Building a good predictive model requires an array of activities such as data imputation, feature transformations, estimator selection, hyper-parameter search and ensemble construction. Given the large, complex and heterogenous space of options, off-the-shelf optimization methods are infeasible for realistic response times. In practice, much of the predictive modeling process is conducted by experienced data scientists, who selectively make use of available tools. Over time, they develop an understanding of the behavior of operators, and perform serial decision making under uncertainty, colloquially referred to as educated guesswork. With an unprecedented demand for application of supervised machine learning, there is a call for solutions that automatically search for a good combination of parameters across these tasks to minimize the modeling error. We introduce a novel system called APRL (Autonomous Predictive modeler via Reinforcement Learning), that uses past experience through reinforcement learning to optimize such sequential decision making from within a set of diverse actions under a time constraint on a previously unseen predictive learning problem. APRL actions are taken to optimize the performance of a final ensemble. This is in contrast to other systems, which maximize individual model accuracy first and create ensembles as a disconnected post-processing step. As a result, APRL is able to reduce up to 71\% of classification error on average over a wide variety of problems.

Matrix completion has attracted much interest in the past decade in machine learning and computer vision. For low-rank promotion in matrix completion, the nuclear norm penalty is convenient due to its convexity but has a bias problem. Recently, various algorithms using nonconvex penalties have been proposed, among which the proximal gradient descent (PGD) algorithm is one of the most efficient and effective. For the nonconvex PGD algorithm, whether it converges to a local minimizer and its convergence rate are still unclear. This work provides a nontrivial analysis on the PGD algorithm in the nonconvex case. Besides the convergence to a stationary point for a generalized nonconvex penalty, we provide more deep analysis on a popular and important class of nonconvex penalties which have discontinuous thresholding functions. For such penalties, we establish the finite rank convergence, convergence to restricted strictly local minimizer and eventually linear convergence rate of the PGD algorithm. Meanwhile, convergence to a local minimizer has been proved for the hard-thresholding penalty. Our result is the first shows that, nonconvex regularized matrix completion only has restricted strictly local minimizers, and the PGD algorithm can converge to such minimizers with eventually linear rate under certain conditions. Illustration of the PGD algorithm via experiments has also been provided. Code is available at https://github.com/FWen/nmc.

Summary: True prescriptive analytics requires the use of real optimization techniques that very few applications actually use. Here's a refresher on optimization with examples of where and how they're best used. Predictive analytics and optimization have gone hand in hand since the very beginning. But in 2014 some erudite journal decided we needed another phrase for this combo and it became Prescriptive Analytics, theoretically differentiating what could happen (predictive) from what should happen (prescriptive) through the application of optimization. Originally I felt strongly that this was a distinction without a difference and only served to confuse our customers who were having a hard enough time five years ago understanding why they should even be doing predictive.

Previous work has shown that popular trending events are important external factors which pose significant influence on user search behavior and also provided a way to computationally model this influence. However, their problem formulation was based on the strong assumption that each event poses its influence independently. This assumption is unrealistic as there are many correlated events in the real world which influence each other and thus, would pose a joint influence on the user search behavior rather than posing influence independently. In this paper, we study this novel problem of Modeling the Joint Influences posed by multiple correlated events on user search behavior. We propose a Joint Influence Model based on the Multivariate Hawkes Process which captures the inter-dependency among multiple events in terms of their influence upon user search behavior. We evaluate the proposed Joint Influence Model using two months query-log data from https://search.yahoo.com/. Experimental results show that the model can indeed capture the temporal dynamics of the joint influence over time and also achieves superior performance over different baseline methods when applied to solve various interesting prediction problems as well as real-word application scenarios, e.g., query auto-completion.

We introduce the active exploration problem in Markov decision processes (MDPs). Each state of the MDP is characterized by a random value and the learner should gather samples to estimate the mean value of each state as accurately as possible. Similarly to active exploration in multi-armed bandit (MAB), states may have different levels of noise, so that the higher the noise, the more samples are needed. As the noise level is initially unknown, we need to trade off the exploration of the environment to estimate the noise and the exploitation of these estimates to compute a policy maximizing the accuracy of the mean predictions. We introduce a novel learning algorithm to solve this problem showing that active exploration in MDPs may be significantly more difficult than in MAB. We also derive a heuristic procedure to mitigate the negative effect of slowly mixing policies. Finally, we validate our findings on simple numerical simulations.

The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction accuracy or the so-called Area Under the Curve (AUC). Minimizing the reciprocals of these measures are the goals of supervised learning. However, when the models are constructed by the means of empirical risk minimization (ERM), surrogate functions such as the logistic loss or hinge loss are optimized instead. In this work, we show that in the case of linear predictors, the expected error and the expected ranking loss can be effectively approximated by smooth functions whose closed form expressions and those of their first (and second) order derivatives depend on the first and second moments of the data distribution, which can be precomputed. Hence, the complexity of an optimization algorithm applied to these functions does not depend on the size of the training data. These approximation functions are derived under the assumption that the output of the linear classifier for a given data set has an approximately normal distribution. We argue that this assumption is significantly weaker than the Gaussian assumption on the data itself and we support this claim by demonstrating that our new approximation is quite accurate on data sets that are not necessarily Gaussian. We present computational results that show that our proposed approximations and related optimization algorithms can produce linear classifiers with similar or better test accuracy or AUC, than those obtained using state-of-the-art approaches, in a fraction of the time.

Wireless communication systems operate in complex time-varying environments. Therefore, selecting the optimal configuration parameters in these systems is a challenging problem. For wireless links, rate selection is used to select the optimal data transmission rate that maximizes the link throughput subject to an application-defined latency constraint. We model rate selection as a stochastic multi-armed bandit (MAB) problem, where a finite set of transmission rates are modeled as independent bandit arms. For this setup, we propose Con-TS, a novel constrained version of the Thompson sampling algorithm, where the latency requirement is modeled by a linear constraint on arm selection probabilities. Since our algorithm learns a Bayesian model of the wireless link, it can be adapted to exploit prior knowledge often available in practical wireless networks. Through numerical results from simulated experiments, we demonstrate that Con-TS significantly outperforms state-of-the-art bandit algorithms proposed in the literature. Further, we compare Con-TS with the outer loop link adaptation (OLLA) scheme, which is the state-of-the-art in practical wireless networks and relies on carefully tuned offline link models. We show that Con-TS outperforms OLLA in simulations, further, it can elegantly incorporate information from the offline link models to substantially improve performance.

Genealogy research is the study of family history using available resources such as historical records. Ancestry provides its customers with one of the world's largest online genealogical index with billions of records from a wide range of sources, including vital records such as birth and death certificates, census records, court and probate records among many others. Search at Ancestry aims to return relevant records from various record types, allowing our subscribers to build their family trees, research their family history, and make meaningful discoveries about their ancestors from diverse perspectives. In a modern search engine designed for genealogical study, the appropriate ranking of search results to provide highly relevant information represents a daunting challenge. In particular, the disparity in historical records makes it inherently difficult to score records in an equitable fashion. Herein, we provide an overview of our solutions to overcome such record disparity problems in the Ancestry search engine. Specifically, we introduce customized coordinate ascent (customized CA) to speed up ranking within a specific record type. We then propose stochastic search (SS) that linearly combines ranked results federated across contents from various record types. Furthermore, we propose a novel information retrieval metric, normalized cumulative entropy (NCE), to measure the diversity of results. We demonstrate the effectiveness of these two algorithms in terms of relevance (by NDCG) and diversity (by NCE) if applicable in the offline experiments using real customer data at Ancestry.

This study develops an online predictive optimization framework for operating a fleet of autonomous vehicles to enhance mobility in an area, where there exists a latent spatio-temporal distribution of demand for commuting between locations. The proposed framework integrates demand prediction and supply optimization in the network design problem. For demand prediction, our framework estimates a marginal demand distribution for each Origin-Destination pair of locations through Quantile Regression, using counts of crowd movements as a proxy for demand. The framework then combines these marginals into a joint demand distribution by constructing a Gaussian copula, which captures the structure of correlation between different Origin-Destination pairs. For supply optimization, we devise a demand-responsive service, based on linear programming, in which route structure and frequency vary according to the predicted demand. We evaluate our framework using a dataset of movement counts, aggregated from WiFi records of a university campus in Denmark, and the results show that our framework outperforms conventional methods for route optimization, which do not utilize the full predictive distribution.

We consider the task of localizing targets of interest in a hyperspectral (HS) image based on their spectral signature(s), by posing the problem as two distinct convex demixing task(s). With applications ranging from remote sensing to surveillance, this task of target detection leverages the fact that each material/object possesses its own characteristic spectral response, depending upon its composition. However, since $\textit{signatures}$ of different materials are often correlated, matched filtering-based approaches may not be apply here. To this end, we model a HS image as a superposition of a low-rank component and a dictionary sparse component, wherein the dictionary consists of the $\textit{a priori}$ known characteristic spectral responses of the target we wish to localize, and develop techniques for two different sparsity structures, resulting from different model assumptions. We also present the corresponding recovery guarantees, leveraging our recent theoretical results from a companion paper. Finally, we analyze the performance of the proposed approach via experimental evaluations on real HS datasets for a classification task, and compare its performance with related techniques.