From 77cdfff36403e13585d6db6b28913f5ec1a5cf37 Mon Sep 17 00:00:00 2001 From: Mack Sweeney Date: Sun, 26 Apr 2015 14:15:17 -0400 Subject: [PATCH] improve formatting for mkdocs ToC; fix eq. rendering --- pymc3/examples/pmf-pymc.ipynb | 523 +++++++++++----------------------- 1 file changed, 159 insertions(+), 364 deletions(-) diff --git a/pymc3/examples/pmf-pymc.ipynb b/pymc3/examples/pmf-pymc.ipynb index 0ddeff6f1f..11a6df73a4 100644 --- a/pymc3/examples/pmf-pymc.ipynb +++ b/pymc3/examples/pmf-pymc.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:429f17292ea0f8875a09417eb7969567126897b6eb418ad1faa35ee20607220f" + "signature": "sha256:50a47d4f6edb62bd73b9f14f110d74e80b2c2817875d7b1290bf98c937b5aa01" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,7 +12,16 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Probabilistic Matrix Factorization for Making Personalized Recommendations\n", + "# Probabilistic Matrix Factorization for Making Personalized Recommendations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The model discussed in this analysis was developed by Ruslan Salakhutdinov and Andriy Mnih. All of the code and supporting text, when not referenced, is the original work of [Mack Sweeney](https://www.linkedin.com/in/macksweeney).\n", + "\n", + "## Motivation\n", "\n", "Say I download a handbook of a hundred jokes, and I'd like to know very quickly which ones will be my favorite. So maybe I read a few, I laugh, I read a few more, I stop laughing, and I indicate on a scale of -10 to 10 how funny I thought each joke was. Maybe I do this for 5 jokes out of the 100. Now I go to the back of the book, and there's a little program included for calculating my preferences for all the other jokes. I enter in my preference numbers and shazam! The program spits out a list of all 100 jokes, sorted in the order I'll like them. That certainly would be nice. Today we'll write a program that does exactly this.\n", "\n", @@ -35,13 +44,18 @@ "To better understand CF techniques, let us explore a particular example. Imagine we are seeking to recommend jokes using a model which infers five latent factors, $V_j$, for $j = 1,2,3,4,5$. In reality, the latent factors are often unexplainable in a straightforward manner, and most models make no attempt to understand what information is being captured by each factor. However, for the purposes of explanation, let us assume the five latent factors might end up capturing the humor profile we were discussing above. So our five latent factors are: dry, sarcastic, crude, sexual, and political. Then for a particular user $i$, imagine we infer a preference vector $U_i = <0.2, 0.1, 0.3, 0.1, 0.3>$. Also, for a particular item $j$, we infer these values for the latent factors: $V_j = <0.5, 0.5, 0.25, 0.8, 0.9>$. Using the dot product as the prediction function, we would calculate 0.575 as the ranking for that item, which is more or less a neutral preference given our -10 to 10 rating scale.\n", "\n", "$$0.2 \\times 0.5 + 0.1 \\times 0.5 + 0.3 \\times 0.25 + 0.1 \\times 0.8 + 0.3\n", - "\\times 0.9 = 0.575$$\n", - "\n", - "## Data\n", + "\\times 0.9 = 0.575$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Data\n", "\n", "The [v1 Jester dataset](http://eigentaste.berkeley.edu/dataset/) provides something very much like the handbook of jokes we have been discussing. The original version of this dataset was constructed in conjunction with the development of the [Eigentaste recommender system](http://eigentaste.berkeley.edu/about.html) [[2]](http://goldberg.berkeley.edu/pubs/eigentaste.pdf). At this point in time, v1 contains over 4.1 million continuous ratings in the range [-10, 10] of 100 jokes from 73,421 users. These ratings were collected between Apr. 1999 and May 2003. In order to reduce the training time of the model for illustrative purposes, 1,000 users who have rated all 100 jokes will be selected randomly. We will implement a model that is suitable for collaborative filtering on this data and evaluate it in terms of root mean squared error (RMSE) to validate the results.\n", "\n", - "Let's begin by exploring our data. We want to get a general feel for what it looks like and a sense for what sort of patterns it might contain.\n" + "Let's begin by exploring our data. We want to get a general feel for what it looks like and a sense for what sort of patterns it might contain." ] }, { @@ -218,7 +232,7 @@ ], "metadata": {}, "output_type": "pyout", - "prompt_number": 62, + "prompt_number": 14, "text": [ " 1 2 3 4 5 6 7 8 9 10 ... 91 \\\n", "0 4.08 -0.29 6.36 4.37 -2.38 -9.66 -0.73 -5.34 8.88 9.22 ... 2.82 \n", @@ -238,7 +252,7 @@ ] } ], - "prompt_number": 62 + "prompt_number": 14 }, { "cell_type": "code", @@ -444,22 +458,22 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Methods\n", + "# Methods\n", "\n", "Having explored the data, we're now ready to dig in and start addressing the problem. We want to predict how much each user is going to like all of the jokes he or she has not yet read.\n", "\n", "\n", - "### Baselines\n", + "## Baselines\n", "\n", "Every good analysis needs some kind of baseline methods to compare against. It's difficult to claim we've produced good results if we have no reference point for what defines \"good\". We'll define three very simple baseline methods and find the RMSE using these methods. Our goal will be to obtain lower RMSE scores with whatever model we produce.\n", "\n", - "#### Uniform Random Baseline\n", + "### Uniform Random Baseline\n", "\n", "Our first baseline is about as dead stupid as you can get. Every place we see a missing value in $R$, we'll simply fill it with a number drawn uniformly at random in the range [-10, 10]. We expect this method to do the worst by far.\n", "\n", "$$R_{ij}^* \\sim Uniform$$\n", "\n", - "#### Global Mean Baseline\n", + "### Global Mean Baseline\n", "\n", "This method is only slightly better than the last. Wherever we have a missing value, we'll fill it in with the mean of all observed ratings.\n", "\n", @@ -467,7 +481,7 @@ "\n", "$$R_{ij}^* = \\text{global_mean}$$\n", "\n", - "#### Mean of Means Baseline\n", + "### Mean of Means Baseline\n", "\n", "Now we're going to start getting a bit smarter. We imagine some users might be easily amused, and inclined to rate all jokes more highly. Other users might be the opposite. Additionally, some jokes might simply be more witty than others, so all users might rate some jokes more highly than others in general. We can clearly see this in our graph of the joke means above. We'll attempt to capture these general trends through per-user and per-joke rating means. We'll also incorporate the global mean to smooth things out a bit. So if we see a missing value in cell $R_{ij}$, we'll average the global mean with the mean of $U_i$ and the mean of $V_j$ and use that value to fill it in.\n", "\n", @@ -574,7 +588,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 146 + "prompt_number": 6 }, { "cell_type": "markdown", @@ -602,19 +616,7 @@ " \\prod_{j=1}^M \\mathcal{N}(V_j \\given 0, \\alpha_V^{-1} \\boldsymbol{I})\n", "\\end{equation}\n", "\n", - "Given small precision parameters, the priors on $U$ and $V$ ensure our latent variables do not grow too far from 0. This prevents overly strong user preferences and item factor compositions from being learned. This is commonly known as complexity control, where the complexity of the model here is measured by the magnitude of the latent variables. Controlling complexity like this helps prevent overfitting, which allows the model to generalize better for unseen data. We must also choose an appropriate $\\alpha$ value for the normal distribution for $R$. So the challenge becomes choosing appropriate values for $\\alpha_U$, $\\alpha_V$, and $\\alpha$. This challenge can be tackled with the soft weight-sharing methods discussed by [Nowland and Hinton, 1992](http://www.cs.toronto.edu/~fritz/absps/sunspots.pdf) [4]. However, for the purposes of this analysis, we will stick to using point estimates obtained from our data.\n", - "\n", - "When the observation noise variance $\\alpha$ and the prior variances $\\alpha_U$ and $\\alpha_V$ are all kept fixed, maximizing the log posterior is equivalent to minimizing the sum-of-squared-errors objective function with quadratic regularization terms.\n", - "\n", - "\\begin{equation}\n", - "E = \\frac{1}{2} \\sum_{i=1}^N \\sum_{j=1}^M I_{ij} (R_{ij} - U_i V_j^T)^2 +\n", - " \\frac{\\lambda_U}{2} \\sum_{i=1}^N \\|U\\|_{Fro}^2 +\n", - " \\frac{\\lambda_V}{2} \\sum_{j=1}^M \\|V\\|_{Fro}^2,\n", - "\\end{equation}\n", - "\n", - "where $\\lambda_U = \\alpha_U / \\alpha$, $\\lambda_V = \\alpha_V / \\alpha$, and $\\|\\cdot\\|_{Fro}^2$ denotes the Frobenius norm [3]. Minimizing this objective function gives a local minimum, which is essentially a maximum a posteriori (MAP) estimate. With this result in mind, we can expect that if we use the MAP found by `pymc3` as our start point, as is common practice with `pymc3` models, subsequent draws from an MCMC sampler is not likely to produce any gains, and it may even harm our predictive performance. Our experiments will show this is the case.\n", - "\n", - "One final thing to note: the dot products in this model are often constrained using a logistic function $g(x) = 1/(1 + exp(-x))$, that bounds the predictions to the range [0, 1]. To facilitate this bounding, the ratings are also mapped to the range [0, 1] using $t(x) = (x + 10) / 20$. The authors of PMF also introduced a constrained version which performs better on users with less ratings [3]. Both models are generally improvements upon the basic model presented here. However, in the interest of time and space, these will not be implemented here." + "Given small precision parameters, the priors on $U$ and $V$ ensure our latent variables do not grow too far from 0. This prevents overly strong user preferences and item factor compositions from being learned. This is commonly known as complexity control, where the complexity of the model here is measured by the magnitude of the latent variables. Controlling complexity like this helps prevent overfitting, which allows the model to generalize better for unseen data. We must also choose an appropriate $\\alpha$ value for the normal distribution for $R$. So the challenge becomes choosing appropriate values for $\\alpha_U$, $\\alpha_V$, and $\\alpha$. This challenge can be tackled with the soft weight-sharing methods discussed by [Nowland and Hinton, 1992](http://www.cs.toronto.edu/~fritz/absps/sunspots.pdf) [4]. However, for the purposes of this analysis, we will stick to using point estimates obtained from our data." ] }, { @@ -690,13 +692,23 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 235 + "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We'll also need functions for calculating the MAP and performing sampling on our PMF model. Since it is a reasonably complex model, we expect the MAP estimation to take some time. So let's save it after we've found it. Note that we define a function for finding the map below, assuming it will receive a namespace with some variables in it. Then we attach that function to the PMF class, where it will have such a namespace after initialization. The PMF class is defined in pieces this way so I can say a few things between each piece to make it clearer." + "We'll also need functions for calculating the MAP and performing sampling on our PMF model. When the observation noise variance $\\alpha$ and the prior variances $\\alpha_U$ and $\\alpha_V$ are all kept fixed, maximizing the log posterior is equivalent to minimizing the sum-of-squared-errors objective function with quadratic regularization terms.\n", + "\n", + "$$\n", + "E = \\frac{1}{2} \\sum_{i=1}^N \\sum_{j=1}^M I_{ij} (R_{ij} - U_i V_j^T)^2 +\n", + " \\frac{\\lambda_U}{2} \\sum_{i=1}^N \\|U\\|_{Fro}^2 +\n", + " \\frac{\\lambda_V}{2} \\sum_{j=1}^M \\|V\\|_{Fro}^2,\n", + "$$\n", + "\n", + "where $\\lambda_U = \\alpha_U / \\alpha$, $\\lambda_V = \\alpha_V / \\alpha$, and $\\|\\cdot\\|_{Fro}^2$ denotes the Frobenius norm [3]. Minimizing this objective function gives a local minimum, which is essentially a maximum a posteriori (MAP) estimate. While it is possible to use a fast Stochastic Gradient Descent procedure to find this MAP, we'll be finding it using the utilities built into `pymc3`. In particular, we'll use `find_MAP` with Powell optimization (`scipy.optimize.fmin_powell`). Having found this MAP estimate, we can use it as our starting point for MCMC sampling.\n", + "\n", + "Since it is a reasonably complex model, we expect the MAP estimation to take some time. So let's save it after we've found it. Note that we define a function for finding the MAP below, assuming it will receive a namespace with some variables in it. Then we attach that function to the PMF class, where it will have such a namespace after initialization. The PMF class is defined in pieces this way so I can say a few things between each piece to make it clearer." ] }, { @@ -786,7 +798,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 236 + "prompt_number": 8 }, { "cell_type": "markdown", @@ -830,13 +842,20 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 30 + "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We could define some kind of default trace property like we did for the MAP, but that would mean using possibly nonsensical values for `nsamples` and `njobs`. Better to leave it as a non-optional call to `draw_samples`. Finally, we'll need a function to make predictions using our inferred values for $U$ and $V$. Recall that each rating is simply a draw from a Normal distribution with mean equal to the dot product $U_i V_j^T$." + "We could define some kind of default trace property like we did for the MAP, but that would mean using possibly nonsensical values for `nsamples` and `njobs`. Better to leave it as a non-optional call to `draw_samples`. Finally, we'll need a function to make predictions using our inferred values for $U$ and $V$. For user $i$ and joke $j$, a prediction is generated by drawing from $\\mathcal{N}(U_i V_j^T, \\alpha)$. To generate predictions from the sampler, we generate an $R$ matrix for each $U$ and $V$ sampled, then we combine these by averaging over the $K$ samples.\n", + "\n", + "\\begin{equation}\n", + "P(R_{ij}^* \\given R, \\alpha, \\alpha_U, \\alpha_V) \\approx\n", + " \\frac{1}{K} \\sum_{k=1}^K \\mathcal{N}(U_i V_j^T, \\alpha)\n", + "\\end{equation}\n", + "\n", + "We'll want to inspect the individual $R$ matrices before averaging them for diagnostic purposes. So we'll write code for the averaging piece during evaluation. The function below simply draws an $R$ matrix given a $U$ and $V$ and the fixed $\\alpha$ stored in the PMF object." ] }, { @@ -864,22 +883,31 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 31 + "prompt_number": 10 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One final thing to note: the dot products in this model are often constrained using a logistic function $g(x) = 1/(1 + exp(-x))$, that bounds the predictions to the range [0, 1]. To facilitate this bounding, the ratings are also mapped to the range [0, 1] using $t(x) = (x + min) / range$. The authors of PMF also introduced a constrained version which performs better on users with less ratings [3]. Both models are generally improvements upon the basic model presented here. However, in the interest of time and space, these will not be implemented here." + ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Evaluation\n", + "# Evaluation\n", "\n", - "### Metrics\n", + "## Metrics\n", "\n", "In order to understand how effective our models are, we'll need to be able to evaluate them. We'll be evaluating in terms of root mean squared error (RMSE), which looks like this:\n", "\n", "\\begin{equation}\n", "RMSE = \\sqrt{ \\frac{ \\sum_{i=1}^N \\sum_{j=1}^M I_{ij} (R_{ij} - R_{ij}^*)^2 }\n", " { \\sum_{i=1}^N \\sum_{j=1}^M I_{ij} } }\n", - "\\end{equation}" + "\\end{equation}\n", + "\n", + "In this case, the RMSE can be thought of as the standard deviation of our predictions from the actual user preferences." ] }, { @@ -900,13 +928,13 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 157 + "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Training Data vs. Test Data\n", + "## Training Data vs. Test Data\n", "\n", "The next thing we need to do is split our data into a training set and a test set. Matrix factorization techniques use [transductive learning](http://en.wikipedia.org/wiki/Transduction_%28machine_learning%29) rather than inductive learning. So we produce a test set by taking a random sample of the cells in the full $N \\times M$ data matrix. The values selected as test samples are replaced with `nan` values in a copy of the original data matrix to produce the training set. Since we'll be producing random splits, let's also write out the train/test sets generated. This will allow us to replicate our results. We'd like to be able to idenfity which split is which, so we'll take a hash of the indices selected for testing and use that to save the data." ] @@ -968,16 +996,8 @@ ], "language": "python", "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stderr", - "text": [ - "INFO:root:writing numpy vars to directory: data/6bb8d06c69c0666e6da14c094d4320d115f1ffc8\n" - ] - } - ], - "prompt_number": 135 + "outputs": [], + "prompt_number": 12 }, { "cell_type": "markdown", @@ -995,13 +1015,13 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 137 + "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Results" + "# Results" ] }, { @@ -1023,7 +1043,7 @@ "output_type": "stream", "stream": "stdout", "text": [ - "Uniform Random Baseline RMSE:\t7.80299\n", + "Uniform Random Baseline RMSE:\t7.77062\n", "Global Mean Baseline RMSE:\t5.25004\n", "Mean Of Means Baseline RMSE:\t4.79832" ] @@ -1036,7 +1056,7 @@ ] } ], - "prompt_number": 166 + "prompt_number": 16 }, { "cell_type": "markdown", @@ -1051,8 +1071,8 @@ "input": [ "# We use a fixed precision for the likelihood.\n", "# This reflects uncertainty in the dot product.\n", - "# We choose 2 in the footsteps Ruslan Salakhutdinov\n", - "# and Andriy Mnihof, the authors of PMF.\n", + "# We choose 2 in the footsteps Salakhutdinov\n", + "# Mnihof.\n", "ALPHA = 2\n", "\n", "# The dimensionality D; the number of latent factors.\n", @@ -1085,7 +1105,14 @@ ] } ], - "prompt_number": 239 + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Predictions Using MAP" + ] }, { "cell_type": "code", @@ -1160,7 +1187,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 17 + "prompt_number": 20 }, { "cell_type": "code", @@ -1178,14 +1205,14 @@ "output_type": "stream", "stream": "stdout", "text": [ - "PMF MAP training RMSE: 4.00775\n", - "PMF MAP testing RMSE: 4.03233\n", - "Train/test difference: 0.02458\n", - "PMF MAP Improvement: 0.76599\n" + "PMF MAP training RMSE: 4.00824\n", + "PMF MAP testing RMSE: 4.02974\n", + "Train/test difference: 0.02150\n", + "PMF MAP Improvement: 0.76858\n" ] } ], - "prompt_number": 41 + "prompt_number": 21 }, { "cell_type": "markdown", @@ -1194,12 +1221,19 @@ "So we see a pretty nice improvement here when compared to our best baseline, which was the mean of means method. We also have a fairly small difference in the RMSE values between the train and the test sets. This indicates that the point estimates for $\\alpha_U$ and $\\alpha_V$ that we calculated from our data are doing a good job of controlling model complexity. Now let's see if we can improve our estimates by approximating our posterior distribution with MCMC sampling. We'll draw 1000 samples and back them up using the `pymc3.backend.Text` backend." ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Predictions using MCMC" + ] + }, { "cell_type": "code", "collapsed": false, "input": [ "# Draw MCMC samples.\n", - "pmf.draw_samples(1000, njobs=3)\n", + "pmf.draw_samples(5000, njobs=3)\n", "\n", "# uncomment to load previous trace rather than drawing new samples.\n", "# pmf.load_trace()" @@ -1211,13 +1245,15 @@ "output_type": "stream", "stream": "stderr", "text": [ - "INFO:root:drawing 1000 samples using 3 jobs\n" + "INFO:root:drawing 5000 samples using 3 jobs\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ + "/home/mack/anaconda/lib/python2.7/site-packages/theano/scan_module/scan_perform_ext.py:133: RuntimeWarning: numpy.ndarray size changed, may indicate binary incompatibility\n", + " from scan_perform.scan_perform import *\n", "INFO:root:backing up trace to directory: data/pmf-mcmc-d5\n" ] }, @@ -1226,284 +1262,40 @@ "stream": "stdout", "text": [ "\r", - 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"prompt_number": 26 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "[-----------------100%-----------------] 1001 of 1000 complete in 1784.3 sec" - ] + "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ + "### Diagnostics and Posterior Predictive Check\n", + "\n", "The next step is to check how many samples we should discard as burn-in. Normally, we'd do this using a traceplot to get some idea of where the sampled variables start to converge. In this case, we have high-dimensional samples, so we need to find a way to approximate them. One way was proposed by [Salakhutdinov and Mnih, p.886](https://www.cs.toronto.edu/~amnih/papers/bpmf.pdf). We can calculate the Frobenius norms of $U$ and $V$ at each step and monitor those for convergence. This essentially gives us some idea when the average magnitude of the latent variables is stabilizing. The equations for the Frobenius norms of $U$ and $V$ are shown below. We will use `numpy`'s `linalg` package to calculate these.\n", "\n", - "\\begin{equation}\n", + "$$\n", "\\|U\\|_{Fro}^2 = \\sqrt{\\sum_{i=1}^N \\sum_{d=1}^D |U_{id}|^2}, \\hspace{40pt}\n", "\\|V\\|_{Fro}^2 = \\sqrt{\\sum_{j=1}^M \\sum_{d=1}^D |V_{jd}|^2}\n", - "\\end{equation}" + "$$" ] }, { @@ -1543,7 +1335,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 34 + "prompt_number": 35 }, { "cell_type": "code", @@ -1557,40 +1349,43 @@ { "metadata": {}, "output_type": "display_data", - "png": 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65VNY+ckT+d5Fc8hO7/3PtfccV8IFc4sBaGgP0ZDgTfKth1o43Np1TnVzkA/9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aw3hrG3345YxhQe8ZkJsRchzLcjObtnxPFa58LVD5cX+1cVHvNiz4x2+sC1tY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"text": [ - "" + "" ] } ], - "prompt_number": 35 + "prompt_number": 36 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "It appears we get convergence of $U$ and $V$ after about 800 samples. In reality, we could probably get away with discarding fewer samples, but since we've already drawn all 1000, we may as well use the best subset we have." + "It appears we get convergence of $U$ and $V$ after about 200 samples. When testing for convergence, we also want to see convergence of the particular statistics we are looking for, since different characteristics of the posterior may converge at different rates. Let's also do a traceplot of the RSME. We'll compute RMSE for both the train and the test set, even though the convergence is indicated by RMSE on the training set alone. In addition, let's compute a running RMSE on the train/test sets to see how aggregate performance improves or decreases as we continue to sample." ] }, { "cell_type": "code", "collapsed": false, "input": [ - "def _running_rmse(pmf_model, test_data, burn_in=0, plot=True):\n", + "def _running_rmse(pmf_model, test_data, train_data, burn_in=0, plot=True):\n", " \"\"\"Calculate RMSE for each step of the trace to monitor convergence.\n", " \"\"\"\n", " burn_in = burn_in if len(pmf_model.trace) >= burn_in else 0\n", - " results = {'per-step': [], 'running': []}\n", + " results = {'per-step-train': [], 'running-train': [],\n", + " 'per-step-test': [], 'running-test': []}\n", " R = np.zeros(test_data.shape)\n", " for cnt, sample in enumerate(pmf_model.trace[burn_in:]):\n", " sample_R = pmf_model.predict(sample['U'], sample['V'])\n", " R += sample_R\n", " running_R = R / (cnt + 1)\n", - " results['per-step'].append(rmse(test_data, sample_R))\n", - " results['running'].append(rmse(test_data, running_R))\n", + " results['per-step-train'].append(rmse(train_data, sample_R))\n", + " results['running-train'].append(rmse(train_data, running_R))\n", + " results['per-step-test'].append(rmse(test_data, sample_R))\n", + " results['running-test'].append(rmse(test_data, running_R))\n", " \n", " results = pd.DataFrame(results)\n", - " \n", + "\n", " if plot:\n", " results.plot(\n", " kind='line', grid=False, figsize=(15, 7),\n", @@ -1605,13 +1400,13 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 37 + "prompt_number": 42 }, { "cell_type": "code", "collapsed": false, "input": [ - "predicted, results = pmf.running_rmse(test, burn_in=800)" + "predicted, results = pmf.running_rmse(test, train, burn_in=200)" ], "language": "python", "metadata": {}, @@ -1619,21 +1414,21 @@ { "metadata": {}, "output_type": "display_data", - "png": 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sWbIEnMNWfgwhMGp52NhgY5hCETMErn7qPdT5vXjw00eWuzkMwzBMBvpDUcQM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kEf3ZZ+VzdUsGmaP3SYFZmTTmZTdQpTSSSxo3ysiCLav1/DmFUDf9tSInkwgs7D1r+REoWMBZsB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\n6zauVXJDl+o2dina0uhnBce9bsjjk2X96bMq5PLehdbvQy/nN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x3nKfkUI1f1GTIYwetmVy/5bWrYjLw7w95nML0LgpQC63cJRnaTU3lFe7cMfC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\nzX+n6VP3sODC2505v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"text": [ - "" + "" ] } ], - "prompt_number": 38 + "prompt_number": 43 }, { "cell_type": "code", "collapsed": false, "input": [ "# And our final RMSE?\n", - "final_test_rmse = results['running'].values[-1]\n", - "final_train_rmse = rmse(train, predicted)\n", + "final_test_rmse = results['running-test'].values[-1]\n", + "final_train_rmse = results['running-train'].values[-1]\n", "print 'Posterior predictive train RMSE: %.5f' % final_train_rmse\n", "print 'Posterior predictive test RMSE: %.5f' % final_test_rmse\n", "print 'Train/test difference: %.5f' % (final_test_rmse - final_train_rmse)\n", @@ -1647,28 +1442,28 @@ "output_type": "stream", "stream": "stdout", "text": [ - "Posterior predictive train RMSE: 3.92234\n", - "Posterior predictive test RMSE: 4.18150\n", - "Train/test difference: 0.25916\n", - "Improvement from MAP: -0.14917\n", - "Improvement from Mean of Means: 0.61682\n" + "Posterior predictive train RMSE: 3.92230\n", + "Posterior predictive test RMSE: 4.18027\n", + "Train/test difference: 0.25797\n", + "Improvement from MAP: -0.15052\n", + "Improvement from Mean of Means: 0.61806\n" ] } ], - "prompt_number": 42 + "prompt_number": 45 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "As expected, our MCMC sampler actually produces lower quality predictions than the ones produced by our MAP estimate. Notice that this is caused by an increased overfitting of the model to the training data. With these results we've verified that the MAP estimate is the most useful thing about the PMF model, and using MCMC sampling to approximate its posterior is a bad idea. Not that this was really doubtful in the first place -- it's simply interesting to look at." + "We have some interesting results here. As expected, our MCMC sampler provides lower error on the training set. However, it seems it does so at the cost of overfitting the data. This results in a decrease in test RMSE as compared to the MAP, even though it is still much better than our best baseline. So why might this be the case? Recall that we used point estimates for our precision paremeters $\\alpha_U$ and $\\alpha_V$ and we chose a fixed precision $\\alpha$. It is quite likely that by doing this, we constrained our posterior in a way that biased it towards the training data. In reality, the variance in the user ratings and the joke ratings is unlikely to be equal to the means of sample variances we used. Also, the most reasonable observation precision $\\alpha$ is likely different as well." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Results\n", + "## Summary of Results\n", "\n", "Let's summarize our results." ] @@ -1677,13 +1472,13 @@ "cell_type": "code", "collapsed": false, "input": [ - "size = 100\n", + "size = 100 # RMSE doesn't really change after 100th sample anyway.\n", "all_results = pd.DataFrame({\n", " 'uniform random': np.repeat(baselines['ur'], size),\n", " 'global means': np.repeat(baselines['gm'], size),\n", " 'mean of means': np.repeat(baselines['mom'], size),\n", " 'PMF MAP': np.repeat(pmf_map_rmse, size),\n", - " 'PMF MCMC': results['running'][:size],\n", + " 'PMF MCMC': results['running-test'][:size],\n", "})\n", "fig, ax = plt.subplots(figsize=(10, 5))\n", "all_results.plot(kind='line', grid=False, ax=ax,\n", @@ -1697,33 +1492,33 @@ { "metadata": {}, "output_type": "pyout", - "prompt_number": 44, + "prompt_number": 67, "text": [ - "" + "" ] }, { "metadata": {}, "output_type": "display_data", - "png": 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mVjIUERGR2LVp06ZAslKiSZMmEduG1jVt2pTNmzcHyo0bNw68r127NvXq1WPz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\n7NM5jH06h7Ejt4wZ86N1OfJ04CL/fV8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0NNLS0soZioiISOzatm1bIFkp0rRp04h1Q8uaNWvG9u3bA/NNmjQJvK9Zsyb1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\nncvQoUPDxp2ZmcnAgQP5+uu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"text": [ - "" + "" ] } ], - "prompt_number": 44 + "prompt_number": 67 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Summary\n", + "# Summary\n", "\n", "We set out to predict user preferences for unseen jokes. First we discussed the intuitive notion behind the user-user and item-item neighborhood approaches to collaborative filtering. Then we formalized our intuitions. With a firm understanding of our problem context, we moved on to exploring our subset of the Jester data. After discovering some general patterns, we defined three baseline methods: uniform random, global mean, and mean of means. With the goal of besting our baseline methods, we implemented the basic version of Probabilistic Matrix Factorization (PMF) using `pymc3`.\n", "\n", - "Our results demonstrate that the mean of means method is our best baseline on our prediction task. As expected, we are able to obtain a significant decrease in RMSE using the PMF MAP estimate obtained via Powell optimization. Since maximizing the log posterior of the PMF model with fixed observation precision and fixed precision in the priors is equivalent to computing MAP, we did not expect to see significant gains from MCMC sampling. Our results showed that attempting to improve the MAP estimation using MCMC sampling actually overfit the training data and increased test RMSE. While these results were largely as expected, it was a useful example to illustrate how to monitor convergence of an MCMC sampler with a high-dimensionality sampling space using the Frobenius norms of the sampled variables.\n", + "Our results demonstrate that the mean of means method is our best baseline on our prediction task. As expected, we are able to obtain a significant decrease in RMSE using the PMF MAP estimate obtained via Powell optimization. We illustrated one way to monitor convergence of an MCMC sampler with a high-dimensionality sampling space using the Frobenius norms of the sampled variables. The traceplots using this method seem to indicate that our sampler converged to the posterior. Results using this posterior showed that attempting to improve the MAP estimation using MCMC sampling actually overfit the training data and increased test RMSE. This was likely caused by the constraining of the posterior via fixed precision parameters $\\alpha$, $\\alpha_U$, and $\\alpha_V$.\n", "\n", - "As a followup to this analysis, it would be interesting to also implement the logistic and constrained versions of PMF. We expect both models to outperform the basic PMF model. We could also implement the [fully Bayesian version of PMF](https://www.cs.toronto.edu/~amnih/papers/bpmf.pdf) (BPMF), which places hyperpriors on the model parameters to automatically learn ideal mean and precision parameters for $U$ and $V$. For a basic (but working!) implementation of BPMF in `pymc3`, see [this gist](https://gist.github.com/macks22/00a17b1d374dfc267a9a).\n", + "As a followup to this analysis, it would be interesting to also implement the logistic and constrained versions of PMF. We expect both models to outperform the basic PMF model. We could also implement the [fully Bayesian version of PMF](https://www.cs.toronto.edu/~amnih/papers/bpmf.pdf) (BPMF), which places hyperpriors on the model parameters to automatically learn ideal mean and precision parameters for $U$ and $V$. This would likely resolve the issue we faced in this analysis. We would expect BPMF to improve upon the MAP estimation produced here by learning more suitable hyperparameters and parameters. For a basic (but working!) implementation of BPMF in `pymc3`, see [this gist](https://gist.github.com/macks22/00a17b1d374dfc267a9a).\n", "\n", "If you made it this far, then congratulations! You now have some idea of how to build a basic recommender system. These same ideas and methods can be used on many different recommendation tasks. Items can be movies, products, advertisements, courses, or even other people. Any time you can build yourself a user-item matrix with user preferences in the cells, you can use these types of collaborative filtering algorithms to predict the missing values. If you want to learn more about recommender systems, the first reference is a good place to start." ]