Classification is the basis of cognition. Unlike other solutions, this study approaches it from the view of outliers. We present an expanding algorithm to detect outliers in univariate datasets, together with the underlying foundation. The expanding algorithm runs in a holistic way, making it a rather robust solution. Synthetic and real data experiments show its power. Furthermore, an application for multi-class problems leads to the introduction of the oscillator algorithm. The corresponding result implies the potential wide use of the expanding algorithm.

Structured sparse coding and the related structured dictionary learning problems are novel research areas in machine learning. In this paper we present a new application of structured dictionary learning for collaborative filtering based recommender systems. Our extensive numerical experiments demonstrate that the presented technique outperforms its state-of-the-art competitors and has several advantages over approaches that do not put structured constraints on the dictionary elements.

Recently, image categorization has been an active research topic due to the urgent need to retrieve and browse digital images via semantic keywords. This paper formulates image categorization as a multi-label classification problem using recent advances in matrix completion. Under this setting, classification of testing data is posed as a problem of completing unknown label entries on a data matrix that concatenates training and testing features with training labels. We propose two convex algorithms for matrix completion based on a Rank Minimization criterion specifically tailored to visual data, and prove its convergence properties.

In this paper, we give a new generalization error bound of Multiple Kernel Learning (MKL) for a general class of regularizations. Our main target in this paper is dense type regularizations including ℓp-MKL that imposes ℓp-mixed-norm regularization instead of ℓ1-mixed-norm regularization. According to the recent numerical experiments, the sparse regularization does not necessarily show a good performance compared with dense type regularizations. Motivated by this fact, this paper gives a general theoretical tool to derive fast learning rates that is applicable to arbitrary monotone norm-type regularizations in a unifying manner. As a by-product of our general result, we show a fast learning rate of ℓp-MKL that is tightest among existing bounds. We also show that our general learning rate achieves the minimax lower bound. Finally, we show that, when the complexities of candidate reproducing kernel Hilbert spaces are inhomogeneous, dense type regularization shows better learning rate compared with sparse ℓ1 regularization.

We address the challenging task of decoupling material properties from lighting properties given a single image. In the last two decades virtually all works have concentrated on exploiting edge information to address this problem. We take a different route by introducing a new prior on reflectance, that models reflectance values as being drawn from a sparse set of basis colors. This results in a Random Field model with global, latent variables (basis colors) and pixel-accurate output reflectance values. We show that without edge information high-quality results can be achieved, that are on par with methods exploiting this source of information. Finally, we present competitive results by integrating an additional edge model. We believe that our approach is a solid starting point for future development in this domain.

We present a joint image segmentation and labeling model (JSL) which, given a bag of figure-ground segment hypotheses extracted at multiple image locations and scales, constructs a joint probability distribution over both the compatible image interpretations (tilings or image segmentations) composed from those segments, andover their labeling into categories. The process of drawing samples from the joint distribution can be interpreted as first sampling tilings, modeled as maximal cliques, from a graph connecting spatially non-overlapping segments in the bag [1], followed by sampling labels for those segments, conditioned on the choice of a particular tiling. We learn the segmentation and labeling parameters jointly,based on Maximum Likelihood with a novel Incremental Saddle Point estimation procedure. The partition function over tilings and labelings is increasingly moreaccurately approximated by including incorrect configurations that a not-yet-competent model rates probable during learning. We show that the proposed methodologymatches the current state of the art in the Stanford dataset [2], as well as in VOC2010, where 41.7% accuracy on the test set is achieved.

Increasingly, optimization problems in machine learning, especially those arising from high-dimensional statistical estimation, have a large number of variables. Modern statistical estimators developed over the past decade have statistical or sample complexity that depends only weakly on the number of parameters when there is some structure to the problem, such as sparsity. A central question is whether similar advances can be made in their computational complexity as well. In this paper, we propose strategies that indicate that such advances can indeed be made. In particular, we investigate the greedy coordinate descent algorithm, and note that performing the greedy step efficiently weakens the costly dependence on the problem size provided the solution is sparse. We then propose a suite of methods that perform these greedy steps efficiently by a reduction to nearest neighbor search. We also devise a more amenable form of greedy descent for composite non-smooth objectives; as well as several approximate variants of such greedy descent. We develop a practical implementation of our algorithm that combines greedy coordinate descent with locality sensitive hashing. Without tuning the latter data structure, we are not only able to significantly speed up the vanilla greedy method, but also outperform cyclic descent when the problem size becomes large. Our results indicate the effectiveness of our nearest neighbor strategies, and also point to many open questions regarding the development of computational geometric techniques tailored towards first-order optimization methods.

We introduce the Gamma-Exponential Process (GEP), a prior over a large family of continuous time stochastic processes. A hierarchical version of this prior (HGEP; the Hierarchical GEP) yields a useful model for analyzing complex time series. Models based on HGEPs display many attractive properties: conjugacy, exchangeability and closed-form predictive distribution for the waiting times, and exact Gibbs updates for the time scale parameters. After establishing these properties, we show how posterior inference can be carried efficiently using Particle MCMC methods [1]. This yields a MCMC algorithm that can resample entire sequences atomically while avoiding the complications of introducing slice and stick auxiliary variables of the beam sampler [2]. We applied our model to the problem of estimating the disease progression in multiple sclerosis [3], and to RNA evolutionary modeling [4]. In both domains, we found that our model outperformed the standard rate matrix estimation approach.

Multi-instance learning (MIL) considers input as bags of instances, in which labels are assigned to the bags. MIL is useful in many real-world applications. For example, in image categorization semantic meanings (labels) of an image mostly arise from its regions (instances) instead of the entire image (bag). Existing MIL methods typically build their models using the Bag-to-Bag (B2B) distance, which are often computationally expensive and may not truly reflect the semantic similarities. To tackle this, in this paper we approach MIL problems from a new perspective using the Class-to-Bag (C2B) distance, which directly assesses the relationships between the classes and the bags.

Extracting good representations from images is essential for many computer vision tasks. In this paper, we propose hierarchical matching pursuit (HMP), which builds a feature hierarchy layer-by-layer using an efficient matching pursuit encoder. It includes three modules: batch (tree) orthogonal matching pursuit, spatial pyramid max pooling, and contrast normalization. We investigate the architecture of HMP, and show that all three components are critical for good performance. To speed up the orthogonal matching pursuit, we propose a batch tree orthogonal matching pursuit that is particularly suitable to encode a large number of observations that share the same large dictionary. HMP is scalable and can efficiently handle full-size images. In addition, HMP enables linear support vector machines (SVM) to match the performance of nonlinear SVM while being scalable to large datasets. We compare HMP with many state-of-the-art algorithms including convolutional deep belief networks, SIFT based single layer sparse coding, and kernel based feature learning. HMP consistently yields superior accuracy on three types of image classification problems: object recognition (Caltech-101), scene recognition (MIT-Scene), and static event recognition (UIUC-Sports).