Discriminative Density-ratio Estimation

The covariate shift is a challenging problem in supervised learning that results from the discrepancy between the training and test distributions. An effective approach which recently drew a considerable attention in the research community is to reweight the training samples to minimize that discrepancy. In specific, many methods are based on developing Density-ratio (DR) estimation techniques that apply to both regression and classification problems. Although these methods work well for regression problems, their performance on classification problems is not satisfactory. This is due to a key observation that these methods focus on matching the sample marginal distributions without paying attention to preserving the separation between classes in the reweighted space. In this paper, we propose a novel method for Discriminative Density-ratio (DDR) estimation that addresses the aforementioned problem and aims at estimating the density-ratio of joint distributions in a class-wise manner. The proposed algorithm is an iterative procedure that alternates between estimating the class information for the test data and estimating new density ratio for each class. To incorporate the estimated class information of the test data, a soft matching technique is proposed. In addition, we employ an effective criterion which adopts mutual information as an indicator to stop the iterative procedure while resulting in a decision boundary that lies in a sparse region. Experiments on synthetic and benchmark datasets demonstrate the superiority of the proposed method in terms of both accuracy and robustness

Approximating Likelihood Ratios with Calibrated Discriminative Classifiers

In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes that tie parameters $\theta$ of an underlying theory and measurement apparatus to high-dimensional observations $\mathbf{x}\in \mathbb{R}^p$. However, simulator often do not provide a way to evaluate the likelihood function for a given observation $\mathbf{x}$, which motivates a new class of likelihood-free inference algorithms. In this paper, we show that likelihood ratios are invariant under a specific class of dimensionality reduction maps $\mathbb{R}^p \mapsto \mathbb{R}$. As a direct consequence, we show that discriminative classifiers can be used to approximate the generalized likelihood ratio statistic when only a generative model for the data is available. This leads to a new machine learning-based approach to likelihood-free inference that is complementary to Approximate Bayesian Computation, and which does not require a prior on the model parameters. Experimental results on artificial problems with known exact likelihoods illustrate the potential of the proposed method.Comment: 35 pages, 5 figure

Bias Reduction via End-to-End Shift Learning: Application to Citizen Science

Citizen science projects are successful at gathering rich datasets for various applications. However, the data collected by citizen scientists are often biased --- in particular, aligned more with the citizens' preferences than with scientific objectives. We propose the Shift Compensation Network (SCN), an end-to-end learning scheme which learns the shift from the scientific objectives to the biased data while compensating for the shift by re-weighting the training data. Applied to bird observational data from the citizen science project eBird, we demonstrate how SCN quantifies the data distribution shift and outperforms supervised learning models that do not address the data bias. Compared with competing models in the context of covariate shift, we further demonstrate the advantage of SCN in both its effectiveness and its capability of handling massive high-dimensional data

An Inhomogeneous Bayesian Texture Model for Spatially Varying Parameter Estimation

In statistical model based texture feature extraction, features based on spatially varying parameters achievehigher discriminative performances compared to spatially constant parameters. In this paper we formulate anovel Bayesian framework which achieves texture characterization by spatially varying parameters based onGaussian Markov random fields. The parameter estimation is carried out by Metropolis-Hastings algorithm.The distributions of estimated spatially varying parameters are then used as successful discriminant texturefeatures in classification and segmentation. Results show that novel features outperform traditional GaussianMarkov random field texture features which use spatially constant parameters. These features capture bothpixel spatial dependencies and structural properties of a texture giving improved texture features for effectivetexture classification and segmentation