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.

We present a framework for online inference in the presence of a nonexhaustively defined set of classes that incorporates supervised classification with class discovery and modeling. A Dirichlet process prior (DPP) model defined over class distributions ensures that both known and unknown class distributions originate according to a common base distribution. In an attempt to automatically discover potentially interesting class formations, the prior model is coupled with a suitably chosen data model, and sequential Monte Carlo sampling is used to perform online inference. Our research is driven by a biodetection application, where a new class of pathogen may suddenly appear, and the rapid increase in the number of samples originating from this class indicates the onset of an outbreak.

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.

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situation where the data variance is already partially explained by other factors, for example sparse conditional dependencies between the covariates, or temporal correlations leaving some residual variance. We decompose the residual variance into its components through a generalised eigenvalue problem, which we call residual component analysis (RCA). We explore a range of new algorithms that arise from the framework, including one that factorises the covariance of a Gaussian density into a low-rank and a sparse-inverse component. We illustrate the ideas on the recovery of a protein-signaling network, a gene expression time-series data set and the recovery of the human skeleton from motion capture 3-D cloud data.

Temporal alignment of sequences is an important problem with many practical applications such as speech recognition [1, 2], activity recognition [3, 4], temporal segmentation [5], curve matching [6], chromatographic and micro-array data analysis [7], synthesis of human motion [8], and temporal alignment of human motion [9, 10]. Dynamic time warping (DTW) is a classical temporal alignment method that aligns two sequences by minimizing the pairwise squared Euclidean distance [1, 2]. An advantage of DTW is that the minimization can be efficiently carried out by dynamic programming (DP) [11]. However, due to the Euclidean formulation, DTW may not be able to find a good alignment when the characteristics of the two sequences are substantially different (e.g., sequences have different amplitudes). Moreover, DTW cannot handle sequences with different dimensions (e.g., image to audio alignment), which limits the range of applications significantly.

Oriental ink painting, called Sumi-e, is one of the most appealing painting styles that has attracted artists around the world. Major challenges in computer-based Sumi-e simulation are to abstract complex scene information and draw smooth and natural brush strokes. To automatically find such strokes, we propose to model the brush as a reinforcement learning agent, and learn desired brush-trajectories by maximizing the sum of rewards in the policy search framework. We also provide elaborate design of actions, states, and rewards tailored for a Sumi-e agent. The effectiveness of our proposed approach is demonstrated through simulated Sumi-e experiments.

Belief Propagation (BP) is one of the most popular methods for inference in probabilistic graphical models. BP is guaranteed to return the correct answer for tree structures, but can be incorrect or non-convergent for loopy graphical models. Recently, several new approximate inference algorithms based on cavity distribution have been proposed. These methods can account for the effect of loops by incorporating the dependency between BP messages. Alternatively, region-based approximations (that lead to methods such as Generalized Belief Propagation) improve upon BP by considering interactions within small clusters of variables, thus taking small loops within these clusters into account. This paper introduces an approach, Generalized Loop Correction (GLC), that benefits from both of these types of loop correction. We show how GLC relates to these two families of inference methods, then provide empirical evidence that GLC works effectively in general, and can be significantly more accurate than both correction schemes.

Effective learning of user preferences is critical to easing user burden in various types of matching problems. Equally important is active query selection to further reduce the amount of preference information users must provide. We address the problem of active learning of user preferences for matching problems, introducing a novel method for determining probabilistic matchings, and developing several new active learning strategies that are sensitive to the specific matching objective. Experiments with real-world data sets spanning diverse domains demonstrate that matching-sensitive active learning outperforms standard techniques.

Algorithms for learning distributions over weight-vectors, such as AROW were recently shown empirically to achieve state-of-the-art performance at various problems, with strong theoretical guaranties. Extending these algorithms to matrix models pose challenges since the number of free parameters in the covariance of the distribution scales as $n^4$ with the dimension $n$ of the matrix, and $n$ tends to be large in real applications. We describe, analyze and experiment with two new algorithms for learning distribution of matrix models. Our first algorithm maintains a diagonal covariance over the parameters and can handle large covariance matrices. The second algorithm factors the covariance to capture inter-features correlation while keeping the number of parameters linear in the size of the original matrix. We analyze both algorithms in the mistake bound model and show a superior precision performance of our approach over other algorithms in two tasks: retrieving similar images, and ranking similar documents. The factored algorithm is shown to attain faster convergence rate.

We consider the problem of parameter estimation using weakly supervised datasets, where a training sample consists of the input and a partially specified annotation, which we refer to as the output. The missing information in the annotation is modeled using latent variables. Previous methods overburden a single distribution with two separate tasks: (i) modeling the uncertainty in the latent variables during training; and (ii) making accurate predictions for the output and the latent variables during testing. We propose a novel framework that separates the demands of the two tasks using two distributions: (i) a conditional distribution to model the uncertainty of the latent variables for a given input-output pair; and (ii) a delta distribution to predict the output and the latent variables for a given input. During learning, we encourage agreement between the two distributions by minimizing a loss-based dissimilarity coefficient. Our approach generalizes latent SVM in two important ways: (i) it models the uncertainty over latent variables instead of relying on a pointwise estimate; and (ii) it allows the use of loss functions that depend on latent variables, which greatly increases its applicability. We demonstrate the efficacy of our approach on two challenging problems---object detection and action detection---using publicly available datasets.