def run(F, X, y):
# Your code goes here
S = []
J = [i for i in range(0, len(X[0]))] # no of features
for f in range(1, F + 1):
# get list of features to iterate on.
f_iter = []
for t in J:
if not (t in S):
f_iter.append(t)
best_j = None
min_error = float("inf")
for j in f_iter:
# get X_ = x_{t,sUj}
S_t = [i for i in S]
S_t.append(j)
X_ = X[:, S_t]
theta_s_u_j = linreg.run(X_, y)
# use theta_s_u_j to get training error
error = (0.5) * np.sum((y - np.dot(X_, theta_s_u_j))**2)
if error < min_error:
min_error = error
best_j = j
S.append(best_j)
#thetaS
X_ = X[:, S]
thetaS = linreg.run(X_, y)
return (np.asarray(S).reshape(F, 1), thetaS)
def run(F,X,y):
n=len(X)
d=len(X[0])
S=[]
for f in range(1, F+1):
MP=dict()
for j in range(d):
if j not in S:
tmpS=S+[j]
thetaS=linreg.run(X[:, tmpS], y)
J=SUM(X[:, tmpS], y, thetaS)
MP.setdefault(J, j)
S+=[MP[min(MP.keys())]]
return (np.asarray(S).reshape((F, 1)), linreg.run(X[:, S], y))
def run(B, X, y):
n = len(X)
d = len(X[0])
z = np.zeros((B, 1))
for i in range(0, B):
u = [0] * n
S = []
for j in range(0, n):
k = np.random.randint(n)
u[j] = k
if not (k in S):
S.append(k)
Se = []
for k in range(0, n):
Se.append(k)
T = list(set(Se) - set(S))
thetahat = linreg.run(X[u, :], y[u, :])
thetahat = thetahat.T
thetahat = np.reshape(thetahat, (np.product(thetahat.shape),))
sumi = 0
for t in T:
sumi = sumi + (y[t][0] - np.dot(thetahat, X[t])) ** 2
z[i][0] = sumi / len(T)
return z
def run(F, X, y):
n = len(X)
d = len(X[0])
S = []
thetaS = np.zeros((F, 1))
tT = np.zeros((d, 1))
for f in range(0, F):
z = np.zeros(n)
tx = []
for j in S:
tx.append(j)
for t in range(0, n):
z[t] = y[t] - np.dot(np.squeeze(tT[tx]), np.squeeze(X[t, tx]))
DJ = np.zeros(d)
for j in range(0, d):
if j not in S:
for t in range(0, n):
DJ[j] -= z[t] * X[t][j]
jp = 0
tmpS = 0
for i in range(0, d):
if (jp < abs(DJ[i]) and i not in S):
jp = abs(DJ[i])
tmpS = i
tT[tmpS] = linreg.run(X[:, [tmpS]], z)
S.append(tmpS)
for i in range(0, F):
thetaS[i] = tT[S[i]]
return (S, thetaS)
def run(B, X, y):
n, d = X.shape
z = np.zeros((B, 1))
for i in range(B):
u = [0] * n
S = set()
for j in range(n):
k = np.random.randint(n)
u[j] = k
S.add(k)
yU = np.zeros((n, 1))
XU = np.zeros((n, d))
for j in range(n):
yU[j] = y[u[j]]
XU[j] = X[u[j]]
T = set(range(n)) - S
thetaHat = linreg.run(XU, yU)
summ = 0
for t in T:
summ += (y[t] - np.dot(X[t], thetaHat))**2
z[i] = (1.0 / len(T)) * summ
return z
def run(F, X, y):
n = len(X)
d = len(X[0])
S = []
thetaS = np.zeros((F, 1))
tT = np.zeros((d, 1))
for f in range(0, F):
J = np.ones((d, 1))
J = -J
z = np.zeros(n)
tx = []
for i in S:
tx.append(i)
for t in range(0, n):
z[t] = y[t] - np.dot(np.squeeze(tT[tx]), np.squeeze(X[t, tx]))
for j in range(0, d):
if j not in S: tT[j] = linreg.run(X[:, [j]], z)
for t in range(0, n):
J[j] += (z[t] - np.dot(tT[j], X[t, j]))**2 / 2
jp = 100000
tmpS = 0
for i in range(0, d):
if (J[i] > 0 and jp > J[i]):
jp = J[i]
tmpS = i
S.append(tmpS)
for i in range(0, F):
thetaS[i] = tT[S[i]]
return (S, thetaS)
def predict():
x = float(request.args.get('x')) / 100
y = float(request.args.get('y')) / 100
z = float(request.args.get('z')) / 100
year = request.args.get('year') # TODO
X = np.array([x, y, z])
# Round to three decimal places, convert to string, and return
return str(round(linreg.run(X, year), 3))
def run(F, X, y):
setS = set()
finalS = []
n, d = X.shape
completeSet = set(range(d))
for f in range(1, F + 1):
J = {}
for j in completeSet - setS:
# Current set to test: S with j
SJ = setS.copy()
SJ.add(j)
# Build matrix X with only features in set SJ
# This will let us do the linear regression with ony those features
tempX = np.delete(X, list(completeSet - SJ), 1)
# Obtain beta vector (argmin)
thetaSJ = linreg.run(tempX, y)
# Build summatory for the beta vector
# This will result in min, as the beta vector is the argmin
summ = 0
for t in range(n):
summ += (y[t] - np.dot(tempX[t], thetaSJ))**2
# Store minimization for this current set
J[j] = 0.5 * summ
# Obtain j with bext minimization
jHat, _ = min(J.items(), key=lambda x: x[1])
# Adds J to final set S
setS.add(jHat)
finalS.append(jHat)
# Build matrix X with only features in final set S
# This will let us do the linear regression with ony those features
tempX = np.delete(X, list(completeSet - setS), 1)
# Compute linear regresion for final set
thetaS = linreg.run(tempX, y)
# Change S format to numpy vector
S = np.reshape(finalS, (F, 1))
return (S, thetaS)
def run(F,X,y):
n, d = X.shape
S = set()
finalS = []
completeSet = set(range(d))
thetaS = np.array([])
z = np.zeros((n, 1))
for _ in range(F):
# Build X matrix for only the features in set S => delete values from complete set - S
XS = np.delete(X,list(completeSet-S),1)
for t in range(n):
dot = np.dot(XS[t], thetaS)
z[t] = y[t] - dot
J = {}
for j in completeSet-S:
# Obtain beta vector (argmin).
# Convert vector of features j into a proper two dimensional array
thetaJ = linreg.run(np.reshape(X[:,j], (n,1)), z)
# Build summatory for the beta vector
# This will result in min, as the beta vector is the argmin
summ = 0
for t in range(n):
summ += (z[t] - thetaJ*X[t][j])**2
# Store minimization for this current set
J[j] = (0.5 * summ[0][0], thetaJ)
#print "thetaJ candidate", thetaJ
# Obtain j with bext minimization (And its corresponding thetaJ)
jHat, (_, thetaJ) = min(J.items(), key=lambda x:x[1][0])
# print "MIN", jHat
# print "minTheta", thetaJ
# Constructs final thetaS
if len(thetaS) == 0:
thetaS = thetaJ
else:
thetaS = np.block([
[thetaS],
[thetaJ]
])
#print "thetaS", thetaS
# Adds J to final set S
S.add(jHat)
finalS.append(jHat)
# Reshape set as numpy list
S = np.reshape(finalS, (F, 1))
return (S, thetaS)
def run(F,X,y):
n, d = X.shape
S = set()
finalS = []
completeSet = set(range(d))
thetaS = np.array([])
z = np.zeros((n, 1))
for _ in range(F):
# Build X matrix for only the features in set S => delete values from complete set - S
XS = np.delete(X,list(completeSet-S),1)
for t in range(n):
dot = np.dot(XS[t], thetaS)
z[t] = y[t] - dot
J = {}
for j in completeSet-S:
summ = 0
for t in range(n):
summ += (z[t]*X[t][j])
# Store minimization for this current set
J[j] = abs(-summ[0])
#print "j candidate", j, "->", -summ[0]
# Obtain j with bext minimization (And its corresponding thetaJ)
jHat, _ = max(J.items(), key=lambda x:x[1])
# print "MAX ", jHat
# Compute weight for selected jHat
thetaJ = linreg.run(np.reshape(X[:,jHat], (n,1)), z)
# print "maxTheta", thetaJ
# Constructs final thetaS
if len(thetaS) == 0:
thetaS = thetaJ
else:
thetaS = np.block([
[thetaS],
[thetaJ]
])
#print "thetaS", thetaS
# Adds J to final set S
S.add(jHat)
finalS.append(jHat)
# Reshape set as numpy list
S = np.reshape(finalS, (F, 1))
return (S, thetaS)
def run(F, X, y):
# Your code goes here
S = []
theta_s = np.empty((0, 0))
# print theta_s
J = [i for i in range(0, len(X[0]))] # no of features
for f in range(1, F + 1):
# calculate z
X_s = X[:, S]
if len(S) == 0:
z = np.copy(y)
else:
z = y - np.dot(X_s, theta_s)
# get list of features to iterate on.
f_iter = []
for t in J:
if not (t in S):
f_iter.append(t)
best_j = None
max_effect = float("-inf")
best_theta_j = None
for j in f_iter:
# get X_ = x_{t,j}
X_j_temp = X[:, j]
X_j = X_j_temp.reshape(len(X_j_temp), 1)
effect = (-1) * np.asscalar(np.dot(z.T, X_j))
effect = abs(effect)
if (effect > max_effect):
max_effect = effect
best_j = j
best_X_j = X_j
best_X_j_temp = X[:, best_j]
best_X_j = best_X_j_temp.reshape(len(best_X_j_temp), 1)
best_theta_j = linreg.run(best_X_j, z)
S.append(best_j)
# update thetaS with concatenation of best_theta_j
theta_s = np.append(theta_s, best_theta_j)
theta_s = theta_s.reshape(len(theta_s), 1)
return (np.asarray(S).reshape(F, 1), theta_s)
def run(F, X, y):
# Your code goes here
S = []
theta_s = np.empty((0, 0))
# print theta_s
J = [i for i in range(0, len(X[0]))] # no of features
for f in range(1, F + 1):
# calculate z
X_s = X[:, S]
if len(S) == 0:
z = np.copy(y)
else:
z = y - np.dot(X_s, theta_s)
# get list of features to iterate on.
f_iter = []
for t in J:
if not (t in S):
f_iter.append(t)
best_j = None
min_error = float("inf")
best_theta_j = None
for j in f_iter:
# get X_ = x_{t,j}
X_j_temp = X[:, j]
X_j = X_j_temp.reshape(len(X_j_temp), 1)
theta_j = linreg.run(X_j, z)
# use theta_j to get training error
error = (1 / 2.0) * np.sum((z - np.dot(X_j, theta_j))**2)
if error < min_error:
min_error = error
best_j = j
best_theta_j = theta_j
S.append(best_j)
# update thetaS with concatenation of best_theta_j
theta_s = np.append(theta_s, best_theta_j)
theta_s = theta_s.reshape(len(theta_s), 1)
#thetaS
return (np.asarray(S).reshape(F, 1), theta_s)
def run(k, X, y):
n, _ = X.shape
z = np.zeros((k, 1))
for i in range(k):
T = set(
range(int(np.floor((n * i) / k)),
int(np.floor(((n * (i + 1)) / k) - 1)) + 1))
S = set(range(0, n)) - T
tList = list(T)
tList.sort()
SX = np.delete(X, tList, 0)
Sy = np.delete(y, tList, 0)
thetaHat = linreg.run(SX, Sy)
summ = 0
for t in T:
summ += (y[t] - np.dot(X[t], thetaHat))**2
z[i] = (1.0 / len(T)) * summ
return z