diff --git a/src/polynomials_and_splines.ipynb b/src/polynomials_and_splines.ipynb
index 866df40..fede905 100644
--- a/src/polynomials_and_splines.ipynb
+++ b/src/polynomials_and_splines.ipynb
@@ -1,980 +1,980 @@
 {
  "cells": [
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# Polynomials and Splines"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 191,
    "metadata": {
     "hide_input": true
    },
    "outputs": [
     {
      "data": {
       "text/html": [
        "<iframe src=\"https://moodle.epfl.ch/mod/hvp/embed.php?id=1037423\" width=\"1080\" height=\"656\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"></iframe>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "IRdisplay::display_html('<iframe src=\"https://moodle.epfl.ch/mod/hvp/embed.php?id=1037423\" width=\"1080\" height=\"656\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"></iframe>')"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "New R commands:\n",
     "* `poly(predictor, order, raw = FALSE)`\n",
     "* `I()`\n",
     "* `cbind()`\n",
     "* `cut(predictor, number_of_cuts)`\n",
     "* `bs(predictor, degree = 3, knots = , df = )`\n",
     "* `ns(predictor, degree = 3, knots = , df = )`\n",
     "* `smooth.spline(predictor, response)`\n",
     "\n",
     "Useful R commands to remember:\n",
     "* `range(column)` gives lower and upper bounds for the data in `column`.\n",
     " \n",
     "\n",
     "This section is inspired by the Lab in chapter 7 from the textbook.\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Regression"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "library(ISLR)\n",
     "attach(Wage)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We will look at the Wage data, which contains the following columns."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "names(Wage)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Let us have a look at the first five rows of columns age (the second column) and wage (the 11th column).\n",
     "We see that the first individual has age 18 and a wage of 75'000 US Dollar per year."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "Wage[1:5,c(2, 11)]"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "To use multiple powers of `age` as predictors, we can use the `poly` function. With the argument `raw = T` (short form of `raw = TRUE`), we see that it effectively computes higher powers of `age`."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "poly(Wage$age[1:5], 4, raw = T)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "By default, `raw = F`, in which case the `poly` function returns an orthogonal basis formed by linear combination of all powers of `age`."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "poly(Wage$age[1:5], 4)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We will now see that the estimate of the coefficients depends on whether we choose the orthogonal or the raw basis, but the predictions do not depend on this choice."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "fit1 = lm(wage ~ poly(age, 4), data = Wage)\n",
     "coef(summary(fit1))"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "fit2 = lm(wage ~ poly(age, 4, raw = TRUE), data = Wage)\n",
     "coef(summary(fit2))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Remember that the `predict` function without any further arguments computes the prediction of the model on the training set.\n",
     "We see here that the prediction for the first individual is approximately 52'000 USD. Remember that the first individiual is 18 years old and has an actual wage of 75'000 USD. There are probably other individuals of 18 years of age in the training set with a much lower income."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "predict(fit1)[1:5]"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "predict(fit2)[1:5]"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "As an alternative to the `poly` function we could have explicitly defined our predictors using the wrappers `I` (the \"as-is\" operator) or `cbind`. These wrappers are needed because `^` has a special meaning in formulas.\n",
     "The `cbind` function builds a matrix from a collection of vectors.\n",
     "\n",
     "Both variants create a predictors of the same form as `poly(age, 4, raw = T)`."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "fit3 = lm(wage ~ I(age) + I(age^2) + I(age^3) + I(age^4), data = Wage)\n",
     "predict(fit3)[1:5]"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "fit4 = lm(wage ~ cbind(age, age^2, age^3, age^4), data = Wage)\n",
     "predict(fit4)[1:5]"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We now create a grid of values for `age` at which predictions. We first extract the lower and upper bound of the values in the `age` column."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "agelims = range(age)\n",
     "agelims"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Then create a grid of 50 points between these bounds."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "age.grid = seq(from = agelims[1], to = agelims[2], length = 50)\n",
     "age.grid"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "And then call the generic `predict()` function, specifying that we want standard errors as well."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "predictions = predict(fit1, newdata = list(age = age.grid), se = T)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "The prediction of the standard errors is stored in the column `se.fit`."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "names(predictions)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We create now a matrix that contains the predictions plus/minus two times the standard deviation, which corresponds to an approximate 95% confidence interval for normally distributed errors."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "se.bands = cbind(predictions$fit - 2 * predictions$se.fit, predictions$fit + 2 * predictions$se.fit)\n",
     "se.bands[1:5,]"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We will plot now the data together with the predictions. Use `?par` or `?plot` to get help on arguments that you don't understand."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "plot(age, wage, xlim = agelims, cex = .5, col = \"darkgrey\")\n",
     "title(\"Degree-4 Polynomial\")\n",
     "lines(age.grid,  predictions$fit, lwd = 2, col = \"blue\")\n",
     "matlines(age.grid, se.bands, lwd = 1, col = \"blue\", lty = 3)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "In order to fit a step function we use the `cut()` function. We use the function `table()` to display what `cut()` does."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "table(cut(age, 4))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Here, `cut()` automatically picked the cutpoints at 33.5, 49 and 64.5 years of age.\n",
     "The lower row displays the number of data points that fall into each region.\n",
     "\n",
     "The function `cut()` returns an ordered categorical variable; the `lm()` function then creates a set of dummy variables for use in the regression. The `age < 33.5` category is left out, so the intercept coefficient of 94'160 USD can be interpreted as the average salary for those under 33.5 years of age, and the other coefficients can be interpreted as the average additional salary for those in the other age groups."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "fit.steps = lm(wage ~ cut(age, 4), data = Wage)\n",
     "coef(summary(fit.steps))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Classification"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Next we consider the task of predicting whether an individual earns more than 250'000 USD per year."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "fit = glm(I(wage > 250) ~ poly(age, 4), data = Wage, family = binomial)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Note that we again use the wrapper `I()` to create this binary response variable on the fly. The expression `wage>250` evaluates to a logical variable containing `TRUE`s and `FALSE`s, which `glm()` coerces to binary by setting the `TRUE`s to 1 and the `FALSE`s to 0.\n",
     "\n",
     "Once again, we make predictions using the `predict()` function."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "preds = predict(fit, newdata = list(age = age.grid), se = T)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "However, calculating the confidence intervals is slightly more involved than in the linear regression case.\n",
     "The default prediction type for a `glm()` model is `type = \"link\"`, which is what we use here. This means we get predictions for the logit."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "se.bands.logit = cbind(preds$fit - 2*preds$se.fit, preds$fit + 2*preds$se.fit)\n",
     "se.bands.logit[1:5,]"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "To transform them to probabilities we use the formula $p(Y=1|X) = \\frac{\\exp(\\beta X)}{1 + \\exp(\\beta X)}$, where  $\\beta X = \\beta_0 + \\beta_1 X + \\beta_2 X^2 + \\beta_3X^3 + \\beta_4X^4$."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "se.bands = exp(se.bands.logit)/(1 + exp(se.bands.logit))\n",
     "cbind(age.grid[1:5], se.bands[1:5,])"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We see that the predicted confidence interval for the probabilities to earn more than 250'000USD per year is rather narrow and at low probabilities for ages up to 23 years.\n",
     "\n",
     "Now we will plot again. The `jitter` function is used to jitter the `age` values a bit so that observations with the same `age` value do not cover each other up. This is often called a rug plot."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "plot(age, I(wage>250), xlim = agelims, type = \"n\", col = \"darkgrey\", ylim = c(0, .2))\n",
     "points(jitter(age), I((wage>250)*.2), cex = .5, pch = \"|\", col = \"darkgrey\") # since we plot only up to 0.2 we plot the TRUEs at 0.2\n",
     "title(\"Degree-4 Polynomial\")\n",
     "lines(age.grid,  exp(preds$fit)/(1 + exp(preds$fit)), lwd = 2, col = \"blue\")\n",
     "matlines(age.grid, se.bands, lwd = 1, col = \"blue\", lty = 3)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Splines"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We use the `splines` library.\n",
     "\n",
     "In the lecture we saw that regression splines can be fit by constructing an appropriate matrix of basis functions. The `bs()` function generates the entire matrix of basis functions for splines with the specified set of knots. By default, cubic splines are produced."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "library(splines)\n",
     "spline.fit = lm(wage ~ bs(age, knots = c(25, 40, 60)), data = Wage)\n",
     "spline.pred = predict(spline.fit, newdata = list(age = age.grid), se = T)\n",
     "plot(age, wage, col = \"gray\")\n",
     "lines(age.grid, spline.pred$fit, lwd = 2)\n",
     "lines(age.grid, spline.pred$fit - 2*spline.pred$se.fit, lty = \"dashed\")\n",
     "lines(age.grid, spline.pred$fit + 2*spline.pred$se.fit, lty = \"dashed\")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Above we have prespecified knots at ages 25, 40 and 60. This produces a spline with six basis functions.\n",
     "Recall that a cubic spline with three knots has seven degrees of freedom; these degrees of freedom are used up by an intercept, plus six basis functions. "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "dim(bs(age, knots = c(25, 40, 60)))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We could also use the `df` option to produce a spline with knots at uniform quantiles of the data."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "dim(bs(age, df = 6))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "In this case `R` chooses knots at ages 33.8, 42 and 51, which corresponds to the 25th, 50th and 75th percentiles of age."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "attr(bs(age, df = 6), \"knots\")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "The function `bs()` also has a `degree` argument, so we can fit splines of any degree, rather than the default degree of 3 (which yields a cubic spline)."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "dim(bs(age, knots = c(25, 40, 60), degree = 5))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "In order to instead fit a natural spline, we use the `ns()` function."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "ns.fit = lm(wage ~ ns(age, knots = c(25, 40, 60), Boundary.knots = c(0, 100)), data = Wage)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "To compare the different methods in how they interpolate and extrapolate we use now a larger range and plot the predictions of the different methods."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "age.grid = seq(0, 100, length = 100)\n",
     "ns.pred = predict(ns.fit, newdata = list(age = age.grid), se = T)\n",
     "bs.pred = predict(lm(wage ~ bs(age, knots = c(25, 40, 60), Boundary.knots = c(0, 100)), data = Wage), newdata = list(age = age.grid), se = T)\n",
     "p4.pred = predict(lm(wage ~ poly(age, 4), data = Wage), newdata = list(age = age.grid), se = T)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "To make the plotting a bit more convenient we use the following function"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "plot.predictions = function(ages, pred, col = \"blue\") {\n",
     "    se.bands = cbind(pred$fit - 2 * pred$se.fit, pred$fit + 2 * pred$se.fit)\n",
     "    lines(ages, pred$fit, lwd = 2, col = col)\n",
     "    matlines(ages, se.bands, lty = \"dashed\", col = col)\n",
     "}\n",
     "plot(age, wage, cex = .5, col = \"darkgrey\", xlim = c(0, 100), ylim = c(-20, 300))\n",
     "plot.predictions(age.grid, ns.pred, col = \"red\")\n",
     "plot.predictions(age.grid, bs.pred, col = \"darkgreen\")\n",
     "plot.predictions(age.grid, p4.pred, col = \"blue\")\n",
     "legend(x = 25, y = 20, legend = c(\"natural cubic spline\", \"cubic spline\", \"4th order polynomial\"),\n",
     "       col = c(\"red\", \"darkgreen\", \"blue\"), lty = 1)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Smoothing Splines"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "In order to fit a smoothing spline, we use the `smooth.spline()` function."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "fit.smooth.cv = smooth.spline(age, wage)\n",
     "fit.smooth.cv"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We see the selected Degrees of Freedom using cross-validation.\n",
     "If instead we wish to set the defgrees of freedom manually, we can use"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "fit.smooth = smooth.spline(age, wage, df = 16)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Now, let us plot the two smoothing splines."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "plot(age, wage, cex = .5, col = \"darkgrey\", xlim = agelims)\n",
     "lines(fit.smooth, col = \"red\", lwd = 2)\n",
     "lines(fit.smooth.cv, col = \"blue\", lwd = 2)\n",
     "legend(\"topright\", legend = c(\"16 Df\", \"6.5 DF\"), col = c(\"red\", \"blue\"), lty - 1, lwd = 2, cex = .8)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## GAMs"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We now fit a GAM to predict `wage` using natural spline functions of `year` and `age`, treating `education` as a qualitative predictor. Since this is just a big linear regressions model using an appropriate choice of basis functions, we can simply do this using the `lm()` function."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "gam1 = lm(wage ~ ns(year, 4) + ns(age, 5) + education, data = Wage)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We can now plot predictions of `wage` given `age` while fixing the other variables to e.g. `year = 2005` and `education = \"1. < HS Grad\"`."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "pred.1 = predict(gam1, newdata = data.frame(age = age.grid,\n",
     "                                          year = rep(2005, length(age.grid)),\n",
     "                                          education = rep(\"1. < HS Grad\", length(age.grid))))\n",
     "pred.2 = predict(gam1, newdata = data.frame(age = age.grid,\n",
     "                                          year = rep(2005, length(age.grid)),\n",
     "                                          education = rep(\"4. College Grad\", length(age.grid))))\n",
     "pred.3 = predict(gam1, newdata = data.frame(age = age.grid,\n",
     "                                          year = rep(2009, length(age.grid)),\n",
     "                                          education = rep(\"1. < HS Grad\", length(age.grid))))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "For plotting we select now all data in the years 2004 to 2006 for individuals with less than a High School degree and plot it together with our prediction."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
-    "subset = year >= 2004 && year <= 2006 & education == \"1. < HS Grad\"\n",
+    "subset = year >= 2004 & year <= 2006 & education == \"1. < HS Grad\"\n",
     "plot(age[subset], wage[subset])\n",
     "lines(age.grid, pred.1, type = \"l\", col = \"red\")\n",
     "lines(age.grid, pred.2, type = \"l\", col = \"blue\")\n",
     "lines(age.grid, pred.3, type = \"l\", col = \"darkgreen\")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Note that the prediction for individual with a College Graduation or the prediction for the year 2009 is merely a shifted version of the original prediction. This is a consequence of the additivity of the model. The shape of the function `wage = f(age)` is independent of the other predictors; only the absolute level is influenced by the intercept and the other predictors."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "For smoothing splines we use the `gam` library. The `s()` function is used to indicate that we would like to use a smoothing spline.\n",
     " \n",
     "The `gam` library also has a built-in plotting function that allows us to see the dependence of the `wage` independently of the other variables. Note that we would have to add the intercept and the choices for the other predictors to get the effective prediction of wage."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "library(gam)\n",
     "gam.m3 = gam(wage ~ s(year, 4) + s(age, 5) + education, data = Wage)\n",
     "plot(gam.m3, se = T, col = \"red\")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Bias-Variance Decomposition (optional)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "In the first lecture we saw the decomposition of the test error into bias and variance as a function of the flexibility of the method. With smoothing splines one can nicely generate such plots.\n",
     "\n",
     "The following code is at parts more involved than what you are used to. Try nevertheless to understand what is happing. You are not yet expected to write such code without guidance.\n",
     "\n",
     "The idea is to generate artificial data, where we know exactly what the true model is. The true model is given by the non-linear function `noisefree.generator`. The function `data.generator` creates each time a new data set by sampling some `x` values, applying the `noisefree.generator` function and adding normal noise with standard deviation 1 to get `y`."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "noisefree.generator = function(x) (-.1*(x-1)^4*(x < 1) - 2*x^3*sin(5*x) + x^2 - 4*x*(x > 0))\n",
     "data.generator = function(n) {\n",
     "  x = 3*runif(n) - 1.5\n",
     "  y = noisefree.generator(x) + rnorm(length(x))\n",
     "  data.frame(x = x, y = y)\n",
     "}"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Let us plot some data points and some smooth spline fits together with the true function in red."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "data = data.generator(200)\n",
     "fit.1 = smooth.spline(data$x, data$y, df = 2)\n",
     "fit.2 = smooth.spline(data$x, data$y, df = 20)\n",
     "fit.3 = smooth.spline(data$x, data$y, df = 100)\n",
     "plot(data, col = \"darkgray\")\n",
     "lines(fit.1, col = \"purple\")\n",
     "lines(fit.2, col = \"darkgreen\")\n",
     "lines(fit.3, col = \"blue\")\n",
     "plot(noisefree.generator, add = T, xlim = c(-1.5, 1.5), col = \"red\")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Now we create to functions that compute test and training errors for a given fit. The test error will be evaluated over 10000 new data points."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "test.error = function(fit) {\n",
     "  test.data = data.generator(10000)\n",
     "  pred = predict(fit, test.data$x)\n",
     "  mean((pred$y - test.data$y)^2)\n",
     "}\n",
     "train.error = function(fit, x, y) {\n",
     "  mean((predict(fit, x)$y - y)^2)\n",
     "}"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "list(test.error(fit.1), test.error(fit.2), test.error(fit.3))"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "list(train.error(fit.1, data$x, data$y), train.error(fit.2, data$x, data$y), train.error(fit.3, data$x, data$y))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "The following function `bias.variance` takes as input the number `k` of repetitions and the degree of freedom `df`. It then fits `k` times a smoothing spline of degree `df` on `k` different training sets from the same population.\n",
     "\n",
     "The squared bias of the model is then the mean squared difference between the average of the `k` smoothing splines and the true function.\n",
     "\n",
     "The variance is simply the variance of the `k` smoothing splines.\n",
     "\n",
     "Additionally we return the average test and training error."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "bias.variance = function(k, df = df) {\n",
     "  predictions = matrix(rep(NA, k*1000), k, 1000)\n",
     "  train.errors = rep(NA, k)\n",
     "  test.errors = rep(NA, k)\n",
     "  test.x = seq(-1.5, 1.5, length = 1000)\n",
     "  for (i in 1:k) {\n",
     "    data = data.generator(200) # each time another training set\n",
     "    fit = smooth.spline(data$x, data$y, df = df)\n",
     "    train.errors[i] = train.error(fit, data$x, data$y)\n",
     "    test.errors[i] = test.error(fit)\n",
     "    predictions[i,] = predict(fit, test.x)$y # function values for this fit\n",
     "  }\n",
     "  mean.pred = apply(predictions, 2, mean)\n",
     "  bias.squared = mean((mean.pred - noisefree.generator(test.x))^2)\n",
     "  var = mean(sweep(predictions, 2, mean.pred)^2)\n",
     "  data.frame(bias.squared = bias.squared,\n",
     "             variance = var, \n",
     "             test.error = mean(test.errors), \n",
     "             train.error = mean(train.errors))\n",
     "}"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Now we run this function for many different degrees of freedom and plot the result. Evaluating this cell takes some minutes. You can also just look at the output from a previous run. We marked the irreducible error with a dashed line."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 185,
    "metadata": {},
    "outputs": [
     {
      "data": {
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EaRJPfJAgAAZAJhpwKzGTu9XiKEGTsA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OblKHJbJ3LHa2TBCE7OxsqVMQkZyYWk2WAnek+qMYOXoAACAASURBVEhedV5udW5j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\ngg==",
       "text/plain": [
        "plot without title"
       ]
      },
      "metadata": {
       "image/png": {
        "height": 420,
        "width": 420
       },
       "text/plain": {
        "height": 420,
        "width": 420
       }
      },
      "output_type": "display_data"
     }
    ],
    "source": [
     "biases = rep(NA, 50)\n",
     "variances = rep(NA, 50)\n",
     "trainerr = rep(NA, 50)\n",
     "testerr = rep(NA, 50)\n",
     "for (i in 1:50) {\n",
     "  res = bias.variance(1000, 2*i)\n",
     "  biases[i] = res$bias.squared\n",
     "  variances[i] = res$variance\n",
     "  trainerr[i] = res$train.error\n",
     "  testerr[i] = res$test.error\n",
     "}\n",
     "df = 2*(1:50)\n",
     "plot(df, biases, col = \"black\", type = \"l\", ylim = c(0, 4), xlab = \"DF\", ylab = \"error\")\n",
     "lines(df, variances, col = \"darkgreen\")\n",
     "lines(df, trainerr, col = \"blue\")\n",
     "lines(df, testerr, col = \"red\")\n",
     "lines(df, rep(1, 50), lty = \"dashed\")\n",
     "legend(\"topright\", legend = c(\"bias^2\", \"variance\", \"training error\", \"test error\"),\n",
     "       col = c(\"black\", \"darkgreen\", \"blue\", \"red\"), lty = 1)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
    "display_name": "R",
    "language": "R",
    "name": "ir"
   },
   "language_info": {
    "codemirror_mode": "r",
    "file_extension": ".r",
    "mimetype": "text/x-r-source",
    "name": "R",
    "pygments_lexer": "r",
    "version": "3.6.1"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 2
 }