Model-based collaborative filtering analyzes user-item interactions to infer latent factors that represent user preferences and item characteristics in order to predict future interactions. Most collaborative filtering algorithms assume that these latent factors are static, although it has been shown that user preferences and item perceptions drift over time. In this paper, we propose a conjugate and numerically stable dynamic matrix factorization (DCPF) based on compound Poisson matrix factorization that models the smoothly drifting latent factors using Gamma-Markov chains. We propose a numerically stable Gamma chain construction, and then present a stochastic variational inference approach to estimate the parameters of our model. We apply our model to time-stamped ratings data sets: Netflix, Yelp, and Last.fm, where DCPF achieves a higher predictive accuracy than state-of-the-art static and dynamic factorization models.

In my previous post, we saw that R-squared can lead to a misleading interpretation of the quality of our regression fit, in terms of prediction power. One thing that R-squared offers no protection against is overfitting. On the other hand, cross validation, by allowing us to have cases in our testing set that are different from the cases in our training set, inherently offers protection against overfittting. In this type of validation, one case in our data set is used as the test set, while the remaining cases are used as the training set. We iterate through the data set, until all cases have served as the test set.

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.

A recent Compliance Week story on how artificial intelligence could revolutionize compliance depicted how technology firms "are offering software platforms that promise to automate otherwise routine tasks and improve upon fraud detection audits, anti-money laundering protocols, and know-your-customer screening." With the advent of cyber-security attacks, developers of advanced artificial intelligence security monitoring solutions have also emerged. However, understanding when and how often monitoring solutions should be executed presents trade-offs to be considered. Legacy approaches to risk monitoring look for recognized threats by known signatures and pre-built event detection logic. Often these standby methods rest on technology confines and as a result are not aligned to business risk.

Stripe builds products that enable hundreds of thousands of e-commerce companies, SaaS businesses, on-demand marketplaces, nonprofits, and platforms to conduct business online. One inescapable facet of online commerce--and one that, unfortunately, frequently comes as an unpleasant surprise--is fraud. Unlike businesses that accept payments in person, internet businesses are liable for fraudulent purchases--this despite the fact that they are no more experts on fraud than their brick-and-mortar counterparts. As a result, many internet businesses have had to build up teams of fraud analysts and expend engineering effort on fraud detection systems. At Stripe, we want to help businesses focus on their product and customer experiences and not on fraud, so we've developed Stripe Radar, a suite of modern tools for fraud detection and prevention. The goal of this guide is to provide more detail on the machine learning that powers the core of Radar, explain how we think about the efficacy and performance of fraud detection systems, and describe how other tools in the Radar suite can help businesses optimize their outcomes.

This work characterizes the benefits of averaging techniques widely used in conjunction with stochastic gradient descent (SGD). In particular, this work sharply analyzes: (1) mini-batching, a method of averaging many samples of the gradient to both reduce the variance of a stochastic gradient estimate and for parallelizing SGD and (2) tail-averaging, a method involving averaging the final few iterates of SGD in order to decrease the variance in SGD's final iterate. This work presents the first tight non-asymptotic generalization error bounds for these schemes for the stochastic approximation problem of least squares regression. Furthermore, this work establishes a precise problem-dependent extent to which mini-batching can be used to yield provable near-linear parallelization speedups over SGD with batch size one. These results are utilized in providing a highly parallelizable SGD algorithm that obtains the optimal statistical error rate with nearly the same number of serial updates as batch gradient descent, which improves significantly over existing SGD-style methods. Finally, this work sheds light on some fundamental differences in SGD's behavior when dealing with agnostic noise in the (non-realizable) least squares regression problem. In particular, the work shows that the stepsizes that ensure optimal statistical error rates for the agnostic case must be a function of the noise properties. The central analysis tools used by this paper are obtained through generalizing the operator view of averaged SGD, introduced by Defossez and Bach (2015) followed by developing a novel analysis in bounding these operators to characterize the generalization error. These techniques may be of broader interest in analyzing various computational aspects of stochastic approximation.

We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrices to have equal entries and also encourage zeros in the precision matrix. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze an EEG dataset to demonstrate our method's interpretability and classification accuracy.

My colleague Amy Nicholson is the UK expert on Azure Machine Learning, the following blog post is after a quizzing session to get understand how to get started with Azure Machine Learning" Each student receives $100 of Azure credit per month, for 6 months. The Faculty member receives $250 per month, for 12 months. The Azure machine learning team provided a very nice walkthrough tutorial which covers a lot of the basics. This tutorial is really useful as it takes you through the entire process of creating an AzureML workspace, uploading data, creating an experiment to predict someone's credit risk, building, training, and evaluating the models, publishing your best model as a web service, and calling that web service. Now you need to learn how to import a data set into Azure Machine Learning, and where to find interesting data to build something amazing.

There's only one WWE pay-per-view scheduled until Survivor Series in November, and it's set for Sunday night in Boston. Hell in a Cell 2016, a "Monday Night Raw" PPV, will feature three matches inside of the cage, including a first for WWE. While WWE is calling the three matches a "triple main event," the women's championship match might close the show. Sasha Banks defends her title against Charlotte in what should be the conclusion of their long-running feud, and it's the first time ever that women will compete in Hell in a Cell. Roman Reigns and Rusev will fight inside of the cell, as well, in a United States Championship match. Bayley vs. Dana Brooke could potentially be added to the card before the end of the week, but only six matches are officially scheduled for Hell in a Cell following "Monday Night Raw."

Predictive modeling is increasingly being employed to assist human decision-makers. One purported advantage of replacing human judgment with computer models in high stakes settings-- such as sentencing, hiring, policing, college admissions, and parole decisions-- is the perceived "neutrality" of computers. It is argued that because computer models do not hold personal prejudice, the predictions they produce will be equally free from prejudice. There is growing recognition that employing algorithms does not remove the potential for bias, and can even amplify it, since training data were inevitably generated by a process that is itself biased. In this paper, we provide a probabilistic definition of algorithmic bias. We propose a method to remove bias from predictive models by removing all information regarding protected variables from the permitted training data. Unlike previous work in this area, our framework is general enough to accommodate arbitrary data types, e.g. binary, continuous, etc. Motivated by models currently in use in the criminal justice system that inform decisions on pre-trial release and paroling, we apply our proposed method to a dataset on the criminal histories of individuals at the time of sentencing to produce "race-neutral" predictions of re-arrest. In the process, we demonstrate that the most common approach to creating "race-neutral" models-- omitting race as a covariate-- still results in racially disparate predictions. We then demonstrate that the application of our proposed method to these data removes racial disparities from predictions with minimal impact on predictive accuracy.