Skip to content

Instantly share code, notes, and snippets.

@gngdb
Created January 22, 2014 18:57
Show Gist options
  • Star 0 You must be signed in to star a gist
  • Fork 0 You must be signed in to fork a gist
  • Save gngdb/8565000 to your computer and use it in GitHub Desktop.
Save gngdb/8565000 to your computer and use it in GitHub Desktop.
tutorial 1
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"# Question 6\n",
"\n",
"> Suppose that X and Y are independent and each is uniformly distributed on (0, 1). Let U = X +\n",
"> Y and V = X - Y.\n",
">\n",
"> * Sketch the range (the region of non zero probability) of (X, Y) and the range of (U, V).\n",
"> * Find the density function of (U, V).\n",
"> * Find the density function of U.\n",
"> * Find the density function of V.\n",
"\n",
"Ok, so can draw the pdfs for both random variables pretty easily."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = linspace(-1,2,100)\n",
"y = []\n",
"#there is probably a better way of doing this\n",
"for element in x:\n",
" if element > 0 and element <1:\n",
" y.append(1)\n",
" else:\n",
" y.append(0)\n",
"plot(x,y)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 2,
"text": [
"[<matplotlib.lines.Line2D at 0x42b76d0>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEACAYAAABI5zaHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKEP/Bzhlrpjg+7UMAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x3f6e190>"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then what we're being asked to do is plot the region of nonzero probability in (X,Y). Since both X and Y are zero everywhere except between 0 and 1 this is just a square between 0 and 1 in both axes. Can also find this computationally."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = rand(10000)\n",
"y = rand(10000)\n",
"# code blatantly copied from stackexchange\n",
"def drawheatmap(x,y):\n",
" heatmap, xedges, yedges = histogram2d(y, x, bins=50)\n",
" extent = [xedges[0], xedges[-1], yedges[0], yedges[-1]]\n",
" plt.clf()\n",
" plt.imshow(heatmap, extent=extent)\n",
" plt.show()\n",
" return None\n",
"drawheatmap(x,y)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAQcAAAEACAYAAAC+rrMfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text": [
"<matplotlib.figure.Figure at 0x42d72d0>"
]
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we have to sketch the region of nonzero probability for U and V. To do this analytically involves translating all the possible values for both probability distributions. But, we don't actually have to consider all possible values - just the corners because they define the square. Specifically, these points:\n",
"\n",
"$$ (X,Y)={(0,0),(0,1),(1,0),(1,1)} $$\n",
"\n",
"For each point apply the two equations:\n",
"\n",
"$$ U = X+Y $$\n",
"$$ V = X-Y $$\n",
"\n",
"Yielding:\n",
"\n",
"$$ (U,V)={(0,0),(1,-1),(1,1),(2,0)} $$\n",
"\n",
"Which is a larger square turned on it's corner. The translation can also be done using a Jacobian matrix:\n",
"\n",
"$$ J = \\left| \\begin{array}{cc}\n",
" \\frac{\\delta U}{\\delta x} & \\frac{\\delta U}{\\delta y} \\\\[0.3em]\n",
" \\frac{\\delta V}{\\delta x} & \\frac{\\delta V}{\\delta y} \\end{array} \\right| $$\n",
" \n",
"Where $\\frac{\\delta U}{\\delta x} = 1$, $\\frac{\\delta U}{\\delta y} = 1$, $\\frac{\\delta V}{\\delta x} = 1$ and $\\frac{\\delta V}{\\delta y} = -1$.\n",
"\n",
"$$ \\begin{pmatrix}\n",
" U \\\\\n",
" V \\end{pmatrix} = \\left| \\begin{array}{cc}\n",
" \\frac{\\delta U}{\\delta x} & \\frac{\\delta U}{\\delta y} \\\\[0.3em]\n",
" \\frac{\\delta V}{\\delta x} & \\frac{\\delta V}{\\delta y} \\end{array} \\right|\n",
" \\begin{pmatrix}\n",
" X \\\\\n",
" Y \\end{pmatrix} $$\n",
" \n",
"Which works out the same as above. Now we know the range and we know it's uniformly distributed so we could just say that since the area of the new square is 2 the uniform density must be $\\frac{1}{2}$ over the region. Or we could use the Jacobian. Then, from Murphy (Multivariate change of variables p.50 and 51), it's possible to transfer the probability distribution onto this new range.\n",
"\n",
"$$ P(U,V) = \\left|\\frac{1}{det(J)}\\right| P(X,Y) = \\frac{1}{2} \\times 1 = \\frac{1}{2} $$\n",
"\n",
"Can draw this by solving computationally aswell:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"u = x+y\n",
"v = x-y\n",
"drawheatmap(u,v)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAQMAAAD7CAYAAABuZ/ELAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x3fcac10>"
]
}
],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we have to find the density functions of U and V. To do this we marginalise along the axes. The above graph defines $P(U,V)$ and we want $P(U)$ and $P(V)$. Marginalising:\n",
"\n",
"$$ P(U) = \\int_V P(U,V) dV $$\n",
"and\n",
"$$ P(V) = \\int_U P(U,V) dU $$\n",
"\n",
"Unfortunately, it's kind of difficult to define the region that the graph exists over because it's on a corner. One thing you can do is look at the graph and just say how the area will change as you travel across either axis. On the u axis it will be zero at -1 and 1 and in the middle it will be 2; these three points will be joined by lines because the area between them will increase linearly (no curves on the sides of the square). That means P(V) is:\n",
"\n",
"$$ P(V) = 2x + 2 \\text{ for } -1 \\leq V \\leq 0 $$\n",
"$$ P(V) = -2x + 2 \\text{ for } 0 < V \\leq 1 $$\n",
"\n",
"Along the v axis the same thing will happen but the maximum and minimum will be 0 and 2. So:\n",
"\n",
"$$ P(U) = 2x + 2 \\text{ for } 0 \\leq V \\leq 1 $$\n",
"$$ P(U) = -2x + 2 \\text{ for } 1 < V \\leq 2 $$\n",
"\n",
"To prove this is right here are the histograms:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a = hist(u, bins=50, label='u')\n",
"a = hist(v, bins=50, label='v')\n",
"legend()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 19,
"text": [
"<matplotlib.legend.Legend at 0x49db610>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJnoiIpH7f61/mI7A971UAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x5421e10>"
]
}
],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Question 7\n",
"\n",
"This takes a long time to read.\n",
"\n",
"> Suppose you wish to predict a binary class label y , given one variable x.\n",
"> You know the class label is created from that variable by thresholding at some value a: $y(x) = H(x-a)$, $H(x)=1$ if $x \\geq 0$, $H(x) = 0$ if $ x < 0^{1}$(why $0^{1}$?), but that value a is unknown.\n",
"> You know that the true threshold is\n",
"> somewhere between 1 and 9 with equal probability. What is your best guess of threshold and why?\n",
"> You observe a new data point with the value of 7. You classify this as a 1 using your threshold.\n",
"> How can you update your best-guess threshold using this new information? What would your new\n",
"> threshold be? An expert now confirms that the classification you made for the new data point\n",
"> was right. How can you update your threshold using this new information? What would your\n",
"> new threshold be? A friend proposes you should train a machine learning algorithm by using the\n",
"> machine learning algorithm until it makes a mistake, and then adjust the algorithm to correct for\n",
"> that mistake (without upsetting previous predictions). What would you say to the friend?\n",
"\n",
"Basically he's saying there's an unknown threshold where the output of this formula switches from 0 to 1 but you don't know where it is in the range $1 \\to 9$. So you guess by taking the expected value of the range:\n",
"\n",
"$$ E[X] = \\int_{1}^{9} X \\frac{1}{8} dX = 5 $$\n",
"\n",
"Then you see apply this new range to the data point and say it's a 1. You shouldn't update your threshold with this new information because you don't really have any new information.\n",
"\n",
"Then the expert confirms that you're right so now you can define a new range where you know it's somewhere between 1 and 7. So now you do the same thing and take the expected value again:\n",
"\n",
"$$ E[X] = \\int_{1}^{7} X \\frac{1}{6} dX = 4 $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Question 8\n",
"\n",
"> You are an auditor of a firm. You receive details about the sales that a particular salesman is\n",
"> making. He attempts to make 4 sales a day to independent companies. You receive a list of the\n",
"> number of sales by this agent made on a number of days. Explain why you would expect the total\n",
"> number of sales to be binomially distributed.\n",
"> If the agent was making the sales numbers up as part of a fraud, you might expect the agent (as he\n",
"> is a bit dim) to choose the number of sales at random from a uniform distribution. You are aware\n",
"> of the fraud possibility, and you understand there is something like a 1/5 chance this salesman is\n",
"> involved. Given daily sales counts of 1 2 2 4 1 4 3 2 4 1 3 3 2 4 3 3 2 3 3, do you think the salesman\n",
"> is lying?\n",
"\n",
"So this is a complicated way of saying we're going to be comparing two models that could describe the data we've got here.\n",
"The data is that sequence of numbers and the two models are a uniform model where he just picks a random number from between 0 and 4 whenever he's asked how many sales he's made and a binomial where he attempts to make a sale and it fails or succeeds with some probability $\\theta$. If we call the binomial model $M_{1}$ then:\n",
"\n",
"$$ P(D|M_{1}, \\theta , n, k) = \\prod_D \\frac{n!}{(n-k)!k!} \\theta^{k}(1-\\theta)^{n-k} $$\n",
"\n",
"And we call the uniform model $M_{2}$ then:\n",
"\n",
"$$ P(D|M_{2}, p) = \\prod_{D} \\frac{1}{p} = (0.2)^{19} $$\n",
"\n",
"What we want is:\n",
"\n",
"$$ \\frac{P(M_{1}|D, n, k)}{P(M_{2}|D, p)} = \\frac{P(D|M_{1}, n, k) P(M_{1})}{P(D|M_{2},p) P(M_{2}} $$\n",
"\n",
"Luckily we already know $P(M_{2}) = 0.2$, so therefore $P(M_{1})=0.8$. Unfortunately:\n",
"\n",
"$$ P(D|M_{1}, n, k) = \\int P(D|M_{1}, \\theta, n, k)P(\\theta) d\\theta $$\n",
"\n",
"Somehow, we can assume:\n",
"\n",
"$$ P(\\theta) = 1 $$\n",
"\n",
"Using the beta integral and $K$ is the constant formed by multiplying binomial distributions together:\n",
"\n",
"$$ \\int P(D|M_{1}, \\theta, n, k)P(\\theta) d\\theta = \\int K \\theta^{k}(1-\\theta)^{n-k} = K (\\frac{k!(n-k)!}{(n+1)!}) $$\n",
"\n",
"If we treat every day as a different binomial sampling then K is:\n",
"\n",
"$$ K = \\left(\\frac{4!}{(4-1)!1!}\\right)^{3} \\times \\left(\\frac{4!}{(4-2)!2!}\\right)^{5} \\times \\left(\\frac{4!}{(4-3)!3!}\\right)^{7} = 4^{3} 6^{5} 4^{7} = 4^{10} 6^{5} $$\n",
"\n",
"\n",
"For $n=76$ and $k=50$:\n",
"\n",
"$$ \\frac{P(D|M_{1}, n, k) P(M_{1})}{P(D|M_{2},p) P(M_{2}} = \\frac{0.8 \\times 4^{10}6^{5}\\frac{50!26!}{77!}}{0.2 \\times (0.2)^{19}} $$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mf = math.factorial\n",
"(0.8*(4**10)*(6**5)*(mf(60)*mf(26))/(mf(77)))/(0.2*(0.2**19))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 2,
"text": [
"1.4378847364546443e+19"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Which is wrong. Seems very similar to the expression in the solutions though. Using that we end up with:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"lg = math.lgamma\n",
"ans = log((4**10)*(6**5)) + lg(51)+lg(27)-lg(78)\n",
"print e**ans"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"6.88864846717e-13\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So if I use this in the above equation instead we get:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"(0.8*e**ans)/(0.2**20)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 19,
"text": [
"52.556216943166717"
]
}
],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Which is approximately 52 times as likely that he's telling the truth. Unfortunately, this isn't what the solutions say (approx. 65) so trying his numbers directly:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"(0.8*6.89*10**-13)/(0.2*5.25*10**-14)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 20,
"text": [
"52.49523809523809"
]
}
],
"prompt_number": 20
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Either the numbers stated in the solutions to calculate the final number are wrong or the final answer is wrong?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Question 9\n",
"\n",
">This question is difficult to copy in. Will copy it in when I have time. In the mean time [link](http://www.inf.ed.ac.uk/teaching/courses/mlpr/fall2013/tutorials/mlpr-tutorial1.pdf).\n",
"\n",
"This is supposed to be something you can do after the [second lecture](http://www.inf.ed.ac.uk/teaching/courses/mlpr/fall2013/lectures/dataandmodels-4up.pdf) I think. That explains at least what the class labels are. Murphy chapter 3 should also explain this. Also, there's a link to some [useful notes by Amos Storkey](http://www.inf.ed.ac.uk/teaching/courses/mlpr/lectures/mlpr-naive.pdf). From the lecture we've got the equation:\n",
"\n",
"$$ P(D|M) = \\prod_{n} P(\\pmb{x}^{n}| y = c^{n}) P(c^{n}) = \\prod_{n} P(c^{n}) \\prod_{d=1}^{D} P(x_{d}^{n}|y=c^{n})$$\n",
"\n",
"Where $n$ is the data point index, $\\pmb{x}$ is a vector of all your attributes $x_{1},x_{2},x_{3}...$ and $c^{n}$ is the class label for these different data points. So $P(c^{n})$ is the prior probability of class $n$.\n",
"\n",
"What's slightly confusing in this question is it looks like the data is the class labels? Whereas in the lectures the class is inferred from the data. Also the lecture notes just say to apply maximum likelihood and don't go into how that's actually done.\n",
"\n",
"Ok, so $x_{4}$ is the class label and the rest are the data. Meaning we have a set of training and test data.\n",
"\n",
"(1;0;1;1);(0;1;0;1);(0;1;1;0);(0;0;0;0);(1;1;1;1);(0;0;0;0);(1;0;1;0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Working from the solutions backwards\n",
"\n",
"Splitting the data and the model we can get the equation for our model:\n",
"\n",
"$$ P(x_{1},x_{2},x_{3}|x_{4}) = \\prod_{n} P(x_{4}^{n}) \\prod_{d=1}^{3} P(x_{d}^{n}|y=x_{4}^{n}) $$\n",
"\n",
"Then we can apply Bayes' theorem:\n",
"\n",
"$$ P(x_{4}|x_{1},x_{2},x_{3}) = \\frac{P(x_{1},x_{2},x_{3}|x_{4})P(x_{4})}{P(x_{1},x_{2},x_{3})} = \\frac{\\prod_{n} P(x_{4}^{n}) \\prod_{d=1}^{3} P(x_{d}^{n}|y=x_{4}^{n})P(x_{4})}{P(x_{1},x_{2},x_{3})} $$\n",
"\n",
"The term on the bottom has to be derived by marginalising the model above:\n",
"\n",
"$$ P(x_{1},x_{2},x_{3}) = \\sum_{n} P(x_{1}^{n},x_{2}^{n},x_{3}^{n}|x_{4}^{n})P(x_{4}^{n}) $$\n",
"\n",
"So the final equation is:\n",
"\n",
"$$ P(x_{4}|x_{1},x_{2},x_{3}) = \\frac{\\prod_{n} P(x_{4}^{n}) \\prod_{d=1}^{3} P(x_{d}^{n}|y=x_{4}^{n})P(x_{4})}{\\sum_{n} P(x_{1}^{n},x_{2}^{n},x_{3}^{n}|x_{4}^{n})P(x_{4}^{n})} $$\n",
"\n",
"Which is what the question asks for at the start. So the next thing to do is to show the maximum likelihood estimate of the parameter $p(x_{i}=0|x_{4}=1)$ is proportional to the number of times attribute i is 0 for class 1 data. Class 1 data is the data where $x_{4}$ is 1 (I am reminding myself here).\n",
"\n",
"Ok, so this is where the solutions get weird. It doesn't say why it's calculating the maximum likelihood or how it jumps several lines of working and substitutes in $\\gamma_{i}$ for some reason."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Working backwards from tutor's notes\n",
"\n",
"So first we want to define the likelihood for $x_{4} = 1$. We take the product of the joint probability over the data points where $x_{4}=1$ (there are three of these).\n",
"\n",
"$$ P(D|M) = \\prod_{d=1}^{3} P(x_{1}^{n},x_{2}^{n},x_{3}^{n},x_{4}^{n}=1) = \\prod_{d=1}^{3} P(x_{1}^{n},x_{2}^{n},x_{3}^{n})P(x_{4}^{n}=1) $$\n",
"\n",
"Then, since they're conditionally independent:\n",
"\n",
"$$ P(D|M) = \\prod_{d=1}^{3} P(x_{1}^{n})P(x_{2}^{n})P(x_{3}^{n})P(x_{4}^{n}=1) $$\n",
"\n",
"Then take the log of all this to make the maths easier (was there another reason?):\n",
"\n",
"$$ P(D|M) = 3 log(P(x_{4}^{n}=1)) + \\sum_{n=1}^{3} \\sum_{i=1}^{3} log(P(x_{i}^{n}|x_{4}^{n}=1)) $$\n",
"\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from sympy import *"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment