In real-world classification problems, the class balance in the training dataset does not necessarily reflect that of the test dataset, which can cause significant estimation bias. If the class ratio of the test dataset is known, instance re-weighting or resampling allows systematical bias correction. However, learning the class ratio of the test dataset is challenging when no labeled data is available from the test domain. In this paper, we propose to estimate the class ratio in the test dataset by matching probability distributions of training and test input data. We demonstrate the utility of the proposed approach through experiments.

In many real-world applications of machine learning classifiers, it is essential to predict the probability of an example belonging to a particular class. This paper proposes a simple technique for predicting probabilities based on optimizing a ranking loss, followed by isotonic regression. This semi-parametric technique offers both good ranking and regression performance, and models a richer set of probability distributions than statistical workhorses such as logistic regression. We provide experimental results that show the effectiveness of this technique on real-world applications of probability prediction.

A wide variety of machine learning algorithms such as support vector machine (SVM), minimax probability machine (MPM), and Fisher discriminant analysis (FDA), exist for binary classification. The purpose of this paper is to provide a unified classification model that includes the above models through a robust optimization approach. This unified model has several benefits. One is that the extensions and improvements intended for SVM become applicable to MPM and FDA, and vice versa. Another benefit is to provide theoretical results to above learning methods at once by dealing with the unified model. We give a statistical interpretation of the unified classification model and propose a non-convex optimization algorithm that can be applied to non-convex variants of existing learning methods.

In this paper we propose a simple yet powerful method for learning representations in supervised learning scenarios where each original input datapoint is described by a set of vectors and their associated outputs may be given by soft labels indicating, for example, class probabilities. We represent an input datapoint as a mixture of probabilities over the corresponding set of feature vectors where each probability indicates how likely each vector is to belong to an unknown prototype pattern. We propose a probabilistic model that parameterizes these prototype patterns in terms of hidden variables and therefore it can be trained with conventional approaches based on likelihood maximization. More importantly, both the model parameters and the prototype patterns can be learned from data in a discriminative way. We show that our model can be seen as a probabilistic generalization of learning vector quantization (LVQ). We apply our method to the problems of shape classification, hyperspectral imaging classification and people's work class categorization, showing the superior performance of our method compared to the standard prototype-based classification approach and other competitive benchmark methods.

We propose a general information-theoretic approach called Seraph (SEmi-supervised metRic leArning Paradigm with Hyper-sparsity) for metric learning that does not rely upon the manifold assumption. Given the probability parameterized by a Mahalanobis distance, we maximize the entropy of that probability on labeled data and minimize it on unlabeled data following entropy regularization, which allows the supervised and unsupervised parts to be integrated in a natural and meaningful way. Furthermore, Seraph is regularized by encouraging a low-rank projection induced from the metric. The optimization of Seraph is solved efficiently and stably by an EM-like scheme with the analytical E-Step and convex M-Step. Experiments demonstrate that Seraph compares favorably with many well-known global and local metric learning methods.

In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings on high dimensional data. The supervised learning problem can be formulated as an energy functional minimization under Tikhonov regularization scheme, where the energy is composed of a squared loss and a total variation smoothing (or Euler's elastica smoothing). Its solution via variational principles leads to an Euler-Lagrange PDE. However, the PDE is always high-dimensional and cannot be directly solved by common methods. Instead, radial basis functions are utilized to approximate the target function, reducing the problem to finding the linear coefficients of basis functions. We apply the proposed methods to supervised learning tasks (including binary classification, multi-class classification, and regression) on benchmark data sets. Extensive experiments have demonstrated promising results of the proposed methods.

Driven by the multi-level structure of human intracranial electroencephalogram (iEEG) recordings of epileptic seizures, we introduce a new variant of a hierarchical Dirichlet Process---the multi-level clustering hierarchical Dirichlet Process (MLC-HDP)---that simultaneously clusters datasets on multiple levels. Our seizure dataset contains brain activity recorded in typically more than a hundred individual channels for each seizure of each patient. The MLC-HDP model clusters over channels-types, seizure-types, and patient-types simultaneously. We describe this model and its implementation in detail. We also present the results of a simulation study comparing the MLC-HDP to a similar model, the Nested Dirichlet Process and finally demonstrate the MLC-HDP's use in modeling seizures across multiple patients. We find the MLC-HDP's clustering to be comparable to independent human physician clusterings. To our knowledge, the MLC-HDP model is the first in the epilepsy literature capable of clustering seizures within and between patients.

The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered trees on the basis of their subpaths, which are vertical substructures of trees responsible for hierarchical information in them. Their kernel exhibits practically good performance in terms of accuracy and speed; however, linear-time computation is not guaranteed theoretically, unlike the case of the other unordered tree kernel proposed by Vishwanathan and Smola (2003). In this paper, we propose a theoretically guaranteed linear-time kernel computation algorithm that is practically fast, and we present an efficient prediction algorithm whose running time depends only on the size of the input tree. Experimental results show that the proposed algorithms are quite efficient in practice.

Advances in sensing technologies and the growth of the internet have resulted in an explosion in the size of modern datasets, while storage and processing power continue to lag behind. This motivates the need for algorithms that are efficient, both in terms of the number of measurements needed and running time. To combat the challenges associated with large datasets, we propose a general framework for active hierarchical clustering that repeatedly runs an off-the-shelf clustering algorithm on small subsets of the data and comes with guarantees on performance, measurement complexity and runtime complexity. We instantiate this framework with a simple spectral clustering algorithm and provide concrete results on its performance, showing that, under some assumptions, this algorithm recovers all clusters of size ?(log n) using O(n log^2 n) similarities and runs in O(n log^3 n) time for a dataset of n objects. Through extensive experimentation we also demonstrate that this framework is practically alluring.

Traditionally, multitask learning (MTL) assumes that all the tasks are related. This can lead to negative transfer when tasks are indeed incoherent. Recently, a number of approaches have been proposed that alleviate this problem by discovering the underlying task clusters or relationships. However, they are limited to modeling these relationships at the task level, which may be restrictive in some applications. In this paper, we propose a novel MTL formulation that captures task relationships at the feature-level. Depending on the interactions among tasks and features, the proposed method construct different task clusters for different features, without even the need of pre-specifying the number of clusters. Computationally, the proposed formulation is strongly convex, and can be efficiently solved by accelerated proximal methods. Experiments are performed on a number of synthetic and real-world data sets. Under various degrees of task relationships, the accuracy of the proposed method is consistently among the best. Moreover, the feature-specific task clusters obtained agree with the known/plausible task structures of the data.