The work presented here involves the design of a Multi Layer Perceptron (MLP) based pattern classifier for recognition of handwritten Bangla digits using a 76 element feature vector. Bangla is the second most popular script and language in the Indian subcontinent and the fifth most popular language in the world. The feature set developed for representing handwritten Bangla numerals here includes 24 shadow features, 16 centroid features and 36 longest-run features. On experimentation with a database of 6000 samples, the technique yields an average recognition rate of 96.67% evaluated after three-fold cross validation of results. It is useful for applications related to OCR of handwritten Bangla Digit and can also be extended to include OCR of handwritten characters of Bangla alphabet.

Database theory and database practice are typically the domain of computer scientists who adopt what may be termed an algorithmic perspective on their data. This perspective is very different than the more statistical perspective adopted by statisticians, scientific computers, machine learners, and other who work on what may be broadly termed statistical data analysis. In this article, I will address fundamental aspects of this algorithmic-statistical disconnect, with an eye to bridging the gap between these two very different approaches. A concept that lies at the heart of this disconnect is that of statistical regularization, a notion that has to do with how robust is the output of an algorithm to the noise properties of the input data. Although it is nearly completely absent from computer science, which historically has taken the input data as given and modeled algorithms discretely, regularization in one form or another is central to nearly every application domain that applies algorithms to noisy data. By using several case studies, I will illustrate, both theoretically and empirically, the nonobvious fact that approximate computation, in and of itself, can implicitly lead to statistical regularization. This and other recent work suggests that, by exploiting in a more principled way the statistical properties implicit in worst-case algorithms, one can in many cases satisfy the bicriteria of having algorithms that are scalable to very large-scale databases and that also have good inferential or predictive properties.

We define and discuss the first sparse coding algorithm based on closed-form EM updates and continuous latent variables. The underlying generative model consists of a standard `spike-and-slab' prior and a Gaussian noise model. Closed-form solutions for E- and M-step equations are derived by generalizing probabilistic PCA. The resulting EM algorithm can take all modes of a potentially multi-modal posterior into account. The computational cost of the algorithm scales exponentially with the number of hidden dimensions. However, with current computational resources, it is still possible to efficiently learn model parameters for medium-scale problems. Thus the model can be applied to the typical range of source separation tasks. In numerical experiments on artificial data we verify likelihood maximization and show that the derived algorithm recovers the sparse directions of standard sparse coding distributions. On source separation benchmarks comprised of realistic data we show that the algorithm is competitive with other recent methods.

Sparsity-promoting priors have become increasingly popular over recent years due to an increased number of regression and classification applications involving a large number of predictors. In time series applications where observations are collected over time, it is often unrealistic to assume that the underlying sparsity pattern is fixed. We propose here an original class of flexible Bayesian linear models for dynamic sparsity modelling. The proposed class of models expands upon the existing Bayesian literature on sparse regression using generalized multivariate hyperbolic distributions. The properties of the models are explored through both analytic results and simulation studies. We demonstrate the model on a financial application where it is shown that it accurately represents the patterns seen in the analysis of stock and derivative data, and is able to detect major events by filtering an artificial portfolio of assets.

Risk bounds for Classification and Regression Trees (CART, Breiman et. al. 1984) classifiers are obtained under a margin condition in the binary supervised classification framework. These risk bounds are obtained conditionally on the construction of the maximal deep binary tree and permit to prove that the linear penalty used in the CART pruning algorithm is valid under a margin condition. It is also shown that, conditionally on the construction of the maximal tree, the final selection by test sample does not alter dramatically the estimation accuracy of the Bayes classifier. In the two-class classification framework, the risk bounds that are proved, obtained by using penalized model selection, validate the CART algorithm which is used in many data mining applications such as Biology, Medicine or Image Coding.

mlpy is a Python Open Source Machine Learning library built on top of NumPy/SciPy and the GNU Scientific Libraries. mlpy provides a wide range of state-of-the-art machine learning methods for supervised and unsupervised problems and it is aimed at finding a reasonable compromise among modularity, maintainability, reproducibility, usability and efficiency. mlpy is multiplatform, it works with Python 2 and 3 and it is distributed under GPL3 at the website http://mlpy.fbk.eu.

Personalized web services strive to adapt their services (advertisements, news articles, etc) to individual users by making use of both content and user information. Despite a few recent advances, this problem remains challenging for at least two reasons. First, web service is featured with dynamically changing pools of content, rendering traditional collaborative filtering methods inapplicable. Second, the scale of most web services of practical interest calls for solutions that are both fast in learning and computation. In this work, we model personalized recommendation of news articles as a contextual bandit problem, a principled approach in which a learning algorithm sequentially selects articles to serve users based on contextual information about the users and articles, while simultaneously adapting its article-selection strategy based on user-click feedback to maximize total user clicks. The contributions of this work are three-fold. First, we propose a new, general contextual bandit algorithm that is computationally efficient and well motivated from learning theory. Second, we argue that any bandit algorithm can be reliably evaluated offline using previously recorded random traffic. Finally, using this offline evaluation method, we successfully applied our new algorithm to a Yahoo! Front Page Today Module dataset containing over 33 million events. Results showed a 12.5% click lift compared to a standard context-free bandit algorithm, and the advantage becomes even greater when data gets more scarce.

We consider the problem of learning classifiers for labeled data that has been distributed across several nodes. Our goal is to find a single classifier, with small approximation error, across all datasets while minimizing the communication between nodes. This setting models real-world communication bottlenecks in the processing of massive distributed datasets. We present several very general sampling-based solutions as well as some two-way protocols which have a provable exponential speed-up over any one-way protocol. We focus on core problems for noiseless data distributed across two or more nodes. The techniques we introduce are reminiscent of active learning, but rather than actively probing labels, nodes actively communicate with each other, each node simultaneously learning the important data from another node.

This paper introduces a class of k-nearest neighbor ($k$-NN) estimators called bipartite plug-in (BPI) estimators for estimating integrals of non-linear functions of a probability density, such as Shannon entropy and R\'enyi entropy. The density is assumed to be smooth, have bounded support, and be uniformly bounded from below on this set. Unlike previous $k$-NN estimators of non-linear density functionals, the proposed estimator uses data-splitting and boundary correction to achieve lower mean square error. Specifically, we assume that $T$ i.i.d. samples ${X}_i \in \mathbb{R}^d$ from the density are split into two pieces of cardinality $M$ and $N$ respectively, with $M$ samples used for computing a k-nearest-neighbor density estimate and the remaining $N$ samples used for empirical estimation of the integral of the density functional. By studying the statistical properties of k-NN balls, explicit rates for the bias and variance of the BPI estimator are derived in terms of the sample size, the dimension of the samples and the underlying probability distribution. Based on these results, it is possible to specify optimal choice of tuning parameters $M/T$, $k$ for maximizing the rate of decrease of the mean square error (MSE). The resultant optimized BPI estimator converges faster and achieves lower mean squared error than previous $k$-NN entropy estimators. In addition, a central limit theorem is established for the BPI estimator that allows us to specify tight asymptotic confidence intervals.

We derive and analyze a new, efficient, pool-based active learning algorithm for halfspaces, called ALuMA. Most previous algorithms show exponential improvement in the label complexity assuming that the distribution over the instance space is close to uniform. This assumption rarely holds in practical applications. Instead, we study the label complexity under a large-margin assumption -- a much more realistic condition, as evident by the success of margin-based algorithms such as SVM. Our algorithm is computationally efficient and comes with formal guarantees on its label complexity. It also naturally extends to the non-separable case and to non-linear kernels. Experiments illustrate the clear advantage of ALuMA over other active learning algorithms.