-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathonline_algorithms.R
251 lines (209 loc) · 7.51 KB
/
online_algorithms.R
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
### projection for ONS
generalized_projection <- function(P,theta,D) {
x <- CVXR::Variable(d)
objective <- CVXR::Minimize(CVXR::matrix_frac(x-theta, P)) # min (x-theta) P^-1 (x-theta)
constraint <- list(CVXR::norm2(x) <= D) # s.t. norm(x) <= D
prob <- CVXR::Problem(objective, constraint)
result <- CVXR::solve(prob)
if (result$status != 'optimal')
result <- CVXR::solve(prob, solver = 'SCS')
if (result$status != 'optimal') {
print(paste('Generalized projection error: optimization is not optimal and ends with status',
result$status))
}
result$getValue(x)
}
### instantaneous likelihood, gradient and hessian
instgrad <- function(t, t0, hat_T, delta, X, beta, R_t) {
N <- length(t0)
d <- dim(X)[2]
grad <- matrix(0,d,1)
hess <- matrix(0,d,d)
lik <- matrix(0,1,1)
for (i in R_t) {
lik <- lik - ((t-1 < hat_T[i] )*( hat_T[i] <= t )* delta[i]*t(beta)%*%X[i,]+ exp(t(beta)%*%X[i,])*max(0, min(t,hat_T[i]) - max(t0[i],t-1)))/N
hess <- hess + X[i,]%*%t(X[i,])*exp(beta*X[i,])[1]*
max(0, min(t,hat_T[i]) - max(t0[i],t-1)) / N
grad <- grad + X[i,] * exp(crossprod(beta,X[i,])[1]) *
max(0, min(t,hat_T[i]) - max(t0[i],t-1)) / N
if (t-1 < hat_T[i] & hat_T[i] <= t & delta[i])
grad <- grad - X[i,] / N
}
list(grad = grad, hess = hess, lik = lik)
}
###complete likelihood
complete_likelihood <- function(t0,hat_T,delta,X,n,beta){
N <- length(t0)
d <- dim(X)[2]
likelihood <- matrix(0,n,1)
for (t in 1:n){
for (i in 1:N){
likelihood[t] <- delta[i]*t(beta[t,])%*%X[i,]/N+ exp(t(beta[t,])%*%X[i,])*(hat_T[i]-t0[i])/N
}
}
list(likelihood = likelihood)
}
### original ONS
ons <- function(t0, hat_T, delta, X, D, gamma, n, epsilon, R) {
N <- length(t0)
d <- dim(X)[2]
beta <- matrix(0,d,1)
beta_arr <- matrix(0,n,d)
A_inv <- (1/epsilon)*diag(d)
mu_temp <- matrix(0,n,1)
gamma_temp <- matrix(0,n,1)
grad_ons <- matrix(0,n,d)
for (t in 1:n) {
beta_arr[t,] <- beta
### compute gradient
inst <- instgrad(t, t0, hat_T, delta, X, beta, R[[t]])
grad <- inst$grad
hess <- inst$hess
norm_grad <- sqrt(sum(grad^2))
grad_ons[t,] <- grad
### compute the optimal constants
mu <- as.numeric(t(grad)%*%hess%*%grad/max(10^-9,norm_grad^4))
gamma_t <- as.numeric(2*((-1/mu)*log(1 + mu*norm_grad*D) + norm_grad*D)/max(10^-9,norm_grad*D)^2)
gamma_temp[t] <- gamma_t
mu_temp[t] <- mu
### original ONS step
A_inv <- A_inv - tcrossprod(A_inv %*% grad) / (1 + crossprod(grad, A_inv %*% grad)[1])
beta <- beta - gamma^-1 * A_inv %*% grad
if (sqrt(crossprod(beta)[1]) > D)
beta <- generalized_projection(A_inv,beta,D)
}
list(beta_arr=beta_arr, gamma_temp = gamma_temp, mu_temp = mu_temp, grad_ons = grad_ons)
}
### gradient descent
grad_descent <- function(t0,hat_T,delta, X,D,gamma,n, R){
N <- length(t0)
d <- dim(X)[2]
beta <- matrix(0,d,1)
beta_arr <- matrix(0,n,d)
like_arr <- matrix(0,n,1)
I <- diag(d)
for (t in 1:n) {
beta_arr[t,] <- beta
### compute gradient
grad <- instgrad(t, t0, hat_T, delta, X, beta, R[[t]])$grad
like_arr[t] <- instgrad(t, t0, hat_T, delta, X, beta, R[[t]])$lik
### gradient descent step
beta <- beta - (gamma/sqrt(t)) * grad
if (sqrt(crossprod(beta)[1]) > D)
beta <- generalized_projection(I,beta,D)
}
list(beta_arr=beta_arr, like_arr = like_arr)
}
###original BOA
ons_boa <- function(t0, hat_T, delta, X, D, GAMMA, n, EPSILON, R) {
N <- length(t0)
d <- dim(X)[2]
K <- length(GAMMA)
BETA <- matrix(0,d,K)
BETA_ARR <- array(0,dim=c(n,d,K))
A_INV_ARR <- array(0,dim=c(d,d,K))
for (i in 1:K)
A_INV_ARR[,,i] <- (1/EPSILON[i])*diag(d)
pi_boa <- matrix(1/K, K, 1)
L <- matrix(0, K, 1)
renorm <- matrix(0, K, 1)
BETA_BOA_ARR <- matrix(0, n, d)
PI_BOA_ARR <- matrix(0, n, K)
LIK_BOA <- matrix(0,n,1)
for (t in 1:n) {
for (k in 1:K) {
BETA_ARR[t,,k] <- BETA[,k]
### compute gradient
grad <- instgrad(t, t0, hat_T, delta, X, BETA[,k], R[[t]])$grad
### ONS step
A_inv <- matrix(A_INV_ARR[,,k], d, d)
A_inv <- A_inv - tcrossprod(A_inv %*% grad) / (1 + crossprod(grad, A_inv %*% grad)[1])
A_INV_ARR[,,k] <- A_inv
BETA[,k] <- BETA[,k] - GAMMA[k]^-1 * A_inv %*% grad
if (sqrt(crossprod(BETA[,k])[1]) > D)
BETA[,k] <- generalized_projection(A_inv,BETA[,k],D)
}
### BOA aggregation
beta_boa <- BETA %*% pi_boa
inst <- instgrad(t, t0, hat_T, delta, X, beta_boa, R[[t]])
LIK_BOA[t] <- inst$lik
grad_boa <- inst$grad
term1 <- as.numeric(crossprod(grad_boa, BETA-tcrossprod(beta_boa, matrix(1,K,1))))
renorm <- renorm + 2.2*term1^2
if (sum(renorm)>0) {
eta <- 1/sqrt(renorm)
L <- L - term1 - eta * term1^2
pi_boa <- eta * exp(pmax(-100, pmin(100, eta * L - max(eta * L))))
pi_boa <- pi_boa / sum(pi_boa)
}
if (t < n) {
BETA_BOA_ARR[t+1,] <- BETA %*% pi_boa
PI_BOA_ARR[t+1,] <- pi_boa
}
}
list(BETA_ARR=BETA_ARR, BETA_BOA_ARR=BETA_BOA_ARR, PI_BOA_ARR=PI_BOA_ARR, LIK_BOA = LIK_BOA)
}
### SurvONS
ons_boa_max <- function(t0, hat_T, delta, X, D, GAMMA, n, EPSILON, R, max0 = FALSE) {
N <- length(t0)
d <- dim(X)[2]
K <- length(GAMMA)
BETA <- matrix(0,d,K)
BETA_ARR <- array(0,dim=c(n,d,K))
A_INV_ARR <- array(0,dim=c(d,d,K))
for (i in 1:K){
A_INV_ARR[,,i] <- (1/EPSILON[i])*diag(d)
}
pi_boa <- matrix(1/K, K, 1)
pi_boa2 <- pi_boa
L <- matrix(0, K, 1)
renorm <- matrix(0, K, 1)
BETA_BOA_ARR <- matrix(0, n, d)
GRAD_BOA <- matrix(0,n,d)
GRAD_BOA_HAT <- array(0, dim = c(n,d,K))
PI_BOA_ARR <- matrix(0, n, K)
LIK_BOA <- matrix(0,n,1)
gamma_temp <- matrix(0,n,1)
for (t in 1:n) {
###update beta_boa
beta_boa <- BETA %*% pi_boa
###observe gradients
inst <- instgrad(t, t0, hat_T, delta, X, beta_boa, R[[t]])
grad_boa <- inst$grad
GRAD_BOA[t,] <- grad_boa
hess_boa <- inst$hess
LIK_BOA[t] <-inst$lik
###compute the constants
norm_grad_boa <- sqrt(sum(grad_boa^2))
mu <- as.numeric(t(grad_boa)%*%hess_boa%*%grad_boa/max(10^-9,norm_grad_boa^4))
gamma_t <- as.numeric(2*((-1/mu)*log(1 + mu*norm_grad_boa*D) + norm_grad_boa*D)/max(10^-9,norm_grad_boa*D)^2)
if (max0)
gamma_t <- 0
gamma_temp[t] <- gamma_t
for (k in 1:K) {
BETA_ARR[t,,k] <- BETA[,k]
###condition for gamma
gamma_max <- max(gamma_t/4,GAMMA[k])
### compute gradient and hessian
grad_hat <- grad_boa * as.numeric(1+gamma_max*crossprod(grad_boa, BETA[,k]- beta_boa))
GRAD_BOA_HAT[t,,k] <- grad_hat
### ONS step
A_inv <- matrix(A_INV_ARR[,,k], d, d)
A_inv <- A_inv - tcrossprod(A_inv %*% grad_hat) / (1 + crossprod(grad_hat, A_inv %*% grad_hat)[1])
A_INV_ARR[,,k] <- A_inv
BETA[,k] <- BETA[,k] - GAMMA[k]^{-1} * A_inv %*% grad_hat
if (sqrt(crossprod(BETA[,k])[1]) > D)
BETA[,k] <- generalized_projection(A_inv, BETA[,k], D)
}
### BOA aggregation step
term1 <- GAMMA*as.numeric(crossprod(grad_boa, BETA-tcrossprod(beta_boa, matrix(1,K,1))))
pi_boa2 <- exp(pmax(-100,pmin(100, log(pi_boa2) -term1 - term1^2)))
pi_boa2 <- pi_boa2/sum(pi_boa2)
pi_boa <- (GAMMA*pi_boa2)/sum(GAMMA*pi_boa2)
if (t < n) {
BETA_BOA_ARR[t+1,] <- BETA %*% pi_boa
PI_BOA_ARR[t+1,] <- pi_boa
}
}
list(BETA_ARR=BETA_ARR, BETA_BOA_ARR=BETA_BOA_ARR, PI_BOA_ARR=PI_BOA_ARR, LIK_BOA = LIK_BOA, gamma_temp = gamma_temp,GRAD_BOA=GRAD_BOA, GRAD_BOA_HAT=GRAD_BOA_HAT )
}