We consider the scenario where training and test data are drawn from different distributions, commonly referred to as sample selection bias. Most algorithms for this setting try to first recover sampling distributions and then make appropriate corrections based on the distribution estimate. We present a nonparametric method which directly produces resampling weights without distribution estimation. Our method works by matching distributions between training and testing sets in feature space. Experimental results demonstrate that our method works well in practice.

Traditional machine learning makes a basic assumption: the training and test data should be under the same distribution. However, in many cases, this identicaldistribution assumption does not hold. The assumption might be violated when a task from one new domain comes, while there are only labeled data from a similar old domain. Labeling the new data can be costly and it would also be a waste to throw away all the old data. In this paper, we present a novel transfer learning framework called TrAdaBoost, which extends boosting-based learning algorithms (Freund & Schapire, 1997). TrAdaBoost allows users to utilize a small amount of newly labeled data to leverage the old data to construct a high-quality classification model for the new data. We show that this method can allow us to learn an accurate model using only a tiny amount of new data and a large amount of old data, even when the new data are not sufficient to train a model alone. We show that TrAdaBoost allows knowledge to be effectively transferred from the old data to the new. The effectiveness of our algorithm is analyzed theoretically and empirically to show that our iterative algorithm can converge well to an accurate model.

We address classification problems for which the training instances are governed by a distribution that is allowed to differ arbitrarily from the test distribution—problems also referred to as classification under covariate shift. We derive a solution that is purely discriminative: neither training nor test distribution are modeled explicitly. We formulate the general problem of learning under covariate shift as an integrated optimization problem. We derive a kernel logistic regression classifier for differing training and test distributions. 1.

Abstract. We describe a technique for comparing distributions without the need for density estimation as an intermediate step. Our approach relies on mapping the distributions into a reproducing kernel Hilbert space. Applications of this technique can be found in two-sample tests, which are used for determining whether two sets of observations arise from the same distribution, covariate shift correction, local learning, measures of independence, and density estimation. Kernel methods are widely used in supervised learning [1, 2, 3, 4], however they are much less established in the areas of testing, estimation, and analysis of probability distributions, where information theoretic approaches [5, 6] have long been dominant. Recent examples include [7] in the context of construction of graphical models, [8] in the context of feature extraction, and [9] in the context of independent component analysis. These methods have by and large a common issue: to compute quantities such as the mutual information, entropy, or Kullback-Leibler divergence, we require sophisticated space partitioning and/or

We study a setting that is motivated by the problem of filtering spam messages for many users. Each user receives messages according to an individual, unknown distribution, reflected only in the unlabeled inbox. The spam filter for a user is required to perform well with respect to this distribution. Labeled messages from publicly available sources can be utilized, but they are governed by a distinct distribution, not adequately representing most inboxes. We devise a method that minimizes a loss function with respect to a user’s personal distribution based on the available biased sample. A nonparametric hierarchical Bayesian model furthermore generalizes across users by learning a common prior which is imposed on new email accounts. Empirically, we observe that bias-corrected learning outperforms naive reliance on the assumption of independent and identically distributed data; Dirichlet-enhanced generalization across users outperforms a single (“one size fits all”) filter as well as independent filters for all users. 1

We present a unified and complete account of maximum entropy density estimation subject to constraints represented by convex potential functions or, alternatively, by convex regularization. We provide fully general performance guarantees and an algorithm with a complete convergence proof. As special cases, we easily derive performance guarantees for many known regularization types, including ℓ1, ℓ2, ℓ 2 2, and ℓ1+ ℓ 2 2 style regularization. We propose an algorithm solving a large and general subclass of generalized maximum entropy problems, including all discussed in the paper, and prove its convergence. Our approach generalizes and unifies techniques based on information geometry and Bregman divergences as well as those based more directly on compactness. Our work is motivated by a novel application of maximum entropy to species distribution modeling, an important problem in conservation biology and ecology. In a set of experiments on real-world data, we demonstrate the utility of maximum entropy in this setting. We explore effects of different feature types, sample sizes, and regularization levels on the performance of maxent, and discuss interpretability of the resulting models.

Abstract. This paper presents a theoretical analysis of sample selection bias correction. The sample bias correction technique commonly used in machine learning consists of reweighting the cost of an error on each training point of a biased sample to more closely reflect the unbiased distribution. This relies on weights derived by various estimation techniques based on finite samples. We analyze the effect of an error in that estimation on the accuracy of the hypothesis returned by the learning algorithm for two estimation techniques: a cluster-based estimation technique and kernel mean matching. We also report the results of sample bias correction experiments with several data sets using these techniques. Our analysis is based on the novel concept of distributional stability which generalizes the existing concept of point-based stability. Much of our work and proof techniques can be used to analyze other importance weighting techniques and their effect on accuracy when using a distributionally stable algorithm. 1

Accurate modeling of geographic distributions of species is crucial to various applications in ecology and conservation. The best performing techniques often require some parameter tuning, which may be prohibitively time-consuming to do separately for each species, or unreliable for small or biased datasets. Additionally, even with the abundance of good quality data, users interested in the application of species models need not have the statistical knowledge required for detailed tuning. In such cases, it is desirable to use ‘‘default settings’’, tuned and validated on diverse datasets. Maxent is a recently introduced modeling technique, achieving high predictive accuracy and enjoying several additional attractive properties. The performance of Maxent is influenced by a moderate number of parameters. The first contribution of this paper is the empirical tuning of these parameters. Since many datasets lack information about species absence, we present a tuning method that uses presence-only data. We evaluate our method on independently collected high-quality presenceabsence data. In addition to tuning, we introduce several concepts that improve the predictive accuracy and running time of Maxent. We introduce ‘‘hinge features’ ’ that model more complex relationships in the training data; we describe a new logistic output format that gives an estimate of probability of presence; finally we explore ‘‘background sampling’’ strategies that cope with sample selection bias and decrease model-building time. Our evaluation, based on a diverse dataset of 226 species from 6 regions, shows: 1) default settings tuned on presence-only data achieve performance which is almost as good as if they had been tuned on the evaluation data itself; 2) hinge features substantially improve model

Sample selection bias is a common problem in many real world applications, where training data are obtained under realistic constraints that make them follow a different distribution from the future testing data. For example, in the application of hospital clinical studies, it is common practice to build models from the eligible volunteers as the training data, and then apply the model to the entire populations. Because these volunteers are usually not selected at random, the training set may not be drawn from the same distribution as the test set. Thus, such a dataset suffers from “sample selection bias ” or “covariate shift”. In the past few years, much work has been proposed to reduce sample selection bias, mainly by statically matching the distribution between training set and test set. But in this paper, we do not explore the different distributions directly. Instead, we propose

Maximum entropy (maxent) approach, formally equivalent to maximum likelihood, is a widely used density-estimation method. When input datasets are small, maxent is likely to overfit. Overfitting can be eliminated by various smoothing techniques, such as regularization and constraint relaxation, but theory explaining their properties is often missing or needs to be derived for each case separately. In this dissertation, we propose a unified treatment for a large and general class of smoothing techniques. We provide fully general guarantees on their statistical performance and propose optimization algorithms with complete convergence proofs. As special cases, we can easily derive performance guarantees for many known regularization types including L1 and L2-squared regularization. Furthermore, our general approach enables us to derive entirely new regularization functions with superior statistical guarantees. The new regularization functions use information about the structure of the feature space, incorporate information about sample selection bias, and combine information across several related density-estimation tasks. We propose algorithms solving a large and general subclass of generalized maxent problems, including all