December 2012

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“Semantic Hashing”

In “Semantic Hashing“, Salakhutdinov and Hinton (2007) show how to classify documents with binary vectors.  They combine deep learning and graphical models to assign each document a binary vector.  Similar documents can be found by using the L1 difference between the binary vectors.  Here is their abstract.

We show how to learn a deep graphical model of the word-count vectors obtained from a large set of documents. The values of the latent variables in the deepest layer are easy to infer and give a much better representation of each document than Latent Semantic Analysis. When the deepest layer is forced to use a small number of binary variables (e.g. 32), the graphical model performs “semantic hashing”: Documents are mapped to memory addresses in such away that semantically similar documents are located at nearby addresses. Documents similar to a query document can then be found by simply accessing all the addresses that differ by only a few bits from the address of the query document. This way of extending the efficiency of hash-coding to approximate matching is much faster than locality sensitive hashing, which is the fastest current method. By using semantic hashing to ﬁlter the documents given to TF-IDF, we achieve higher accuracy than applying TF-IDF to the entire document set.

Cool 3D Printer

Here’s a link to the video.  The tiny “Alien” skull below is printed in less than three minutes.

Product of Experts

“A Product of Experts model (PoE) (Hinton 2002) combines a number of individual component models (the experts) by taking their product and normalizing the result.”  Here’s the Scholarpedia page.

“Rotation Forest: A New Classifier Ensemble Method”

In “Rotation Forest: A New Classifier Ensemble Method“, Rodrıguez and Kuncheva (2006) develop a Random Forest method where the decision boundaries are not of the form   original data feature value <= fixed number. They do this by creating new features by “rotating” the data in the high dimensional feature space before creating a decision tree.  Each decision tree is created with a different rotation of the data, but all of the rotations are generated from Principal Component Analysis. The trees are combined to generate the final classifier.  Here is their abstract

We propose a method for generating classifier ensembles based on feature extraction. To create the training data for a base classifier, the feature set is randomly split into K subsets (K is a parameter of the algorithm) and Principal Component Analysis (PCA) is applied to each subset. All principal components are retained in order to preserve the variability information in the data. Thus, K axis rotations take place to form the new features for a base classifier. The idea of the rotation approach is to encourage simultaneously individual accuracy and diversity within the ensemble. Diversity is promoted through the feature extraction for each base classifier. Decision trees were chosen here because they are sensitive to rotation of the feature axes, hence the name “forest.” Accuracy is sought by keeping all principal components and also using the whole data set to train each base classifier. Using WEKA, we examined the Rotation Forest ensemble on a random selection of 33 benchmark data sets from the UCI repository and compared it with Bagging, AdaBoost, and Random Forest. The results were favorable to Rotation Forest and prompted an investigation into diversity-accuracy landscape of the ensemble models. Diversity-error diagrams revealed that Rotation Forest ensembles construct individual classifiers which are more accurate than these in AdaBoost and Random Forest, and more diverse than these in Bagging, sometimes more accurate as well.

Stochastic Optimization Talk at NIPS

At NIPS yesterday, James Spall gave a nice overview of stochastic optimization. Stochastic optimization is the process of finding the minimum of a function $f(x)$ where are measurements or samples of the function are noisy.  He stressed that the no free lunch theorems (Wolpert & Macready 1995) limit the efficiency of any global minimization problem if there are no restrictions on $f$.  He described in detail the Simultaneous Perturbation Stochastic Approximation (SPSA) method which appears to be a great method for optimizing with noisy measurements. The basic is idea is that you don’t need to approximate the gradient by making $p+1$ measurements in a $p$ dimensional domain.  Instead, you sample $f$ at two nearby randomly generated points and make a nearly unbiased estimate of the gradient from those two measurements.   There is also way to form estimates of the Hessian with just 4 samples which leads to a stochastic algorithm similar to Newton-Raphson.  None of these methods can converge faster than $O(1/\sqrt{n})$ due to the noise, but they may be very useful as robust semi-global optimizers for functions with lots of local minima or high frequencies.

Principles for Applying Machine Learning Techniques

at Factual Blog has this cool list of 5 principles for Applying Machine Learning Techniques.  His datacentric techniques are:

• Don’t Ignore the Corners – The “Corners” are unusual cases in the Data
• Be Attentive to the Boundaries – If you use a linear discriminant or decision tree, pay special attention to boundary cases.
• Spend Time on Special Cases – i.e. special cases in the data.
• Listen to the Data
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