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gradient_descent:output01 [2025/12/18 02:13] – created hkimscilgradient_descent:output01 [2025/12/18 18:53] (current) – hkimscil
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 <code> <code>
-> +> library(tidyverse) 
 +> library(data.table)
 > library(ggplot2) > library(ggplot2)
 > library(ggpmisc) > library(ggpmisc)
-> library(tidyverse) 
-> library(data.table) 
 >  > 
-> # settle down 
 > rm(list=ls()) > rm(list=ls())
->  +> # set.seed(191) 
-> ss <- function(x) {  +> nx <- 200 
-+   return(sum((x-mean(x))^2)) +> mx <- 4.5 
-+ } +> sdx <- mx * 0.56 
->  +> x <- rnorm(nx, mx, sdx) 
-> # data preparation +> slp <- 12 
-> set.seed(101) +> y <-  slp * x + rnorm(nx, 0, slp*sdx*3)
-> nx <- 50 # variable x, sample size  +
-> mx <- 4.5 # mean of x +
-> sdx <- mx * 0.56  # sd of x  +
-> x <- rnorm(nx, mx, sdx) # generating x  +
-> slp <- 4 # slop of x = coefficient, b +
-> # y variable  +
-> y <-  slp * x + rnorm(nx, 0, slp*3*sdx)+
 >  > 
 > data <- data.frame(x, y) > data <- data.frame(x, y)
-> head(data) 
-         x          y 
-1 3.678388 -20.070168 
-2 5.892204  15.268808 
-3 2.799142  28.672292 
-4 5.040186 -22.081593 
-5 5.283138  43.784059 
-6 7.458395  -1.954306 
 >  > 
-> # check with regression 
 > mo <- lm(y ~ x, data = data) > mo <- lm(y ~ x, data = data)
 > summary(mo) > summary(mo)
Line 41: Line 23:
  
 Residuals: Residuals:
-    Min      1Q  Median      3Q     Max  +     Min       1Q   Median       3Q      Max  
--58.703 -20.303   0.331  19.381  51.929 +-259.314  -59.215    6.683   58.834  309.833 
  
 Coefficients: Coefficients:
-            Estimate Std. Error t value Pr(>|t|)    +            Estimate Std. Error t value Pr(>|t|)     
-(Intercept)   -2.708      8.313  -0.326  0.74601    +(Intercept)    8.266     12.546   0.659    0.511     
-x              5.005      1.736   2.884  0.00587 **+x             11.888      2.433   4.887 2.11e-06 ***
 --- ---
 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
  
-Residual standard error: 28.54 on 48 degrees of freedom +Residual standard error: 88.57 on 198 degrees of freedom 
-Multiple R-squared:  0.1477, Adjusted R-squared:  0.1299  +Multiple R-squared:  0.1076, Adjusted R-squared:  0.1031  
-F-statistic: 8.316 on 1 and 48 DF,  p-value: 0.005867+F-statistic: 23.88 on 1 and 198 DF,  p-value: 2.111e-06
  
 >  > 
-> # graph 
 > ggplot(data = data, aes(x = x, y = y)) +  > ggplot(data = data, aes(x = x, y = y)) + 
 +   geom_point() + +   geom_point() +
Line 62: Line 43:
 +   stat_poly_eq(use_label(c("eq", "R2"))) + +   stat_poly_eq(use_label(c("eq", "R2"))) +
 +   theme_classic()  +   theme_classic() 
 +> # set.seed(191)
 +> # Initialize random betas
 +> # 우선 b를 고정하고 a만 
 +> # 변화시켜서 이해
 +> b <- summary(mo)$coefficients[2]
 +> a <- 0
 >  > 
-> # from what we know +> b.init <- b 
-> # get covariance value +> a.init <- a
-> sp.yx <- sum((x-mean(x))*(y-mean(y))) +
-> df.yx <- length(y)-1 +
-> sp.yx/df.yx  +
-[1] 27.61592 +
-> # check with cov function +
-> cov(x,y) +
-[1] 27.61592 +
-> # correlation value +
-> cov(x,y)/(sd(x)*sd(y)) +
-[1] 0.3842686 +
-> cor(x,y) +
-[1] 0.3842686 +
->  +
-> # regression by hand  +
-> # b and a  +
-> b <- sp.yx / ss(x) # b2 <- cov(x,y)/var(x) +
-> a <- mean(y) - b*(mean(x)) +
-> a +
-[1] -2.708294 +
-> b +
-[1] 5.004838 +
->  +
-> # check a and b value from the lm  +
-> summary(mo)$coefficient[1] +
-[1] -2.708294 +
-> summary(mo)$coefficient[2] +
-[1] 5.004838 +
-> summary(mo) +
- +
-Call: +
-lm(formula = y ~ x, data = data) +
- +
-Residuals: +
-    Min      1Q  Median      3Q     Max  +
--58.703 -20.303   0.331  19.381  51.929  +
- +
-Coefficients: +
-            Estimate Std. Error t value Pr(>|t|)    +
-(Intercept)   -2.708      8.313  -0.326  0.74601    +
-x              5.005      1.736   2.884  0.00587 ** +
---- +
-Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 +
- +
-Residual standard error: 28.54 on 48 degrees of freedom +
-Multiple R-squared:  0.1477, Adjusted R-squared:  0.1299  +
-F-statistic: 8.316 on 1 and 48 DF,  p-value: 0.005867 +
- +
->  +
-> fit.yx <- a + b*x # predicted value of y from x data +
-> res <- y - fit.yx # error residuals +
-> reg <- fit.yx - mean(y) # error regressions  +
-> ss.res <- sum(res^2) +
-> ss.reg <- sum(reg^2) +
-> ss.res+ss.reg +
-[1] 45864.4 +
-> ss.tot <- ss(y) +
-> ss.tot +
-[1] 45864.4 +
->  +
-> plot(x,y) +
-> abline(a, b, col="red", lwd=2) +
-> plot(x, fit.yx) +
-> plot(x, res) +
->  +
-> df.y <- length(y)-1 +
-> df.reg <- 2-1 +
-> df.res <- df.y - df.reg +
-> df.res +
-[1] 48 +
->  +
-> r.sq <- ss.reg / ss.tot +
-> r.sq +
-[1] 0.1476624 +
-> summary(mo)$r.square +
-[1] 0.1476624 +
-> ms.reg <- ss.reg / df.reg +
-> ms.res <- ss.res / df.res +
->  +
->  +
-> f.cal <- ms.reg / ms.res +
-> f.cal  +
-[1] 8.315713 +
-> pf(f.cal, df.reg, df.res,lower.tail = F) +
-[1] 0.005867079 +
-> t.cal <- sqrt(f.cal) +
-> t.cal +
-[1] 2.883698 +
-> se.b <- sqrt(ms.res/ss(x)) +
-> se.b +
-[1] 1.735562 +
-> t.cal <- (b-0)/se.b +
-> t.cal +
-[1] 2.883698 +
-> pt(t.cal, df=df.res, lower.tail = F)*2 +
-[1] 0.005867079 +
-> summary(mo) +
- +
-Call: +
-lm(formula = y ~ x, data = data) +
- +
-Residuals: +
-    Min      1Q  Median      3Q     Max  +
--58.703 -20.303   0.331  19.381  51.929  +
- +
-Coefficients: +
-            Estimate Std. Error t value Pr(>|t|)    +
-(Intercept)   -2.708      8.313  -0.326  0.74601    +
-x              5.005      1.736   2.884  0.00587 ** +
---- +
-Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 +
- +
-Residual standard error: 28.54 on 48 degrees of freedom +
-Multiple R-squared:  0.1477, Adjusted R-squared:  0.1299  +
-F-statistic: 8.316 on 1 and 48 DF,  p-value: 0.005867 +
- +
->  +
->  +
-> # getting a and b from +
-> # gradient descent +
-> a <- rnorm(1) +
-> b <- rnorm(1) +
-> a.start <- a +
-> b.start <- b +
-> a.start +
-[1] 0.2680658 +
-> b.start +
-[1] -0.5922083+
 >  > 
 > # Predict function: > # Predict function:
Line 199: Line 59:
 >  > 
 > # And loss function is: > # And loss function is:
-> residuals <- function(fit, y) { +> residuals <- function(predictions, y) { 
-+   return(y - fit)++   return(y - predictions)
 + } + }
 >  > 
-> gradient <- function(x, res){ +> # we use sum of square of error which oftentimes become big 
-+   db = -2 * mean(x * res) +> ssrloss <- function(predictions, y) { 
-+   da = -2 * mean(res) ++   residuals <- (y - predictions) 
-+   return(list("b" = db, "a" = da))++   return(sum(residuals^2))
 + } + }
 >  > 
-> # to check ms.residual +> ssrs <- c() # for sum  of square residuals 
-> msrloss <- function(fit, y) { +> srs <- c() # sum of residuals  
-+   res <- residuals(fit, y) +> as <- c() # for as (intercepts)
-+   return(mean(res^2)) +
-+ }+
 >  > 
-> # Train the model with scaled features +> for (i in seq(from = -50, to = 50, by = 0.01)) { 
-> learning.rate = 1e-1 # 0.1 ++   pred <- predict(x, i, b) 
->  ++   res <- residuals(pred, y) 
-> # Record Loss for each epoch: ++   ssr <- ssrloss(pred, y) 
-> as = c() ++   ssrs <- append(ssrs, ssr) 
-> bs = c() ++   srs <- append(srs, sum(res)) 
-> msrs = c() ++   as <- append(as, i)
-> ssrs = c() +
-> mres = c() +
-> zx <- (x-mean(x))/sd(x) +
->  +
-> nlen <- 75 +
-> for (epoch in 1:nlen) { +
-+   fit.val <- predict(zx, a, b) +
-+   residual <- residuals(fit.val, y) +
-+   loss <- msrloss(fit.val, y) +
-+   mres <- append(mres, mean(residual)) +
-+   msrs <- append(msrs, loss) +
-+    +
-+   grad <- gradient(zx, residual) +
-+   step.b <- grad$b * learning.rate  +
-+   step.a <- grad$a * learning.rate +
-+   b <- b-step.b +
-+   a <- a-step.a +
-+    +
-+   as <- append(as, a) +
-+   bs <- append(bs, b)+
 + } + }
-> msrs +> length(ssrs) 
- [1] 1254.6253 1085.3811  976.7258  906.9672  862.1801  833.4247  814.9621  803.1078  795.4963  790.6089 +[1] 10001 
-[11]  787.4707  785.4556  784.1615  783.3306  782.7970  782.4543  782.2342  782.0929  782.0021  781.9438 +> length(srs) 
-[21]  781.9064  781.8823  781.8669  781.8569  781.8506  781.8465  781.8439  781.8422  781.8411  781.8404 +[1] 10001 
-[31]  781.8399  781.8396  781.8395  781.8393  781.8393  781.8392  781.8392  781.8392  781.8392  781.8391 +> length(as) 
-[41]  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391 +[1] 10001
-[51]  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391 +
-[61]  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391 +
-[71]  781.8391  781.8391  781.8391  781.8391  781.8391 +
-> mres +
- [1] 1.798187e+01 1.438549e+01 1.150839e+01 9.206716e+00 7.365373e+00 5.892298e+00 4.713838e+00 +
- [8] 3.771071e+00 3.016857e+00 2.413485e+00 1.930788e+00 1.544631e+00 1.235704e+00 9.885636e-01 +
-[15] 7.908509e-01 6.326807e-01 5.061446e-01 4.049156e-01 3.239325e-01 2.591460e-01 2.073168e-01 +
-[22] 1.658534e-01 1.326828e-01 1.061462e-01 8.491697e-02 6.793357e-02 5.434686e-02 4.347749e-02 +
-[29] 3.478199e-02 2.782559e-02 2.226047e-02 1.780838e-02 1.424670e-02 1.139736e-02 9.117890e-03 +
-[36] 7.294312e-03 5.835449e-03 4.668360e-03 3.734688e-03 2.987750e-03 2.390200e-03 1.912160e-03 +
-[43] 1.529728e-03 1.223782e-03 9.790260e-04 7.832208e-04 6.265766e-04 5.012613e-04 4.010090e-04 +
-[50] 3.208072e-04 2.566458e-04 2.053166e-04 1.642533e-04 1.314026e-04 1.051221e-04 8.409769e-05 +
-[57] 6.727815e-05 5.382252e-05 4.305802e-05 3.444641e-05 2.755713e-05 2.204570e-05 1.763656e-05 +
-[64] 1.410925e-05 1.128740e-05 9.029921e-06 7.223936e-06 5.779149e-06 4.623319e-06 3.698655e-06 +
-[71] 2.958924e-06 2.367140e-06 1.893712e-06 1.514969e-06 1.211975e-06 +
-> as +
- [1]  3.864439  6.741538  9.043217 10.884560 12.357635 13.536094 14.478862 15.233076 15.836447 16.319144 +
-[11] 16.705302 17.014228 17.261369 17.459082 17.617252 17.743788 17.845017 17.926000 17.990787 18.042616 +
-[21] 18.084079 18.117250 18.143786 18.165016 18.181999 18.195586 18.206455 18.215151 18.222107 18.227672 +
-[31] 18.232124 18.235686 18.238535 18.240815 18.242638 18.244097 18.245264 18.246198 18.246945 18.247542 +
-[41] 18.248021 18.248403 18.248709 18.248954 18.249149 18.249306 18.249431 18.249532 18.249612 18.249676 +
-[51] 18.249727 18.249768 18.249801 18.249828 18.249849 18.249865 18.249879 18.249890 18.249898 18.249905 +
-[61] 18.249911 18.249915 18.249919 18.249921 18.249924 18.249925 18.249927 18.249928 18.249929 18.249930 +
-[71] 18.249930 18.249931 18.249931 18.249931 18.249932 +
-> bs +
- [1]  1.828121  3.774066  5.338606  6.596496  7.607839  8.420960  9.074708  9.600322 10.022916 10.362681 +
-[11] 10.635852 10.855482 11.032064 11.174036 11.288182 11.379955 11.453741 11.513064 11.560760 11.599108 +
-[21] 11.629940 11.654728 11.674658 11.690682 11.703565 11.713923 11.722251 11.728946 11.734330 11.738658 +
-[31] 11.742138 11.744935 11.747185 11.748993 11.750447 11.751616 11.752556 11.753312 11.753920 11.754408 +
-[41] 11.754801 11.755117 11.755370 11.755575 11.755739 11.755871 11.755977 11.756062 11.756131 11.756186 +
-[51] 11.756230 11.756266 11.756294 11.756317 11.756336 11.756351 11.756363 11.756372 11.756380 11.756386 +
-[61] 11.756391 11.756395 11.756399 11.756401 11.756403 11.756405 11.756406 11.756407 11.756408 11.756409 +
-[71] 11.756410 11.756410 11.756410 11.756411 11.756411+
 >  > 
-> # scaled +> min(ssrs) 
-> a +[1] 1553336 
-[1] 18.24993 +> min.pos.ssrs <- which(ssrs == min(ssrs)) 
-> b +> min.pos.ssrs 
-[1] 11.75641 +[1] 5828 
->  +> print(as[min.pos.ssrs]) 
-> # unscale coefficients to make them comprehensible +[1] 8.27
-> # see http://commres.net/wiki/gradient_descent#why_normalize_scale_or_make_z-score_xi +
-> # and  +
-> # http://commres.net/wiki/gradient_descent#how_to_unnormalize_unscale_a_and_b +
-> #   +
-> a =  a - (mean(x) / sd(x)) * b +
-> b =  b / sd(x) +
-> a +
-[1] -2.708293 +
-> b +
-[1] 5.004837 +
->  +
-> # changes of estimators +
-> as <- as - (mean(x) /sd(x)) * bs +
-> bs <- bs / sd(x) +
->  +
-> as +
- [1]  0.60543638  0.01348719 -0.47394836 -0.87505325 -1.20490696 -1.47600164 -1.69867560 -1.88147654 +
- [9] -2.03146535 -2.15446983 -2.25529623 -2.33790528 -2.40555867 -2.46094055 -2.50625843 -2.54332669 +
-[17] -2.57363572 -2.59840909 -2.61865082 -2.63518431 -2.64868455 -2.65970460 -2.66869741 -2.67603377 +
-[25] -2.68201712 -2.68689566 -2.69087236 -2.69411311 -2.69675345 -2.69890410 -2.70065549 -2.70208142 +
-[33] -2.70324211 -2.70418670 -2.70495527 -2.70558050 -2.70608902 -2.70650253 -2.70683873 -2.70711203 +
-[41] -2.70733415 -2.70751464 -2.70766129 -2.70778042 -2.70787718 -2.70795575 -2.70801956 -2.70807135 +
-[49] -2.70811340 -2.70814753 -2.70817522 -2.70819769 -2.70821592 -2.70823071 -2.70824271 -2.70825244 +
-[57] -2.70826033 -2.70826672 -2.70827191 -2.70827611 -2.70827952 -2.70828228 -2.70828452 -2.70828634 +
-[65] -2.70828781 -2.70828900 -2.70828996 -2.70829074 -2.70829137 -2.70829189 -2.70829230 -2.70829264 +
-[73] -2.70829291 -2.70829313 -2.70829331 +
-> bs +
- [1] 0.7782519 1.6066627 2.2727050 2.8082030 3.2387434 3.5848979 3.8632061 4.0869659 4.2668688 4.4115107 +
-[11] 4.5278028 4.6213016 4.6964747 4.7569138 4.8055069 4.8445757 4.8759871 4.9012418 4.9215466 4.9378716 +
-[21] 4.9509970 4.9615498 4.9700342 4.9768557 4.9823401 4.9867497 4.9902949 4.9931453 4.9954370 4.9972795 +
-[31] 4.9987609 4.9999520 5.0009096 5.0016795 5.0022985 5.0027962 5.0031963 5.0035180 5.0037767 5.0039846 +
-[41] 5.0041518 5.0042863 5.0043943 5.0044812 5.0045511 5.0046073 5.0046524 5.0046887 5.0047179 5.0047414 +
-[51] 5.0047603 5.0047754 5.0047876 5.0047974 5.0048053 5.0048117 5.0048168 5.0048209 5.0048242 5.0048268 +
-[61] 5.0048289 5.0048307 5.0048320 5.0048331 5.0048340 5.0048347 5.0048353 5.0048358 5.0048362 5.0048365 +
-[71] 5.0048367 5.0048369 5.0048370 5.0048372 5.0048373 +
-> mres +
- [1] 1.798187e+01 1.438549e+01 1.150839e+01 9.206716e+00 7.365373e+00 5.892298e+00 4.713838e+00 +
- [8] 3.771071e+00 3.016857e+00 2.413485e+00 1.930788e+00 1.544631e+00 1.235704e+00 9.885636e-01 +
-[15] 7.908509e-01 6.326807e-01 5.061446e-01 4.049156e-01 3.239325e-01 2.591460e-01 2.073168e-01 +
-[22] 1.658534e-01 1.326828e-01 1.061462e-01 8.491697e-02 6.793357e-02 5.434686e-02 4.347749e-02 +
-[29] 3.478199e-02 2.782559e-02 2.226047e-02 1.780838e-02 1.424670e-02 1.139736e-02 9.117890e-03 +
-[36] 7.294312e-03 5.835449e-03 4.668360e-03 3.734688e-03 2.987750e-03 2.390200e-03 1.912160e-03 +
-[43] 1.529728e-03 1.223782e-03 9.790260e-04 7.832208e-04 6.265766e-04 5.012613e-04 4.010090e-04 +
-[50] 3.208072e-04 2.566458e-04 2.053166e-04 1.642533e-04 1.314026e-04 1.051221e-04 8.409769e-05 +
-[57] 6.727815e-05 5.382252e-05 4.305802e-05 3.444641e-05 2.755713e-05 2.204570e-05 1.763656e-05 +
-[64] 1.410925e-05 1.128740e-05 9.029921e-06 7.223936e-06 5.779149e-06 4.623319e-06 3.698655e-06 +
-[71] 2.958924e-06 2.367140e-06 1.893712e-06 1.514969e-06 1.211975e-06 +
-> msrs +
- [1] 1254.6253 1085.3811  976.7258  906.9672  862.1801  833.4247  814.9621  803.1078  795.4963  790.6089 +
-[11]  787.4707  785.4556  784.1615  783.3306  782.7970  782.4543  782.2342  782.0929  782.0021  781.9438 +
-[21]  781.9064  781.8823  781.8669  781.8569  781.8506  781.8465  781.8439  781.8422  781.8411  781.8404 +
-[31]  781.8399  781.8396  781.8395  781.8393  781.8393  781.8392  781.8392  781.8392  781.8392  781.8391 +
-[41]  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391 +
-[51]  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391 +
-[61]  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391  781.8391 +
-[71]  781.8391  781.8391  781.8391  781.8391  781.8391 +
->  +
-> parameters <- data.frame(as, bs, mres, msrs) +
->  +
-> cat(paste0("Intercept: ", a, "\n", "Slope: ", b, "\n")) +
-Intercept: -2.7082933069293 +
-Slope: 5.00483726695576 +
->  +
-> summary(mo)$coefficients +
-             Estimate Std. Error    t value    Pr(>|t|) +
-(Intercept) -2.708294   8.313223 -0.3257815 0.746005708 +
-x            5.004838   1.735562  2.8836978 0.005867079 +
->  +
-> msrs <- data.frame(msrs) +
-> msrs.log <- data.table(epoch = 1:nlen, msrs) +
-> ggplot(msrs.log, aes(epoch, msrs)) + +
-+   geom_line(color="blue") + +
-+   theme_classic() +
->  +
-> mres <- data.frame(mres) +
-> mres.log <- data.table(epoch = 1:nlen, mres) +
-> ggplot(mres.log, aes(epoch, mres)) + +
-+   geom_line(color="red") + +
-+   theme_classic() +
->  +
-> ch <- data.frame(mres, msrs) +
-> ch +
-           mres      msrs +
-1  1.798187e+01 1254.6253 +
-2  1.438549e+01 1085.3811 +
-3  1.150839e+01  976.7258 +
-4  9.206716e+00  906.9672 +
-5  7.365373e+00  862.1801 +
-6  5.892298e+00  833.4247 +
-7  4.713838e+00  814.9621 +
-8  3.771071e+00  803.1078 +
-9  3.016857e+00  795.4963 +
-10 2.413485e+00  790.6089 +
-11 1.930788e+00  787.4707 +
-12 1.544631e+00  785.4556 +
-13 1.235704e+00  784.1615 +
-14 9.885636e-01  783.3306 +
-15 7.908509e-01  782.7970 +
-16 6.326807e-01  782.4543 +
-17 5.061446e-01  782.2342 +
-18 4.049156e-01  782.0929 +
-19 3.239325e-01  782.0021 +
-20 2.591460e-01  781.9438 +
-21 2.073168e-01  781.9064 +
-22 1.658534e-01  781.8823 +
-23 1.326828e-01  781.8669 +
-24 1.061462e-01  781.8569 +
-25 8.491697e-02  781.8506 +
-26 6.793357e-02  781.8465 +
-27 5.434686e-02  781.8439 +
-28 4.347749e-02  781.8422 +
-29 3.478199e-02  781.8411 +
-30 2.782559e-02  781.8404 +
-31 2.226047e-02  781.8399 +
-32 1.780838e-02  781.8396 +
-33 1.424670e-02  781.8395 +
-34 1.139736e-02  781.8393 +
-35 9.117890e-03  781.8393 +
-36 7.294312e-03  781.8392 +
-37 5.835449e-03  781.8392 +
-38 4.668360e-03  781.8392 +
-39 3.734688e-03  781.8392 +
-40 2.987750e-03  781.8391 +
-41 2.390200e-03  781.8391 +
-42 1.912160e-03  781.8391 +
-43 1.529728e-03  781.8391 +
-44 1.223782e-03  781.8391 +
-45 9.790260e-04  781.8391 +
-46 7.832208e-04  781.8391 +
-47 6.265766e-04  781.8391 +
-48 5.012613e-04  781.8391 +
-49 4.010090e-04  781.8391 +
-50 3.208072e-04  781.8391 +
-51 2.566458e-04  781.8391 +
-52 2.053166e-04  781.8391 +
-53 1.642533e-04  781.8391 +
-54 1.314026e-04  781.8391 +
-55 1.051221e-04  781.8391 +
-56 8.409769e-05  781.8391 +
-57 6.727815e-05  781.8391 +
-58 5.382252e-05  781.8391 +
-59 4.305802e-05  781.8391 +
-60 3.444641e-05  781.8391 +
-61 2.755713e-05  781.8391 +
-62 2.204570e-05  781.8391 +
-63 1.763656e-05  781.8391 +
-64 1.410925e-05  781.8391 +
-65 1.128740e-05  781.8391 +
-66 9.029921e-06  781.8391 +
-67 7.223936e-06  781.8391 +
-68 5.779149e-06  781.8391 +
-69 4.623319e-06  781.8391 +
-70 3.698655e-06  781.8391 +
-71 2.958924e-06  781.8391 +
-72 2.367140e-06  781.8391 +
-73 1.893712e-06  781.8391 +
-74 1.514969e-06  781.8391 +
-75 1.211975e-06  781.8391 +
-> max(y) +
-[1] 83.02991 +
-> ggplot(data, aes(x = x, y = y)) +  +
-+   geom_point(size = 2) +  +
-+   geom_abline(aes(intercept = as, slope = bs), +
-+               data = parameters, linewidth = 0.5,  +
-+               color = 'green') +  +
-+   stat_poly_line() + +
-+   stat_poly_eq(use_label(c("eq", "R2"))) + +
-+   theme_classic() + +
-+   geom_abline(aes(intercept = as, slope = bs),  +
-+               data = parameters %>% slice_head(),  +
-+               linewidth = 1, color = 'blue') +  +
-+   geom_abline(aes(intercept = as, slope = bs),  +
-+               data = parameters %>% slice_tail(),  +
-+               linewidth = 1, color = 'red') + +
-+   labs(title = 'Gradient descent. blue: start, red: end, green: gradients')+
 > summary(mo) > summary(mo)
  
Line 471: Line 101:
  
 Residuals: Residuals:
-    Min      1Q  Median      3Q     Max  +     Min       1Q   Median       3Q      Max  
--58.703 -20.303   0.331  19.381  51.929 +-259.314  -59.215    6.683   58.834  309.833 
  
 Coefficients: Coefficients:
-            Estimate Std. Error t value Pr(>|t|)    +            Estimate Std. Error t value Pr(>|t|)     
-(Intercept)   -2.708      8.313  -0.326  0.74601    +(Intercept)    8.266     12.546   0.659    0.511     
-x              5.005      1.736   2.884  0.00587 **+x             11.888      2.433   4.887 2.11e-06 ***
 --- ---
 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
  
-Residual standard error: 28.54 on 48 degrees of freedom +Residual standard error: 88.57 on 198 degrees of freedom 
-Multiple R-squared:  0.1477, Adjusted R-squared:  0.1299  +Multiple R-squared:  0.1076, Adjusted R-squared:  0.1031  
-F-statistic: 8.316 on 1 and 48 DF,  p-value: 0.005867+F-statistic: 23.88 on 1 and 198 DF,  p-value: 2.111e-06
  
-> a.start +> plot(seq(1, length(ssrs)), ssrs) 
-[1] 0.2680658 +> plot(seq(1, length(ssrs)), srs) 
-> b.start +> tail(ssrs) 
-[1] -0.5922083 +[1] 1900842 1901008 1901175 1901342 1901509 1901676 
-> a +> max(ssrs) 
-[1] -2.708293 +[1] 2232329 
-> b +> min(ssrs) 
-[1] 5.004837 +[1] 1553336 
-> summary(mo)$coefficient[1] +> tail(srs) 
-[1] -2.708294 +[1] -8336.735 -8338.735 -8340.735 -8342.735 -8344.735 -8346.735 
-> summary(mo)$coefficient[2] +> max(srs) 
-[1] 5.004838+[1] 11653.26 
 +> min(srs) 
 +[1] -8346.735
 >  > 
 +> 
 +
 </code> </code>
gradient_descent/output01.1766023992.txt.gz · Last modified: by hkimscil
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