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@marcusway
Last active January 27, 2023 16:08
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Feasibility of Learning
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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Learning From Data\n",
"## Chapter 1.3: Is Learning Feasible? \n",
"This is a solution to an exercise that I found particularly compelling in Abu-Mostafa, et al.'s book, _Learning from Data_. The exercise is from section 1.3 of the book, which examines whether it is reasonable for us to make predictions about yet unobserved data based on that data that we have observed, which is the essence of learning. To be able to make such predictions, we need some sort of indication that our unobserved data is at least something like our observed data. While a guarantee is too much to ask, if we assume that our observations are independent from one another, we can at least make probabilistic statments about how closely our observations agree with reality at large. "
]
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{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"%matplotlib inline \n",
"import seaborn as sns\n",
"from __future__ import division\n",
"sns.set_style(\"whitegrid\")\n",
"sns.set_context(font_scale=5)\n",
"sns.plt.xkcd();"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 107
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 1.10\n",
"\n",
"Here is an experiment that illustrates the difference between a single bin and multiple bins. Run a computer simulation for flipping 1000 fair coins. Flip each coin independently 10 times. Let's focus on 3 coins as follows: $c_1$ is the first coin flipped; $c_{rand}$ is a coin you choose at random, and $c_{min}$ is the coin that had the minimum frequency of heads (pick the earlier one in the case of a tie). Let $v_1$, $v_{rand}$, and $v_{min}$ be the fraction of heads you optain for the respective three coins. \n",
"\n",
"- (a) What is $\\mu$ for the three coins selected? \n",
"- (b) Repeat this experiment a large number of times (e.g. 100,000 runs of the entire experiment) to get several instances of $v_1$, $v_{rand}$, and $v_{min}$ and plot the histograms of the distributions for $v_1$, $v_{rand}$, and $v_{min}$. Notice that which coins end up being $c_1$, $c_{rand}$, and $c_{min}$ may differ from one run to another. \n",
"- (c) Using (b), plot estimates for $P[|v - \\mu| > \\epsilon]$ as a function of $\\epsilon$, together with the Hoeffding bound, $2e^{-2\\epsilon^2N}$\n",
"- (d) Which coins obey the Hoeffding bound, and which ones do not? Explain why. \n",
"- (e) Relate part (d) to the multiple bins in Figure 1.10"
]
},
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"cell_type": "markdown",
"metadata": {},
"source": [
"### (a) What is $\\mu$ for the three coins selected? "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since $\\mu$ refers to the true probability of flipping heads, and we're assuming that we're flipping a fair coin, then $P(heads) = P(tails) = 0.5$. Therefore, $\\mu = 0.5$ for each of $c_1$, $c_{min}$, and $c_{rand}$, as well as for all other coins, regardless of what the outcomes are for the flips of those coins in our sample. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### (b) Repeat this experiment a large number of times (e.g. 100,000 runs of the entire experiment) to get several instances of $v_1$, $v_{rand}$, and $v_{min}$ and plot the histograms of the distributions for $v_1$, $v_{rand}$, and $v_{min}$. Notice that which coins end up being $c_1$, $c_{rand}$, and $c_{min}$ may differ from one run to another. \n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def conduct_experiment(p, n_flips, n_coins, n_trials):\n",
" \n",
" \"\"\"\n",
" Conducts `n_trials` trials of the coin-flipping experiment where\n",
" `n_coins` coins are flipped `n_times` times each. The probability\n",
" of flipping heads on any single coin flip is `p`. Returns v_1s,\n",
" v_mins, and v_rands, where each is an array of length `n_trials`, with\n",
" the i-th entry corresponding to the number of heads flipped for the \n",
" corresponding coin in trial i. Note that this is _not_ the fraction of \n",
" heads. To get the fraction of heads, divide by `n_flips`.\n",
" \n",
" :param: p: the probability of a single flip resulting in heads\n",
" :param: n_flips: the number of times each coin is flipped\n",
" :param: n_coins: the number of separate coins used in each trial \n",
" :param: n_trials: the number of repeated trials of the n_flips by n_coins experiment\n",
" :return: v_1s: array of length `n_trials`; v_1s[i] is the number of heads flipped by c_1 in trial `i` \n",
" v_mins: array of length `n_trials`; v_mins[i] is the number of heads flipped by c_min in trial `i`\n",
" v_rands: array of length `n_trials`; v_mins[i] is the number of heads flipped by c_rand in trial `i`\n",
" \"\"\"\n",
" \n",
" # Get an n_trials x n_coins matrix\n",
" outcome = np.random.binomial(n_flips, p, (n_trials, n_coins))\n",
" \n",
" # First coin in every trial\n",
" v_1s = outcome[:, 0] \n",
" \n",
" # Coin with minimum number of heads for every trial\n",
" v_mins = outcome.min(axis=1) \n",
" \n",
" # Random coin from every trial\n",
" v_rands = np.apply_along_axis(np.random.choice, 1, outcome) \n",
" \n",
" return (v_1s, v_mins, v_rands)\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 120
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"P = 0.5\n",
"N_FLIPS = 10\n",
"N_COINS = 1000\n",
"N_TRIALS = 100000\n",
"v_1s, v_mins, v_rands = conduct_experiment(P, N_FLIPS, N_COINS, N_TRIALS)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 115
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def plot_dist(x, bins=10): \n",
" sns.distplot(\n",
" x,\n",
" hist=True,\n",
" bins=bins, \n",
" hist_kws={\"align\": \"left\", \"normed\":True},\n",
" kde_kws={\"bw\": 1,\"shade\": True}\n",
" );"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 110
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sns.plt.figure(figsize=(12,7))\n",
"sns.plt.subplot(3,1,1)\n",
"plot_dist(v_1s);\n",
"sns.plt.ylabel(\"Fraction\")\n",
"sns.plt.title(\"$v_1$\");\n",
"sns.plt.xlim(0,10)\n",
"sns.plt.xticks([])\n",
"\n",
"sns.plt.subplot(3,1,2)\n",
"plot_dist(v_rands);\n",
"sns.plt.ylabel(\"Fraction\");\n",
"sns.plt.title(\"$v_{rand}$\");\n",
"sns.plt.xlim(0,10)\n",
"sns.plt.xticks([])\n",
"\n",
"sns.plt.subplot(3,1,3)\n",
"plot_dist(v_mins, bins=2);\n",
"sns.plt.xlabel(\"$P(heads)$\");\n",
"sns.plt.ylabel(\"Fraction\");\n",
"sns.plt.title(\"$v_{min}$\");\n",
"sns.plt.xlim(0,10)\n",
"sns.despine()\n",
"\n",
"sns.plt.xticks(np.arange(11), np.arange(11)/10);"
],
"language": "python",
"metadata": {},
"outputs": [
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FPPzww9x8880sWrSICy+8sETv9/v9FBTJ5ZSXl0ft2ocGrOzdu5d69eoB4sf+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zBNsRWaFnFtf4jHEeWVMXtZEi1awIMPwubNshnRb38ri0BffBF69IDTT5dFomp/QsWxUCWifMmS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\nBEEQBEFQ+ApBEARBEARBmA6JcoIgCIIgCIIwGRLlBEEQBEEQB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"text": [
"<matplotlib.figure.Figure at 0x13fe06090>"
]
}
],
"prompt_number": 119
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that $v_1$ and $v_{rand}$ behave identically, as one might expect, since there is nothing special about the first coin--it might as well be a random coin. In other words, $c_1$ and $c_{rand}$, the coins that produce $v_1$ and $v_{rand}$, respectively, are chosen independent of the observed data, and could be fixed prior to doing any flipping at all. On the other hand, $c_{min}$ is only chosen after all the flipping is done. In almost every trial, there was at least one coin where the observed probability of flipping heads was $\\le0.1$ \n",
"\n",
"This is why the distributions of $v_1$ and $v_{rand}$ are centered over the true mean, $\\mu$, while $v_{min}$ is not."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### (c) Using (b), plot estimates for $P[|v - \\mu| > \\epsilon]$ as a function of $\\epsilon$, together with the Hoeffding bound, $2e^{-2\\epsilon^2N}$\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def hoeffding(epsilon, N=N_FLIPS): \n",
" return 2 * np.exp(-2 * (epsilon**2) * N)\n",
"\n",
"def p_big_error(v, mu, epsilon):\n",
" return (np.abs(v - mu)/N_FLIPS > epsilon).mean()\n",
"\n",
"epsilons = np.linspace(0,10,100)/N_FLIPS\n",
"\n",
"c1_errs = [p_big_error(c_1s, 5, e) for e in epsilons]\n",
"c_rand_errs = [p_big_error(c_rands, 5, e) for e in epsilons]\n",
"c_min_errs = [p_big_error(c_mins, 5, e) for e in epsilons]\n",
"\n",
"sns.plt.figure(figsize=(8,5));\n",
"sns.plt.plot(epsilons, c1_errs, linewidth=6, linestyle= \"--\");\n",
"sns.plt.plot(epsilons, c_rand_errs);\n",
"sns.plt.plot(epsilons, c_min_errs);\n",
"sns.plt.plot(epsilons, np.apply_along_axis(hoeffding, 0, epsilons));\n",
"sns.plt.legend(\n",
" [\n",
" \"$P(|v_1 - \\mu| < \\epsilon)$\",\n",
" \"$P(|v_{rand} - \\mu| < \\epsilon)$\",\n",
" \"$P(|v_{min} - \\mu| < \\epsilon)$\",\n",
" \"Hoeffding Bound\"\n",
" ]\n",
");\n",
"sns.despine();\n",
"sns.plt.xlabel(\"$\\epsilon$\");\n",
"sns.plt.ylabel(\"Upper bound on $P(|v - \\mu| > \\epsilon)$\");\n",
"sns.plt.title(\"$P(|v - \\mu| > \\epsilon)$ as a function of $\\epsilon$\");"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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Dh4XS4d4OaC5NZjAUQojTTJw4kb1791abqKg2ERERKIqC2WzG4/EQGxvL5s2b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\nWEPZ62XRDitm5NlsAJRJQiBEXOgRCYGIjGOPhQceoDkh2LCBvgUBzj4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"text": [
"<matplotlib.figure.Figure at 0x142b53bd0>"
]
}
],
"prompt_number": 122
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### (d) Which coins obey the Hoeffding bound, and which ones do not? Explain why. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see from the plot that $v_{rand}$ and $v_{first}$ obey the Hoeffding inequality, but $v_{min}$ does not. That's because $v_{min}$ was specifically chosen from a set of 100,000 samples based on the sample results. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### (e) Relate part (d) to the multiple bins in Figure 1.10"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is analogous to the situation where $h$ is not chosen a priori, but rather chosen from a hypothesis set, $H$, according to the observed data. The number of possible hypotheses, $M$, is not accounted for. Regarding the \"bins\", each of which represents a different hypothesis, $h$, for $v_{rand}$ and $v_{first}$, we've decided on a particular $h$ before seeing the data, so it's as though we're only looking at one bin, $h$ is fixed, and Hoeffding holds. In the case of $v_{min}$, we pick a bin after being presented with all of the data. The Hoeffding inequality, which describes a bound on the difference between our observed fraction of heads, $v$, and the \"actual\" fraction of heads, $\\mu$, assumes that $v$ is from a single random sample. That assumption is violated in the case of $v_{min}$"
]
}
],
"metadata": {}
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}
@DreamyPujara
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what are the values of c_1s and C_min that you are using?? for c_rands and c_error? in part c?

@marcusway
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hi! been a long time since i've looked at this, but it would appear that those aren't defined. Would the v_1s, v_mins, v_rands variables work in place of their c_* counterparts here?

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