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Added: websites/staging/mahout/trunk/content/users/mapreduce/classification/hidden-markov-models.html
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--- websites/staging/mahout/trunk/content/users/mapreduce/classification/hidden-markov-models.html (added)
+++ websites/staging/mahout/trunk/content/users/mapreduce/classification/hidden-markov-models.html Thu Mar 19 21:21:45 2015
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+ <h1 id="hidden-markov-models">Hidden Markov Models</h1>
+<p><a name="HiddenMarkovModels-IntroductionandUsage"></a></p>
+<h2 id="introduction-and-usage">Introduction and Usage</h2>
+<p>Hidden Markov Models are used in multiple areas of Machine Learning, such
+as speech recognition, handwritten letter recognition or natural language
+processing. </p>
+<p><a name="HiddenMarkovModels-FormalDefinition"></a></p>
+<h2 id="formal-definition">Formal Definition</h2>
+<p>A Hidden Markov Model (HMM) is a statistical model of a process consisting
+of two (in our case discrete) random variables O and Y, which change their
+state sequentially. The variable Y with states {y_1, ... , y_n} is called
+the "hidden variable", since its state is not directly observable. The
+state of Y changes sequentially with a so called - in our case first-order
+- Markov Property. This means, that the state change probability of Y only
+depends on its current state and does not change in time. Formally we
+write: P(Y(t+1)=y_i|Y(0)...Y(t)) = P(Y(t+1)=y_i|Y(t)) = P(Y(2)=y_i|Y(1)).
+The variable O with states {o_1, ... , o_m} is called the "observable
+variable", since its state can be directly observed. O does not have a
+Markov Property, but its state probability depends statically on the
+current state of Y.</p>
+<p>Formally, an HMM is defined as a tuple M=(n,m,P,A,B), where n is the number of hidden states, m is the number of observable states, P is an n-dimensional vector containing initial hidden state probabilities, A is the nxn-dimensional "transition matrix" containing the transition probabilities such that A[i,j](i,j.html)
+=P(Y(t)=y_i|Y(t-1)=y_j) and B is the mxn-dimensional "emission matrix"
+containing the observation probabilities such that B[i,j]=
+P(O=o_i|Y=y_j).</p>
+<p><a name="HiddenMarkovModels-Problems"></a></p>
+<h2 id="problems">Problems</h2>
+<p>Rabiner [1](1.html)
+ defined three main problems for HMM models:</p>
+<ol>
+<li>Evaluation: Given a sequence O of observations and a model M, what is
+the probability P(O|M) that sequence O was generated by model M. The
+Evaluation problem can be efficiently solved using the Forward algorithm</li>
+<li>Decoding: Given a sequence O of observations and a model M, what is
+the most likely sequence Y*=argmax(Y) P(O|M,Y) of hidden variables to
+generate this sequence. The Decoding problem can be efficiently solved
+using the Viterbi algorithm.</li>
+<li>Learning: Given a sequence O of observations, what is the most likely
+model M*=argmax(M)P(O|M) to generate this sequence. The Learning problem
+can be efficiently solved using the Baum-Welch algorithm.</li>
+</ol>
+<p><a name="HiddenMarkovModels-Example"></a></p>
+<h2 id="example">Example</h2>
+<p>To build a Hidden Markov Model and use it to build some predictions, try a simple example like this:</p>
+<p>Create an input file to train the model. Here we have a sequence drawn from the set of states 0, 1, 2, and 3, separated by space characters.</p>
+<div class="codehilite"><pre>$ <span class="n">echo</span> "0 1 2 2 2 1 1 0 0 3 3 3 2 1 2 1 1 1 1 2 2 2 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 2 2 2 3 3 3 3 3 3 2 3 2 3 2 3 2 1 3 0 0 0 1 0 1 0 2 1 2 1 2 1 2 3 3 3 3 2 2 3 2 1 1 0" <span class="o">></span> <span class="n">hmm</span><span class="o">-</span><span class="n">input</span>
+</pre></div>
+
+
+<p>Now run the baumwelch job to train your model, after first setting MAHOUT_LOCAL to true, to use your local file system.</p>
+<div class="codehilite"><pre>$ <span class="n">export</span> <span class="n">MAHOUT_LOCAL</span><span class="p">=</span><span class="n">true</span>
+$ $<span class="n">MAHOUT_HOME</span><span class="o">/</span><span class="n">bin</span><span class="o">/</span><span class="n">mahout</span> <span class="n">baumwelch</span> <span class="o">-</span><span class="nb">i</span> <span class="n">hmm</span><span class="o">-</span><span class="n">input</span> <span class="o">-</span><span class="n">o</span> <span class="n">hmm</span><span class="o">-</span><span class="n">model</span> <span class="o">-</span><span class="n">nh</span> 3 <span class="o">-</span><span class="n">no</span> 4 <span class="o">-</span><span class="n">e</span> <span class="p">.</span>0001 <span class="o">-</span><span class="n">m</span> 1000
+</pre></div>
+
+
+<p>Output like the following should appear in the console.</p>
+<div class="codehilite"><pre><span class="n">Initial</span> <span class="n">probabilities</span><span class="p">:</span>
+0 1 2
+1<span class="p">.</span>0 0<span class="p">.</span>0 3<span class="p">.</span>5659361683006626<span class="n">E</span><span class="o">-</span>251
+<span class="n">Transition</span> <span class="n">matrix</span><span class="p">:</span>
+ 0 1 2
+0 6<span class="p">.</span>098919959130616<span class="n">E</span><span class="o">-</span>5 0<span class="p">.</span>9997275322964165 2<span class="p">.</span>1147850399214744<span class="n">E</span><span class="o">-</span>4
+1 7<span class="p">.</span>404648706054873<span class="n">E</span><span class="o">-</span>37 0<span class="p">.</span>9086408633885092 0<span class="p">.</span>09135913661149081
+2 0<span class="p">.</span>2284374545687356 7<span class="p">.</span>01786289571088<span class="n">E</span><span class="o">-</span>11 0<span class="p">.</span>7715625453610858
+<span class="n">Emission</span> <span class="n">matrix</span><span class="p">:</span>
+ 0 1 2 3
+0 0<span class="p">.</span>9999997858591223 2<span class="p">.</span>0536163836449762<span class="n">E</span><span class="o">-</span>39 2<span class="p">.</span>1414087769942127<span class="n">E</span><span class="o">-</span>7 1<span class="p">.</span>052441093535389<span class="n">E</span><span class="o">-</span>27
+1 7<span class="p">.</span>495656581383351<span class="n">E</span><span class="o">-</span>34 0<span class="p">.</span>2241269055449904 0<span class="p">.</span>4510889999455847 0<span class="p">.</span>32478409450942497
+2 0<span class="p">.</span>815051477991782 0<span class="p">.</span>18494852200821799 8<span class="p">.</span>465660634827592<span class="n">E</span><span class="o">-</span>33 2<span class="p">.</span>8603899591778015<span class="n">E</span><span class="o">-</span>36
+14<span class="o">/</span>03<span class="o">/</span>22 09<span class="p">:</span>52<span class="p">:</span>21 <span class="n">INFO</span> <span class="n">driver</span><span class="p">.</span><span class="n">MahoutDriver</span><span class="p">:</span> <span class="n">Program</span> <span class="n">took</span> 180 <span class="n">ms</span> <span class="p">(</span><span class="n">Minutes</span><span class="p">:</span> 0<span class="p">.</span>003<span class="p">)</span>
+</pre></div>
+
+
+<p>The model trained with the input set now is in the file 'hmm-model', which we can use to build a predicted sequence.</p>
+<div class="codehilite"><pre>$ $<span class="n">MAHOUT_HOME</span><span class="o">/</span><span class="n">bin</span><span class="o">/</span><span class="n">mahout</span> <span class="n">hmmpredict</span> <span class="o">-</span><span class="n">m</span> <span class="n">hmm</span><span class="o">-</span><span class="n">model</span> <span class="o">-</span><span class="n">o</span> <span class="n">hmm</span><span class="o">-</span><span class="n">predictions</span> <span class="o">-</span><span class="n">l</span> 10
+</pre></div>
+
+
+<p>To see the predictions:</p>
+<div class="codehilite"><pre>$ <span class="nb">cat</span> <span class="n">hmm</span><span class="o">-</span><span class="n">predictions</span>
+0 1 3 3 2 2 2 2 1 2
+</pre></div>
+
+
+<p><a name="HiddenMarkovModels-Resources"></a></p>
+<h2 id="resources">Resources</h2>
+<p>[1]
+ Lawrence R. Rabiner (February 1989). "A tutorial on Hidden Markov Models
+and selected applications in speech recognition". Proceedings of the IEEE
+77 (2): 257-286. doi:10.1109/5.18626.</p>
+ </div>
+ </div>
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+++ websites/staging/mahout/trunk/content/users/mapreduce/classification/locally-weighted-linear-regression.html Thu Mar 19 21:21:45 2015
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+<h1 id="locally-weighted-linear-regression">Locally Weighted Linear Regression</h1>
+<p>Model-based methods, such as SVM, Naive Bayes and the mixture of Gaussians,
+use the data to build a parameterized model. After training, the model is
+used for predictions and the data are generally discarded. In contrast,
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+the training data, and use it each time a prediction needs to be made.
+Locally weighted regression (LWR) is a memory-based method that performs a
+regression around a point of interest using only training data that are
+"local" to that point. Source:
+http://www.cs.cmu.edu/afs/cs/project/jair/pub/volume4/cohn96a-html/node7.html</p>
+<p><a name="LocallyWeightedLinearRegression-Strategyforparallelregression"></a></p>
+<h2 id="strategy-for-parallel-regression">Strategy for parallel regression</h2>
+<p><a name="LocallyWeightedLinearRegression-Designofpackages"></a></p>
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--- websites/staging/mahout/trunk/content/users/mapreduce/classification/logistic-regression.html (added)
+++ websites/staging/mahout/trunk/content/users/mapreduce/classification/logistic-regression.html Thu Mar 19 21:21:45 2015
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+ <li class="divider"></li>
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+ </ul>
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+</div>
+
+ <div id="content-wrap" class="clearfix">
+ <div id="main">
+ <p><a name="LogisticRegression-LogisticRegression(SGD)"></a></p>
+<h1 id="logistic-regression-sgd">Logistic Regression (SGD)</h1>
+<p>Logistic regression is a model used for prediction of the probability of
+occurrence of an event. It makes use of several predictor variables that
+may be either numerical or categories.</p>
+<p>Logistic regression is the standard industry workhorse that underlies many
+production fraud detection and advertising quality and targeting products.
+The Mahout implementation uses Stochastic Gradient Descent (SGD) to all
+large training sets to be used.</p>
+<p>For a more detailed analysis of the approach, have a look at the <a href="http://www.autonlab.org/autonweb/14709/version/4/part/5/data/komarek:lr_thesis.pdf?branch=main&language=en">thesis of
+Paul Komarek</a>.</p>
+<p>See MAHOUT-228 for the main JIRA issue for SGD.</p>
+<p><a name="LogisticRegression-Parallelizationstrategy"></a></p>
+<h2 id="parallelization-strategy">Parallelization strategy</h2>
+<p>The bad news is that SGD is an inherently sequential algorithm. The good
+news is that it is blazingly fast and thus it is not a problem for Mahout's
+implementation to handle training sets of tens of millions of examples.
+With the down-sampling typical in many data-sets, this is equivalent to a
+dataset with billions of raw training examples.</p>
+<p>The SGD system in Mahout is an online learning algorithm which means that
+you can learn models in an incremental fashion and that you can do
+performance testing as your system runs. Often this means that you can
+stop training when a model reaches a target level of performance. The SGD
+framework includes classes to do on-line evaluation using cross validation
+(the CrossFoldLearner) and an evolutionary system to do learning
+hyper-parameter optimization on the fly (the AdaptiveLogisticRegression).
+The AdaptiveLogisticRegression system makes heavy use of threads to
+increase machine utilization. The way it works is that it runs 20
+CrossFoldLearners in separate threads, each with slightly different
+learning parameters. As better settings are found, these new settings are
+propagating to the other learners.</p>
+<p><a name="LogisticRegression-Designofpackages"></a></p>
+<h2 id="design-of-packages">Design of packages</h2>
+<p>There are three packages that are used in Mahout's SGD system. These
+include</p>
+<ul>
+<li>
+<p>The vector encoding package (found in org.apache.mahout.vectorizer.encoders)</p>
+</li>
+<li>
+<p>The SGD learning package (found in org.apache.mahout.classifier.sgd)</p>
+</li>
+<li>
+<p>The evolutionary optimization system (found in org.apache.mahout.ep)</p>
+</li>
+</ul>
+<p><a name="LogisticRegression-Featurevectorencoding"></a></p>
+<h3 id="feature-vector-encoding">Feature vector encoding</h3>
+<p>Because the SGD algorithms need to have fixed length feature vectors and
+because it is a pain to build a dictionary ahead of time, most SGD
+applications use the hashed feature vector encoding system that is rooted
+at FeatureVectorEncoder.</p>
+<p>The basic idea is that you create a vector, typically a
+RandomAccessSparseVector, and then you use various feature encoders to
+progressively add features to that vector. The size of the vector should
+be large enough to avoid feature collisions as features are hashed.</p>
+<p>There are specialized encoders for a variety of data types. You can
+normally encode either a string representation of the value you want to
+encode or you can encode a byte level representation to avoid string
+conversion. In the case of ContinuousValueEncoder and
+ConstantValueEncoder, it is also possible to encode a null value and pass
+the real value in as a weight. This avoids numerical parsing entirely in
+case you are getting your training data from a system like Avro.</p>
+<p>Here is a class diagram for the encoders package:</p>
+<p><img alt="class diagram" src="../../images/vector-class-hierarchy.png" /></p>
+<p><a name="LogisticRegression-SGDLearning"></a></p>
+<h3 id="sgd-learning">SGD Learning</h3>
+<p>For the simplest applications, you can construct an
+OnlineLogisticRegression and be off and running. Typically, though, it is
+nice to have running estimates of performance on held out data. To do
+that, you should use a CrossFoldLearner which keeps a stable of five (by
+default) OnlineLogisticRegression objects. Each time you pass a training
+example to a CrossFoldLearner, it passes this example to all but one of its
+children as training and passes the example to the last child to evaluate
+current performance. The children are used for evaluation in a round-robin
+fashion so, if you are using the default 5 way split, all of the children
+get 80% of the training data for training and get 20% of the data for
+evaluation.</p>
+<p>To avoid the pesky need to configure learning rates, regularization
+parameters and annealing schedules, you can use the
+AdaptiveLogisticRegression. This class maintains a pool of
+CrossFoldLearners and adapts learning rates and regularization on the fly
+so that you don't have to.</p>
+<p>Here is a class diagram for the classifiers.sgd package. As you can see,
+the number of twiddlable knobs is pretty large. For some examples, see the
+TrainNewsGroups example code.</p>
+<p><img alt="sgd class diagram" src="../../images/sgd-class-hierarchy.png" /></p>
+ </div>
+ </div>
+</div>
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+ <p><a name="NaiveBayes-NaiveBayes"></a></p>
+<h1 id="naive-bayes">Naive Bayes</h1>
+<p>Naive Bayes is an algorithm that can be used to classify objects into
+usually binary categories. It is one of the most common learning algorithms
+in spam filters. Despite its simplicity and rather naive assumptions it has
+proven to work surprisingly well in practice.</p>
+<p>Before applying the algorithm, the objects to be classified need to be
+represented by numerical features. In the case of e-mail spam each feature
+might indicate whether some specific word is present or absent in the mail
+to classify. The algorithm comes in two phases: Learning and application.
+During learning, a set of feature vectors is given to the algorithm, each
+vector labeled with the class the object it represents, belongs to. From
+that it is deduced which combination of features appears with high
+probability in spam messages. Given this information, during application
+one can easily compute the probability of a new message being either spam
+or not.</p>
+<p>The algorithm does make several assumptions, that are not true for most
+datasets, but make computations easier. The worst probably being, that all
+features of an objects are considered independent. In practice, that means,
+given the phrase "Statue of Liberty" was already found in a text, does not
+influence the probability of seeing the phrase "New York" as well.</p>
+<p><a name="NaiveBayes-StrategyforaparallelNaiveBayes"></a></p>
+<h2 id="strategy-for-a-parallel-naive-bayes">Strategy for a parallel Naive Bayes</h2>
+<p>See <a href="https://issues.apache.org/jira/browse/MAHOUT-9">https://issues.apache.org/jira/browse/MAHOUT-9</a>
+.</p>
+<p><a name="NaiveBayes-Examples"></a></p>
+<h2 id="examples">Examples</h2>
+<p><a href="20newsgroups.html">20Newsgroups</a>
+ - Example code showing how to train and use the Naive Bayes classifier
+using the 20 Newsgroups data available at [http://people.csail.mit.edu/jrennie/20Newsgroups/]</p>
+ </div>
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