arXiv subjects

Mu Zhu

Publications and source records attributed to Mu Zhu.

27 records · Page 2Linked to original sources

arXiv2014

Expanded Alternating Optimization of Nonconvex Functions with Applications to Matrix Factorization and Penalized Regression

We propose a general technique for improving alternating optimization (AO) of nonconvex functions. Starting from the solution given by AO, we conduct another sequence of searches over subspaces that are both meaningful to the optimization problem at hand and different from those used by AO. To demonstrate the utility of our approach, we apply it to the matrix factorization (MF) algorithm for recommender systems and the coordinate descent algorithm for penalized regression (PR), and show meaningful improvements using both real-world (for MF) and simulated (for PR) data sets. Moreover, we demonstrate for MF that, by constructing search spaces customized to the given data set, we can significantly increase the convergence rate of our technique.

stat.CO↗

arXiv2013

Threshold-free Evaluation of Medical Tests for Classification and Prediction: Average Precision versus Area Under the ROC Curve

When evaluating medical tests or biomarkers for disease classification, the area under the receiver-operating characteristic (ROC) curve is a widely used performance metric that does not require us to commit to a specific decision threshold. For the same type of evaluations, a different metric known as the average precision (AP) is used much more widely in the information retrieval literature. We study both metrics in some depths in order to elucidate their difference and relationship. More specifically, we explain mathematically why the AP may be more appropriate if the earlier part of the ROC curve is of interest. We also address practical matters, deriving an expression for the asymptotic variance of the AP, as well as providing real-world examples concerning the evaluation of protein biomarkers for prostate cancer and the assessment of digital versus film mammography for breast cancer screening.

stat.ME↗

arXiv2013

When is the majority-vote classifier beneficial?

In his seminal work, Schapire (1990) proved that weak classifiers could be improved to achieve arbitrarily high accuracy, but he never implied that a simple majority-vote mechanism could always do the trick. By comparing the asymptotic misclassification error of the majority-vote classifier with the average individual error, we discover an interesting phase-transition phenomenon. For binary classification with equal prior probabilities, our result implies that, for the majority-vote mechanism to work, the collection of weak classifiers must meet the minimum requirement of having an average true positive rate of at least 50% and an average false positive rate of at most 50%.

math.ST↗

arXiv2013

Content-boosted Matrix Factorization Techniques for Recommender Systems

Many businesses are using recommender systems for marketing outreach. Recommendation algorithms can be either based on content or driven by collaborative filtering. We study different ways to incorporate content information directly into the matrix factorization approach of collaborative filtering. These content-boosted matrix factorization algorithms not only improve recommendation accuracy, but also provide useful insights about the contents, as well as make recommendations more easily interpretable.

stat.ML↗

arXiv2012

On individual neutrality and collective decision making

We derive a simple mathematical "theory" to show that two decision-making entities can work better together only if at least one of them is occasionally willing to stay neutral. This provides a mathematical "justification" for an age-old cliche among marriage counselors.

stat.OT↗

arXiv2011

Stochastic Stepwise Ensembles for Variable Selection

In this article, we advocate the ensemble approach for variable selection. We point out that the stochastic mechanism used to generate the variable-selection ensemble (VSE) must be picked with care. We construct a VSE using a stochastic stepwise algorithm, and compare its performance with numerous state-of-the-art algorithms.

stat.ME↗

arXiv2010

Classifying Network Data with Deep Kernel Machines

Inspired by a growing interest in analyzing network data, we study the problem of node classification on graphs, focusing on approaches based on kernel machines. Conventionally, kernel machines are linear classifiers in the implicit feature space. We argue that linear classification in the feature space of kernels commonly used for graphs is often not enough to produce good results. When this is the case, one naturally considers nonlinear classifiers in the feature space. We show that repeating this process produces something we call "deep kernel machines." We provide some examples where deep kernel machines can make a big difference in classification performance, and point out some connections to various recent literature on deep architectures in artificial intelligence and machine learning.

stat.ML↗

arXiv2008

On the underestimation of model uncertainty by Bayesian K-nearest neighbors

When using the K-nearest neighbors method, one often ignores uncertainty in the choice of K. To account for such uncertainty, Holmes and Adams (2002) proposed a Bayesian framework for K-nearest neighbors (KNN). Their Bayesian KNN (BKNN) approach uses a pseudo-likelihood function, and standard Markov chain Monte Carlo (MCMC) techniques to draw posterior samples. Holmes and Adams (2002) focused on the performance of BKNN in terms of misclassification error but did not assess its ability to quantify uncertainty. We present some evidence to show that BKNN still significantly underestimates model uncertainty.

stat.ML↗

arXiv2007

Kernels and Ensembles: Perspectives on Statistical Learning

Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and ensemble methods. In this expository article, I discuss the main ideas behind these two types of methods, namely how to transform linear algorithms into nonlinear ones by using kernel functions, and how to make predictions with an ensemble or a collection of models rather than a single model. I also share my personal perspectives on how these ideas have influenced and shaped my own research. In particular, I present two recent algorithms that I have invented with my collaborators: LAGO, a fast kernel algorithm for unbalanced classification and rare target detection; and Darwinian evolution in parallel universes, an ensemble method for variable selection.

stat.ME↗