We consider the problem of learning models for forecasting multiple time-series systems together with discovering the leading indicators that serve as good predictors for the system. We model the systems by linear vector autoregressive models (VAR) and link the discovery of leading indicators to inferring sparse graphs of Granger-causality. We propose new problem formulations and develop two new methods to learn such models, gradually increasing the complexity of assumptions and approaches. While the first method assumes common structures across the whole system, our second method uncovers model clusters based on the Granger-causality and leading indicators together with learning the model parameters. We study the performance of our methods on a comprehensive set of experiments and confirm their efficacy and their advantages over state-of-the-art sparse VAR and graphical Granger learning methods.

What has changed in Machine Learning in the past 25 years? You may not care about this question. You may even not realize that Machine Learning as a technical and scientific field is older than 25 years. But I do care about this question. I care because I got a PhD in Machine Learning in 1990.

If you are a software developer who wants to learn how machine learning models work and how to apply them effectively, this book is for you. Familiarity with machine learning fundamentals and Python will be helpful, but is not essential. This book examines machine learning models including logistic regression, decision trees, and support vector machines, and applies them to common problems such as categorizing documents and classifying images. It begins with the fundamentals of machine learning, introducing you to the supervised-unsupervised spectrum, the uses of training and test data, and evaluating models. You will learn how to use generalized linear models in regression problems, as well as solve problems with text and categorical features. You will be acquainted with the use of logistic regression, regularization, and the various loss functions that are used by generalized linear models.

This was the subject of a question asked on Quora: What are the top 10 data mining or machine learning algorithms? Some modern algorithms such as collaborative filtering, recommendation engine, segmentation, or attribution modeling, are missing from the lists below. Algorithms from graph theory (to find the shortest path in a graph, or to detect connected components), from operations research (the simplex, to optimize the supply chain), or from time series, are not listed either. And I could not find MCM (Markov Chain Monte Carlo) and related algorithms used to process hierarchical, spatio-temporal and other Bayesian models. My point of view is of course biased, but I would like to also add some algorithms developed or re-developed at the Data Science Central's research lab: These algorithms are described in the article What you wont learn in statistics classes.

The Joint Optimization of Fidelity and Commensurability (JOFC) manifold matching methodology embeds an omnibus dissimilarity matrix consisting of multiple dissimilarities on the same set of objects. One approach to this embedding optimizes the preservation of fidelity to each individual dissimilarity matrix together with commensurability of each given observation across modalities via iterative majorization of a raw stress error criterion by successive Guttman transforms. In this paper, we exploit the special structure inherent to JOFC to exactly and efficiently compute the successive Guttman transforms, and as a result we are able to greatly speed up the JOFC procedure for both in-sample and out-of-sample embedding. We demonstrate the scalability of our implementation on both real and simulated data examples.

Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models. However, for some applications, this assumption is inappropriate. For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points. These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set. We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property. We compare models within this class to two commonly used clustering models using four entity-resolution data sets.

The iterative nature of the expectation maximization (EM) algorithm presents a challenge for privacy-preserving estimation, as each iteration increases the amount of noise needed. We propose a practical private EM algorithm that overcomes this challenge using two innovations: (1) a novel moment perturbation formulation for differentially private EM (DP-EM), and (2) the use of two recently developed composition methods to bound the privacy "cost" of multiple EM iterations: the moments accountant (MA) and zero-mean concentrated differential privacy (zCDP). Both MA and zCDP bound the moment generating function of the privacy loss random variable and achieve a refined tail bound, which effectively decrease the amount of additive noise. We present empirical results showing the benefits of our approach, as well as similar performance between these two composition methods in the DP-EM setting for Gaussian mixture models. Our approach can be readily extended to many iterative learning algorithms, opening up various exciting future directions.

Many machine learning problems, especially multi-modal learning problems, have two sets of distinct features (e.g., image and text features in news story classification, or neuroimaging data and neurocognitive data in cognitive science research). This paper addresses the joint dimensionality reduction of two feature vectors in supervised learning problems. In particular, we assume a discriminative model where low-dimensional linear embeddings of the two feature vectors are sufficient statistics for predicting a dependent variable. We show that a simple algorithm involving singular value decomposition can accurately estimate the embeddings provided that certain sample complexities are satisfied, without specifying the nonlinear link function (regressor or classifier). The main results establish sample complexities under multiple settings. Sample complexities for different link functions only differ by constant factors.

Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to the best of our knowledge, all existing theoretical guarantees for it assume that the data and the corrupting noise are mutually independent, or at least uncorrelated. This is valid in practice often, but not always. In this paper, we study the PCA problem in the setting where the data and noise can be correlated. Such noise is often also referred to as "data-dependent noise". We obtain a correctness result for the standard eigenvalue decomposition (EVD) based solution to PCA under simple assumptions on the data-noise correlation. We also develop and analyze a generalization of EVD, cluster-EVD, that improves upon EVD in certain regimes.

Extracting actionable intelligence from distributed, heterogeneous, correlated and high-dimensional data sources requires run-time processing and learning both locally and globally. In the last decade, a large number of meta-learning techniques have been proposed in which local learners make online predictions based on their locally-collected data instances, and feed these predictions to an ensemble learner, which fuses them and issues a global prediction. However, most of these works do not provide performance guarantees or, when they do, these guarantees are asymptotic. None of these existing works provide confidence estimates about the issued predictions or rate of learning guarantees for the ensemble learner. In this paper, we provide a systematic ensemble learning method called Hedged Bandits, which comes with both long run (asymptotic) and short run (rate of learning) performance guarantees. Moreover, our approach yields performance guarantees with respect to the optimal local prediction strategy, and is also able to adapt its predictions in a data-driven manner. We illustrate the performance of Hedged Bandits in the context of medical informatics and show that it outperforms numerous online and offline ensemble learning methods.