Convex relaxation of mixture regression with efficient algorithms

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data

Beyond 2D-grids: a dependence maximization view on image browsing

Ideally, one would like to perform image search using an intuitive and friendly approach. Many existing image search engines, however, present users with sets of images arranged in some default order on the screen, typically the relevance to a query, only. While this certainly has its advantages, arguably, a more flexible and intuitive way would be to sort images into arbitrary structures such as grids, hierarchies, or spheres so that images that are visually or semantically alike are placed together. This paper focuses on designing such a navigation system for image browsers. This is a challenging task because arbitrary layout structure makes it difficult -- if not impossible -- to compute cross-similarities between images and structure coordinates, the main ingredient of traditional layouting approaches. For this reason, we resort to a recently developed machine learning technique: kernelized sorting. It is a general technique for matching pairs of objects from different domains without requiring cross-domain similarity measures and hence elegantly allows sorting images into arbitrary structures. Moreover, we extend it so that some images can be preselected for instance forming the tip of the hierarchy allowing to subsequently navigate through the search results in the lower levels in an intuitive way

Estimating labels from label proportions

Consider the following problem: given sets of unlabeled observations, each set with known label proportions, predict the labels of another set of observations, also with known label proportions. This problem appears in areas like e-commerce, spam filtering and improper content detection. We present consistent estimators which can reconstruct the correct labels with high probability in a uniform convergence sense. Experiments show that our method works well in practice.

The supervised IBP: neighbourhood preserving infinite latent feature models

We propose a probabilistic model to infer supervised latent variables in the Hamming space from observed data. Our model allows simultaneous inference of the number of binary latent variables, and their values. The latent variables preserve neighbourhood structure of the data in a sense that objects in the same semantic concept have similar latent values, and objects in different concepts have dissimilar latent values. We formulate the supervised infinite latent variable problem based on an intuitive principle of pulling objects together if they are of the same type, and pushing them apart if they are not. We then combine this principle with a flexible Indian Buffet Process prior on the latent variables. We show that the inferred supervised latent variables can be directly used to perform a nearest neighbour search for the purpose of retrieval. We introduce a new application of dynamically extending hash codes, and show how to effectively couple the structure of the hash codes with continuously growing structure of the neighbourhood preserving infinite latent feature space

Learning based automatic face annotation for arbitrary poses and expressions from frontal images only

Statistical approaches for building non-rigid deformable models, such as the active appearance model (AAM), have enjoyed great popularity in recent years, but typically require tedious manual annotation of training images. In this paper, a learning based approach for the automatic annotation of visually deformable objects from a single annotated frontal image is presented and demonstrated on the example of automatically annotating face images that can be used for building AAMs for fitting and tracking. This approach employs the idea of initially learning the correspondences between landmarks in a frontal image and a set of training images with a face in arbitrary poses. Using this learner, virtual images of unseen faces at any arbitrary pose for which the learner was trained can be reconstructed by predicting the new landmark locations and warping the texture from the frontal image. View-based AAMs are then built from the virtual images and used for automatically annotating unseen images, including images of different facial expressions, at any random pose within the maximum range spanned by the virtually reconstructed images. The approach is experimentally validated by automatically annotating face images from three different databases

Kernel conditional quantile estimation via reduction revisited

Quantile regression refers to the process of estimating the quantiles of a conditional distribution and has many important applications within econometrics and data mining, among other domains. In this paper, we show how to estimate these conditional quantile functions within a Bayes risk minimization framework using a Gaussian process prior. The resulting non-parametric probabilistic model is easy to implement and allows non-crossing quantile functions to be enforced. Moreover, it can directly be used in combination with tools and extensions of standard Gaussian Processes such as principled hyperparameter estimation, sparsification, and quantile regression with input-dependent noise rates. No existing approach enjoys all of these desirable properties. Experiments on benchmark datasets show that our method is competitive with state-of-the-art approaches.

Multitask learning without label correspondences

We propose an algorithm to perform multitask learning where each task has potentially distinct label sets and label correspondences are not readily available. This is in contrast with existing methods which either assume that the label sets shared by different tasks are the same or that there exists a label mapping oracle. Our method directly maximizes the mutual information among the labels, and we show that the resulting objective function can be efficiently optimized using existing algorithms. Our proposed approach has a direct application for data integration with different label spaces for the purpose of classification, such as integrating Yahoo! and DMOZ web directories

Contrastive examples for addressing the tyranny of the majority

Computer vision algorithms, e.g. for face recognition, favour groups of individuals that are better represented in the training data. This happens because of the generalization that classifiers have to make. It is simpler to fit the majority groups as this fit is more important to overall error. We propose to create a balanced training dataset, consisting of the original dataset plus new data points in which the group memberships are intervened, minorities become majorities and vice versa. We show that current generative adversarial networks are a powerful tool for learning these data points, called contrastive examples. We experiment with the equalized odds bias measure on tabular data as well as image data (CelebA and Diversity in Faces datasets). Contrastive examples allow us to expose correlations between group membership and other seemingly neutral features. Whenever a causal graph is available, we can put those contrastive examples in the perspective of counterfactuals

Ambiguity helps: classification with disagreements in crowdsourced annotations

Imagine we show an image to a person and ask her/him to decide whether the scene in the image is warm or not warm, and whether it is easy or not to spot a squirrel in the image. For exactly the same image, the answers to those questions are likely to differ from person to person. This is because the task is inherently ambiguous. Such an ambiguous, therefore challenging, task is pushing the boundary of computer vision in showing what can and can not be learned from visual data. Crowdsourcing has been invaluable for collecting annotations. This is particularly so for a task that goes beyond a clear-cut dichotomy as multiple human judgments per image are needed to reach a consensus. This paper makes conceptual and technical contributions. On the conceptual side, we define disagreements among annotators as privileged information about the data instance. On the technical side, we propose a framework to incorporate annotation disagreements into the classifiers. The proposed framework is simple, relatively fast, and outperforms classifiers that do not take into account the disagreements, especially if tested on high confidence annotations

Inferring individual attributes from search engine queries and auxiliary information

Internet data has surfaced as a primary source for investigation of different aspects of human behavior. A crucial step in such studies is finding a suitable cohort (i.e., a set of users) that shares a common trait of interest to researchers. However, direct identification of users sharing this trait is often impossible, as the data available to researchers is usually anonymized to preserve user privacy. To facilitate research on specific topics of interest, especially in medicine, we introduce an algorithm for identifying a trait of interest in anonymous users. We illustrate how a small set of labeled examples, together with statistical information about the entire population, can be aggregated to obtain labels on unseen examples. We validate our approach using labeled data from the political domain. We provide two applications of the proposed algorithm to the medical domain. In the first, we demonstrate how to identify users whose search patterns indicate they might be suffering from certain types of cancer. In the second, we detail an algorithm to predict the distribution of diseases given their incidence in a subset of the population at study, making it possible to predict disease spread from partial epidemiological data