
'{:15s}'.format('FunctionVal') + \
'{:15s}'.format('OptCond')
else:
print '{:10s}'.format('Iteration') + \
'{:10s}'.format('FunEvals') + \
'{:10s}'.format('Projections') + \
'{:15s}'.format('StepLength') + \
'{:15s}'.format('FunctionVal')
funEvalMultiplier = 1
# evaluate initial point
if options['feasibleInit'] == 0:
x = funProj(x)
[f, g] = funObj(x)
projects = 1
funEvals = 1
# optionally check optimality
if options['testOpt'] == 1:
projects = projects + 1
if np.max(np.abs(funProj(x-g)-x)) < options['optTol']:
if options['verbose'] >= 1:
print "First-order optimality conditions below optTol at initial point"
return (x, f, funEvals, projects)
i = 1
while funEvals <= options['maxIter']:
# compute step direction
if i == 1 or options['useSpectral'] == 0:
alpha = 1.
else:
y = g - g_old
s = x - x_old
if options['bbType'] == 1:
alpha = np.dot(s,s)/np.dot(s,y)
else:
alpha = np.dot(s,y)/np.dot(y,y)
if alpha <= 1e-10 or alpha >= 1e10:
alpha = 1.
d = -alpha * g
f_old = f
x_old = x
g_old = g
# compute projected step
if options['curvilinear'] == 0:
d = funProj(x+d) - x
projects = projects + 1
# check that progress can be made along the direction
gtd = np.dot(g, d)
if gtd > -options['progTol']:
if options['verbose'] >= 1:
print "Directional derivtive below progTol"
break
# select initial guess to step length
if i == 1:
t = np.minimum(1., 1./np.sum(np.abs(g)))
else:
t = 1.
# compute reference function for non-monotone condition
if options['memory'] == 1:
funRef = f
else:
if i == 1:
old_fvals = np.ones(options['memory'])*(-1)*np.infty
if i <= options['memory']:
old_fvals[i-1] = f
else:
old_fvals = np.append(old_fvals[1:], f)
funRef = np.max(old_fvals)
# evaluate the objective and gradient at the initial step
if options['curvilinear'] == 1:
x_new = funProj(x + t*d)
projects = projects + 1
else:
x_new = x + t*d
[f_new, g_new] = funObj(x_new)
funEvals = funEvals + 1
# Backtracking line search
lineSearchIters = 1
while f_new > funRef + options['suffDec']*np.dot(g,x_new-x) or \
isLegal(f_new) == False:
temp = t
if options['interp'] == 0 or isLegal(f_new) == False:
if options['verbose'] == 3:
print 'Halving step size'
t = t/2.
elif options['interp'] == 2 and isLegal(g_new):
if options['verbose'] == 3:
print "Cubic Backtracking"
t = polyinterp(np.array([[0,f,gtd],\
[t,f_new,np.dot(g_new,d)]]))[0]
elif lineSearchIters < 2 or isLegal(f_prev):
if options['verbose'] == 3:
print "Quadratic Backtracking"
t = polyinterp(np.array([[0, f, gtd],\
[t, f_new, np.complex(0,1)]]))[0]
else:
if options['verbose'] == 3:
print "Cubic Backtracking on Function Values"
t = polyinterp(np.array([[0., f, gtd],\
[t,f_new,np.complex(0,1)],\
[t_prev,f_prev,np.complex(0,1)]]))[0]
# adjust if change is too small
if t < temp*1e-3:
if options['verbose'] == 3:
print "Interpolated value too small, Adjusting"
t = temp * 1e-3
elif t > temp * 0.6:
if options['verbose'] == 3:
print "Interpolated value too large, Adjusting"
t = temp * 0.6
# check whether step has become too small
if np.max(np.abs(t*d)) < options['progTol'] or t == 0:
if options['verbose'] == 3:
print "Line Search failed"
t = 0.
f_new = f
g_new = g
break
# evaluate new point
f_prev = f_new
t_prev = temp
if options['curvilinear'] == True:
x_new = funProj(x + t*d)
projects = projects + 1
else:
x_new = x + t*d
[f_new, g_new] = funObj(x_new)
funEvals = funEvals + 1
lineSearchIters = lineSearchIters + 1
# done with line search
# take step
x = x_new
f = f_new
g = g_new
if options['testOpt'] == True:
optCond = np.max(np.abs(funProj(x-g)-x))
projects = projects + 1
# output log
if options['verbose'] >= 2:
if options['testOpt'] == True:
print '{:10d}'.format(i) + \
'{:10d}'.format(funEvals*funEvalMultiplier) + \
'{:10d}'.format(projects) + \
'{:15.5e}'.format(t) + \
'{:15.5e}'.format(f) + \
'{:15.5e}'.format(optCond)
else:
print '{:10d}'.format(i) + \
'{:10d}'.format(funEvals*funEvalMultiplier) + \
'{:10d}'.format(projects) + \
'{:15.5e}'.format(t) + \
'{:15.5e}'.format(f)
# check optimality
if options['testOpt'] == True:
if optCond < options['optTol']:
if options['verbose'] >= 1:
print "First-order optimality conditions below optTol"
break
if np.max(np.abs(t*d)) < options['progTol']:
if options['verbose'] >= 1:
print "Step size below progTol"
break
if np.abs(f-f_old) < options['progTol']:
if options['verbose'] >= 1:
print "Function value changing by less than progTol"
break
if funEvals*funEvalMultiplier > options['maxIter']:
if options['verbose'] >= 1:
print "Function evaluation exceeds maxIter"
break
i = i + 1
return (x, f, funEvals, projects)
def polyinterp(points, doPlot=None, xminBound=None, xmaxBound=None):
""" polynomial interpolation
Parameters
----------
points: shape(pointNum, 3), three columns represents x, f, g
doPolot: set to 1 to plot, default 0
xmin: min value that brackets minimum (default: min of points)
xmax: max value that brackets maximum (default: max of points)
set f or g to sqrt(-1)=1j if they are not known
the order of the polynomial is the number of known f and g values minus 1
Returns
-------
minPos:
fmin:
"""
if doPlot == None:
doPlot = 0
nPoints = points.shape[0]
order = np.sum(np.imag(points[:, 1:3]) == 0) -1
# code for most common case: cubic interpolation of 2 points
if nPoints == 2 and order == 3 and doPlot == 0:
[minVal, minPos] = [np.min(points[:,0]), np.argmin(points[:,0])]
notMinPos = 1 - minPos
d1 = points[minPos,2] + points[notMinPos,2] - 3*(points[minPos,1]-\
points[notMinPos,1])/(points[minPos,0]-points[notMinPos,0])
t_d2 = d1**2 - points[minPos,2]*points[notMinPos,2]
if t_d2 > 0:
d2 = np.sqrt(t_d2)
else:
d2 = np.sqrt(-t_d2) * np.complex(0,1)
if np.isreal(d2):
t = points[notMinPos,0] - (points[notMinPos,0]-points[minPos,0])*\
((points[notMinPos,2]+d2-d1)/(points[notMinPos,2]-\
points[minPos,2]+2*d2))
minPos = np.min([np.max([t,points[minPos,0]]), points[notMinPos,0]])
else:
minPos = np.mean(points[:,0])
fmin = minVal
return (minPos, fmin)
xmin = np.min(points[:,0])
xmax = np.max(points[:,0])
# compute bounds of interpolation area
if xminBound == None:
xminBound = xmin
if xmaxBound == None:
xmaxBound = xmax
# constraints based on available function values
A = np.zeros((0, order+1))
b = np.zeros((0, 1))
for i in range(nPoints):
if np.imag(points[i,1]) == 0:
constraint = np.zeros(order+1)
for j in np.arange(order,-1,-1):
constraint[order-j] = points[i,0]**j
A = np.vstack((A, constraint))
b = np.append(b, points[i,1])
# constraints based on availabe derivatives
for i in range(nPoints):
if np.isreal(points[i,2]):
constraint = np.zeros(order+1)
for j in range(1,order+1):
constraint[j-1] = (order-j+1)* points[i,0]**(order-j)
A = np.vstack((A, constraint))
b = np.append(b,points[i,2])
# find interpolating polynomial
params = np.linalg.solve(A, b)
# compute critical points
dParams = np.zeros(order)
for i in range(params.size-1):
dParams[i] = params[i] * (order-i)
if np.any(np.isinf(dParams)):
cp = np.concatenate((np.array([xminBound, xmaxBound]), points[:,0]))
else:
cp = np.concatenate((np.array([xminBound, xmaxBound]), points[:,0], \
np.roots(dParams)))
# test critical points
fmin = np.infty;
minPos = (xminBound + xmaxBound)/2.
for xCP in cp:
if np.imag(xCP) == 0 and xCP >= xminBound and xCP <= xmaxBound:
fCP = np.polyval(params, xCP)
if np.imag(fCP) == 0 and fCP < fmin:
minPos = np.double(np.real(xCP))
fmin = np.double(np.real(fCP))
# plot situation (omit this part for now since we are not going to use it
# anyway)
return (minPos, fmin)
def pack_gp_params(mean, cov_params, noise_scale, x0, y0):
params = np.append(mean,noise_scale)
params = np.concatenate([params,cov_params])
params = np.concatenate([params,np.ndarray.flatten(np.array(x0))])
params = np.concatenate([params,np.ndarray.flatten(np.array(y0))])
return params
layer_gp_params = unpack_layer_params[layer](layer_params)
for dim in xrange(dimensions[layer+1]):
gp_params = layer_gp_params[dim]
mean, cov_params, noise_scale, x0, y0 = unpack_gp_params_all[layer][dim](gp_params)
lengthscales = cov_params[1:]
if layer == 0:
pairs = itertools.combinations(X, 2)
dists = np.array([np.abs(p1-p2) for p1,p2 in pairs])
smart_lengthscales = np.array([np.log(np.median(dists[:,i])) for i in xrange(len(lengthscales))])
smart_x0 = np.array(X)[rs.choice(len(X), num_pseudo_params, replace=False),:]
smart_y0 = np.ndarray.flatten(smart_x0)
else:
smart_x0 = x0
smart_y0 = np.ndarray.flatten(x0)
smart_lengthscales = np.array([np.log(1) for i in xrange(len(lengthscales))])
cov_params = np.append(cov_params[0],smart_lengthscales)
params = pack_gp_params_all[layer][dim](mean, cov_params, noise_scale, smart_x0, smart_y0)
smart_params = np.append(smart_params, params)
init_params = smart_params
print("Optimizing covariance parameters...")
objective = lambda params: -log_likelihood(params)
params = minimize(value_and_grad(objective), init_params, jac=True,
method='BFGS', callback=callback)
plt.pause(10.0)
#Correct
def KL_via_sampling(params,a2,b2,U):
a1 = params[0]
b1 = params[1]
theta = generate_kumaraswamy(params,U)
E = np.log(kumaraswamy_pdf(theta,params)/kumaraswamy_pdf(theta,np.array([a2,b2])))
E = np.mean(E)
return E
if __name__=='__main__':
n = 100
k = 80
params = np.random.uniform(10,100,2)
params = np.append(params,1.)
m = np.array([0.,0.,0.])
v = np.array([0.,0.,0.])
for i in range(50000):
params,m,v = iterate(params,n,k,i,m,v)
if i%100==0:
print params
#print m,v
#U1=np.random.uniform(0,1,100)
#U2=np.random.uniform(0,1,100)
#U3=np.random.uniform(0,1,n)
#print lower_bound(params,n,k,U1,U2,U3)
print params
plt.clf()
print "true mean"
print (k+1.)/(n+2.)
def pack_gp_params(gp_details):
params = np.append(gp_details["mean"], gp_details["noise_scale"])
params = np.concatenate([params, gp_details["cov_params"]])
params = np.concatenate([params, np.ndarray.flatten(np.array(gp_details["x0"]))])
params = np.concatenate([params, np.ndarray.flatten(np.array(gp_details["y0"]))])
return params
def pack_gp_params(gp_details):
params = np.append(gp_details['mean'],gp_details['noise_scale'])
params = np.concatenate([params,gp_details['cov_params']])
params = np.concatenate([params,np.ndarray.flatten(np.array(gp_details['x0']))])
params = np.concatenate([params,np.ndarray.flatten(np.array(gp_details['y0']))])
return params
