Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we propose a general method to solve the localization problem by learning a regularization matrix from the localized eigenvectors. Using matrix perturbation analysis, we demonstrate that the learned regularizations suppress down the eigenvalues associated with localized eigenvectors and enable us to recover the informative eigenvectors representing the global structure. We show applications of our method in several inference problems: community detection in networks, clustering from pairwise similarities, rank estimation and matrix completion problems. Using extensive experiments, we illustrate that our method solves the localization problem and works down to the theoretical detectability limits in different kinds of synthetic data. This is in contrast with existing spectral algorithms based on data matrix, non-backtracking matrix, Laplacians and those with rank-one regularizations, which perform poorly in the sparse case with noise.

This work addresses decentralized online optimization in non-stationary environments. A network of agents aim to track the minimizer of a global time-varying convex function. The minimizer evolves according to a known dynamics corrupted by an unknown, unstructured noise. At each time, the global function can be cast as a sum of a finite number of local functions, each of which is assigned to one agent in the network. Moreover, the local functions become available to agents sequentially, and agents do not have a prior knowledge of the future cost functions. Therefore, agents must communicate with each other to build an online approximation of the global function. We propose a decentralized variation of the celebrated Mirror Descent, developed by Nemirovksi and Yudin. Using the notion of Bregman divergence in lieu of Euclidean distance for projection, Mirror Descent has been shown to be a powerful tool in large-scale optimization. Our algorithm builds on Mirror Descent, while ensuring that agents perform a consensus step to follow the global function and take into account the dynamics of the global minimizer. To measure the performance of the proposed online algorithm, we compare it to its offline counterpart, where the global functions are available a priori. The gap between the two is called dynamic regret. We establish a regret bound that scales inversely in the spectral gap of the network, and more notably it represents the deviation of minimizer sequence with respect to the given dynamics. We then show that our results subsume a number of results in distributed optimization. We demonstrate the application of our method to decentralized tracking of dynamic parameters and verify the results via numerical experiments.

XGBoost is the high performance implementation of gradient boosting that you can now access directly in Python. The idea of boosting came out of the idea of whether a weak learner can be modified to become better.

Hierarchical temporal memory (HTM) is an emerging machine learning algorithm, with the potential to provide a means to perform predictions on spatiotemporal data. The algorithm, inspired by the neocortex, currently does not have a comprehensive mathematical framework. This work brings together all aspects of the spatial pooler (SP), a critical learning component in HTM, under a single unifying framework. The primary learning mechanism is explored, where a maximum likelihood estimator for determining the degree of permanence update is proposed. The boosting mechanisms are studied and found to be only relevant during the initial few iterations of the network. Observations are made relating HTM to well-known algorithms such as competitive learning and attribute bagging. Methods are provided for using the SP for classification as well as dimensionality reduction. Empirical evidence verifies that given the proper parameterizations, the SP may be used for feature learning.

This article proposes a performance analysis of kernel least squares support vector machines (LS-SVMs) based on a random matrix approach, in the regime where both the dimension of data $p$ and their number $n$ grow large at the same rate. Under a two-class Gaussian mixture model for the input data, we prove that the LS-SVM decision function is asymptotically normal with means and covariances shown to depend explicitly on the derivatives of the kernel function. This provides improved understanding along with new insights into the internal workings of SVM-type methods for large datasets.

This paper investigates the use of distributed processing on the problem of emotion recognition from physiological sensors using a popular machine learning library on distributed mode. Specifically, we run a random forests classifier on the biosignal-data, which have been pre-processed to form exclusive groups in an unsupervised fashion, on a Cloudera cluster using Mahout. The use of distributed processing significantly reduces the time required for the offline training of the classifier, enabling processing of large physiological datasets through many iterations.

This work draws its inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping clustering of Jardine and Sibson, the functorial approach of Carlsson and Memoli to partition-based clustering, and the Isbell/Dress school's study of injective envelopes. Carlsson and Memoli introduce the idea of viewing clustering methods as functors from a category of metric spaces to a category of clusters, with functoriality subsuming many desirable properties. Our first series of results extends their theory of functorial clustering schemes to methods that allow overlapping clusters in the spirit of Jardine and Sibson. This obviates some of the unpleasant effects of chaining that occur, for example with single-linkage clustering. We prove an equivalence between these general overlapping clustering functors and projections of weight spaces to what we term clustering domains, by focusing on the order structure determined by the morphisms. As a specific application of this machinery, we are able to prove that there are no functorial projections to cut metrics, or even to tree metrics. Finally, although we focus less on the construction of clustering methods (clustering domains) derived from injective envelopes, we lay out some preliminary results, that hopefully will give a feel for how the third leg of the stool comes into play.

Extreme multi-label classification refers to supervised multi-label learning involving hundreds of thousands or even millions of labels. Datasets in extreme classification exhibit fit to power-law distribution, i.e. a large fraction of labels have very few positive instances in the data distribution. Most state-of-the-art approaches for extreme multi-label classification attempt to capture correlation among labels by embedding the label matrix to a low-dimensional linear sub-space. However, in the presence of power-law distributed extremely large and diverse label spaces, structural assumptions such as low rank can be easily violated. In this work, we present DiSMEC, which is a large-scale distributed framework for learning one-versus-rest linear classifiers coupled with explicit capacity control to control model size. Unlike most state-of-the-art methods, DiSMEC does not make any low rank assumptions on the label matrix. Using double layer of parallelization, DiSMEC can learn classifiers for datasets consisting hundreds of thousands labels within few hours. The explicit capacity control mechanism filters out spurious parameters which keep the model compact in size, without losing prediction accuracy. We conduct extensive empirical evaluation on publicly available real-world datasets consisting upto 670,000 labels. We compare DiSMEC with recent state-of-the-art approaches, including - SLEEC which is a leading approach for learning sparse local embeddings, and FastXML which is a tree-based approach optimizing ranking based loss function. On some of the datasets, DiSMEC can significantly boost prediction accuracies - 10% better compared to SLECC and 15% better compared to FastXML, in absolute terms.

Take a satellite image, and extract the pixels into a uniform 3-D color space. Then run a clustering algorithm on those pixels, to extract a number of clusters. The centroids of those clusters them make a representative palette of the image. The R package earthtones by Will Cornwell, Mitch Lyons, and Nick Murray -- now available on CRAN -- does all this for you. Pass the get_earthtones function a latitude and longitude, and it will grab the Google Earth tile at the requested zoom level (8 works well for cities) and generate a palette with the desired number of colors.

One of the main goals of the machine learning team here at the Spark Technology Center is to continue to evolve Apache Spark as the foundation for end-to-end, continuous, intelligent enterprise applications. While working on adding multi-class logistic regression to Spark ML (part of the ongoing push towards parity between ml and mllib), STC team member Seth Hendrickson realized that, due to the way that Spark automatically serializes data when inter-node communication is required (e.g. during a reduce or aggregation operation), the aggregation step of the logistic regression training algorithm resulted in 3x more data being communicated than necessary. What does it mean when we refer to Apache Spark as the "foundation for end-to-end, continuous, intelligent enterprise applications"?