Covariate shift is a fundamental problem for learning in non-stationary environments where the conditional distribution p(y x) is the same between training and test data while their marginal distributions ptr(x) and pte(x) are different. Although many covariate shift correction techniques remain effective for real world problems, most do not scale well in practice. In this paper, using inspiration from recent optimization techniques, we apply the Frank-Wolfe algorithm to two well-known covariate shift correction techniques, Kernel Mean Matching (KMM) and Kullback-Leibler Importance Estimation Procedure (KLIEP), and identify an important connection between kernel herding and KMM. Our complexity analysis shows the benefits of the Frank-Wolfe approach over projected gradient methods in solving KMM and KLIEP. An empirical study then demonstrates the effectiveness and efficiency of the Frank-Wolfe algorithm for correcting covariate shift in practice.

Importance weighting is widely applicable in machine learning in general and in techniques dealing with data covariate shift problems in particular. A novel, direct approach to determine such importance weighting is presented. It relies on a nearest neighbor classification scheme and is relatively straightforward to implement. Comparative experiments on various classification tasks demonstrate the effectiveness of our so-called nearest neighbor weighting (NNeW) scheme. Considering its performance, our procedure can act as a simple and effective baseline method for importance weighting.

In binary classification framework, we are interested in making cost sensitive label predictions in the presence of uniform/symmetric label noise. We first observe that $0$-$1$ Bayes classifiers are not (uniform) noise robust in cost sensitive setting. To circumvent this impossibility result, we present two schemes; unlike the existing methods, our schemes do not require noise rate. The first one uses $\alpha$-weighted $\gamma$-uneven margin squared loss function, $l_{\alpha, usq}$, which can handle cost sensitivity arising due to domain requirement (using user given $\alpha$) or class imbalance (by tuning $\gamma$) or both. However, we observe that $l_{\alpha, usq}$ Bayes classifiers are also not cost sensitive and noise robust. We show that regularized ERM of this loss function over the class of linear classifiers yields a cost sensitive uniform noise robust classifier as a solution of a system of linear equations. We also provide a performance bound for this classifier. The second scheme that we propose is a re-sampling based scheme that exploits the special structure of the uniform noise models and uses in-class probability estimates. Our computational experiments on some UCI datasets with class imbalance show that classifiers of our two schemes are on par with the existing methods and in fact better in some cases w.r.t. Accuracy and Arithmetic Mean, without using/tuning noise rate. We also consider other cost sensitive performance measures viz., F measure and Weighted Cost for evaluation.

We propose an inlier-based outlier detection method capable of both identifying the outliers and explaining why they are outliers, by identifying the outlier-specific features. Specifically, we employ an inlier-based outlier detection criterion, which uses the ratio of inlier and test probability densities as a measure of plausibility of being an outlier. For estimating the density ratio function, we propose a localized logistic regression algorithm. Thanks to the locality of the model, variable selection can be outlier-specific, and will help interpret why points are outliers in a high-dimensional space. Through synthetic experiments, we show that the proposed algorithm can successfully detect the important features for outliers. Moreover, we show that the proposed algorithm tends to outperform existing algorithms in benchmark datasets.

Recent years have seen an increasing popularity of learning the sparse \emph{changes} in Markov Networks. Changes in the structure of Markov Networks reflect alternations of interactions between random variables under different regimes and provide insights into the underlying system. While each individual network structure can be complicated and difficult to learn, the overall change from one network to another can be simple. This intuition gave birth to an approach that \emph{directly} learns the sparse changes without modelling and learning the individual (possibly dense) networks. In this paper, we review such a direct learning method with some latest developments along this line of research.

We study the problem of learning sparse structure changes between two Markov networks $P$ and $Q$. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes \emph{directly} via estimating the ratio between two Markov network models. In this paper, we give sufficient conditions for \emph{successful change detection} with respect to the sample size $n_p, n_q$, the dimension of data $m$, and the number of changed edges $d$. When using an unbounded density ratio model we prove that the true sparse changes can be consistently identified for $n_p = \Omega(d^2 \log \frac{m^2+m}{2})$ and $n_q = \Omega({n_p^2})$, with an exponentially decaying upper-bound on learning error. Such sample complexity can be improved to $\min(n_p, n_q) = \Omega(d^2 \log \frac{m^2+m}{2})$ when the boundedness of the density ratio model is assumed. Our theoretical guarantee can be applied to a wide range of discrete/continuous Markov networks.

Covariate shift is a fundamental problem for learning in non-stationary environments where the conditional distribution p(y|x) is the same between training and test data while their marginal distributions p tr (x) and p te (x) are different. Although many covariate shift correction techniques remain effective for real world problems, most do not scale well in practice. In this paper, using inspiration from recent optimization techniques, we apply the Frank-Wolfe algorithm to two well-known covariate shift correction techniques, Kernel Mean Matching (KMM) and Kullback-Leibler Importance Estimation Procedure (KLIEP), and identify an important connection between kernel herding and KMM. Our complexity analysis shows the benefits of the Frank-Wolfe approach over projected gradient methods in solving KMM and KLIEP. An empirical study then demonstrates the effectiveness and efficiency of the Frank-Wolfe algorithm for correcting covariate shift in practice.

We study the problem of learning sparse structure changes between two Markov networks P and Q. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes directly via estimating the ratio between two Markov network models.  Such a direct approach was demonstrated to perform excellently in experiments, although its theoretical properties remained unexplored.  In this paper, we give sufficient conditions for successful change detection with respect to the sample size np, nq, the dimension of data m, and the number of changed edges d.

We propose a new method for detecting changes in Markov network structure between two sets of samples. Instead of naively fitting two Markov network models separately to the two data sets and figuring out their difference, we \emph{directly} learn the network structure change by estimating the ratio of Markov network models. This density-ratio formulation naturally allows us to introduce sparsity in the network structure change, which highly contributes to enhancing interpretability. Furthermore, computation of the normalization term, which is a critical bottleneck of the naive approach, can be remarkably mitigated. We also give the dual formulation of the optimization problem, which further reduces the computation cost for large-scale Markov networks. Through experiments, we demonstrate the usefulness of our method.

We address the problem of estimating the ratio of two probability density functions (a.k.a.~the importance). The importance values can be used for various succeeding tasks such as non-stationarity adaptation or outlier detection. In this paper, we propose a new importance estimation method that has a closed-form solution; the leave-one-out cross-validation score can also be computed analytically. Therefore, the proposed method is computationally very efficient and numerically stable. We also elucidate theoretical properties of the proposed method such as the convergence rate and approximation error bound. Numerical experiments show that the proposed method is comparable to the best existing method in accuracy, while it is computationally more efficient than competing approaches.