Playing Billiard in Version Space

A ray-tracing method inspired by ergodic billiards is used to estimate the theoretically best decision rule for a set of linear separable examples. While the Bayes-optimum requires a majority decision over all Perceptrons separating the example set, the problem considered here corresponds to finding the single Perceptron with best average generalization probability. For randomly distributed examples the billiard estimate agrees with known analytic results. In real-life classification problems the generalization error is consistently reduced compared to the maximal stability Perceptron.Comment: uuencoded, gzipped PostScript file, 127576 bytes To recover 1) save file as bayes.uue. Then 2) uudecode bayes.uue and 3) gunzip bayes.ps.g

From Cutting Planes Algorithms to Compression Schemes and Active Learning

Cutting-plane methods are well-studied localization(and optimization) algorithms. We show that they provide a natural framework to perform machinelearning ---and not just to solve optimization problems posed by machinelearning--- in addition to their intended optimization use. In particular, theyallow one to learn sparse classifiers and provide good compression schemes.Moreover, we show that very little effort is required to turn them intoeffective active learning methods. This last property provides a generic way todesign a whole family of active learning algorithms from existing passivemethods. We present numerical simulations testifying of the relevance ofcutting-plane methods for passive and active learning tasks.Comment: IJCNN 2015, Jul 2015, Killarney, Ireland. 2015, \<http://www.ijcnn.org/\&g

Perceptron learning with random coordinate descent

A perceptron is a linear threshold classifier that separates examples with a hyperplane. It is perhaps the simplest learning model that is used standalone. In this paper, we propose a family of random coordinate descent algorithms for perceptron learning on binary classification problems. Unlike most perceptron learning algorithms which require smooth cost functions, our algorithms directly minimize the training error, and usually achieve the lowest training error compared with other algorithms. The algorithms are also computational efficient. Such advantages make them favorable for both standalone use and ensemble learning, on problems that are not linearly separable. Experiments show that our algorithms work very well with AdaBoost, and achieve the lowest test errors for half of the datasets

Identifying Real Estate Opportunities using Machine Learning

The real estate market is exposed to many fluctuations in prices because of existing correlations with many variables, some of which cannot be controlled or might even be unknown. Housing prices can increase rapidly (or in some cases, also drop very fast), yet the numerous listings available online where houses are sold or rented are not likely to be updated that often. In some cases, individuals interested in selling a house (or apartment) might include it in some online listing, and forget about updating the price. In other cases, some individuals might be interested in deliberately setting a price below the market price in order to sell the home faster, for various reasons. In this paper, we aim at developing a machine learning application that identifies opportunities in the real estate market in real time, i.e., houses that are listed with a price substantially below the market price. This program can be useful for investors interested in the housing market. We have focused in a use case considering real estate assets located in the Salamanca district in Madrid (Spain) and listed in the most relevant Spanish online site for home sales and rentals. The application is formally implemented as a regression problem that tries to estimate the market price of a house given features retrieved from public online listings. For building this application, we have performed a feature engineering stage in order to discover relevant features that allows for attaining a high predictive performance. Several machine learning algorithms have been tested, including regression trees, k-nearest neighbors, support vector machines and neural networks, identifying advantages and handicaps of each of them.Comment: 24 pages, 13 figures, 5 table