This paper studies a novel discriminative part-based model to represent and recognize object shapes with an “And-Or graph”. We define this model consisting of three layers: the leaf-nodes with collaborative edges for localizing local parts, the or-nodes specifying the switch of leaf-nodes, and the root-node encoding the global verification. A discriminative learning algorithm, extended from the CCCP [23], is proposed to train the model in a dynamical manner: the model structure (e.g., the configuration of the leaf-nodes associated with the or-nodes) is automatically determined with optimizing the multi-layer parameters during the iteration. The advantages of our method are two-fold. (i) The And-Or graph model enables us to handle well large intra-class variance and background clutters for object shape detection from images. (ii) The proposed learning algorithm is able to obtain the And-Or graph representation without requiring elaborate supervision and initialization. We validate the proposed method on several challenging databases (e.g., INRIA-Horse, ETHZ-Shape, and UIUC-People), and it outperforms the state-of-the-arts approaches.

Sign-random-projection locality-sensitive hashing (SRP-LSH) is a probabilistic dimension reduction method which provides an unbiased estimate of angular similarity, yet suffers from the large variance of its estimation. In this work, we propose the Super-Bit locality-sensitive hashing (SBLSH). It is easy to implement, which orthogonalizes the random projection vectors in batches, and it is theoretically guaranteed that SBLSH also provides an unbiased estimate of angular similarity, yet with a smaller variance when the angle to estimate is within $(0,\pi/2]$. The extensive experiments on real data well validate that given the same length of binary code, SBLSH may achieve significant mean squared error reduction in estimating pairwise angular similarity. Moreover, SBLSH shows the superiority over SRP-LSH in approximate nearest neighbor (ANN) retrieval experiments.

This paper considers a wide spectrum of regularized stochastic optimization problems where both the loss function and regularizer can be non-smooth. We develop a novel algorithm based on the regularized dual averaging (RDA) method, that can simultaneously achieve the optimal convergence rates for both convex and strongly convex loss. In particular, for strongly convex loss, it achieves the optimal rate of $O(\frac{1}{N}+\frac{1}{N^2})$ for $N$ iterations, which improves the best known rate $O(\frac{\log N }{N})$ of previous stochastic dual averaging algorithms. In addition, our method constructs the final solution directly from the proximal mapping instead of averaging of all previous iterates. For widely used sparsity-inducing regularizers (e.g., $\ell_1$-norm), it has the advantage of encouraging sparser solutions. We further develop a multi-stage extension using the proposed algorithm as a subroutine, which achieves the uniformly-optimal rate $O(\frac{1}{N}+\exp\{-N\})$ for strongly convex loss.

We introduce a large-volume box classification for binary prediction, which maintains a subset of weight vectors, and specifically axis-aligned boxes. Our learning algorithm seeks for a box of large volume that contains ``simple'' weight vectors which most of are accurate on the training set. Two versions of the learning process are cast as convex optimization problems, and it is shown how to solve them efficiently. The formulation yields a natural PAC-Bayesian performance bound and it is shown to minimize a quantity directly aligned with it. The algorithm outperforms SVM and the recently proposed AROW algorithm on a majority of $30$ NLP datasets and binarized USPS optical character recognition datasets.

Although many variants of stochastic gradient descent have been proposed for large-scale convex optimization, most of them require projecting the solution at {\it each} iteration to ensure that the obtained solution stays within the feasible domain. For complex domains (e.g., positive semidefinite cone), the projection step can be computationally expensive, making stochastic gradient descent unattractive for large-scale optimization problems. We address this limitation by developing a novel stochastic gradient descent algorithm that does not need intermediate projections. Instead, only one projection at the last iteration is needed to obtain a feasible solution in the given domain. Our theoretical analysis shows that with a high probability, the proposed algorithms achieve an $O(1/\sqrt{T})$ convergence rate for general convex optimization, and an $O(\ln T/T)$ rate for strongly convex optimization under mild conditions about the domain and the objective function.

We propose an efficient, generalized, nonparametric, statistical Kolmogorov-Smirnov test for detecting distributional change in high-dimensional data. To implement the test, we introduce a novel, hierarchical, minimum-volume sets estimator to represent the distributions to be tested. Our work is motivated by the need to detect changes in data streams, and the test is especially efficient in this context. We provide the theoretical foundations of our test and show its superiority over existing methods.

The problem of estimation of entropy functionals of probability densities has received much attention in the information theory, machine learning and statistics communities. Kernel density plug-in estimators are simple, easy to implement and widely used for estimation of entropy. However, kernel plug-in estimators suffer from the curse of dimensionality, wherein the MSE rate of convergence is glacially slow - of order $O(T^{-{\gamma}/{d}})$, where $T$ is the number of samples, and $\gamma>0$ is a rate parameter. In this paper, it is shown that for sufficiently smooth densities, an ensemble of kernel plug-in estimators can be combined via a weighted convex combination, such that the resulting weighted estimator has a superior parametric MSE rate of convergence of order $O(T^{-1})$. Furthermore, it is shown that these optimal weights can be determined by solving a convex optimization problem which does not require training data or knowledge of the underlying density, and therefore can be performed offline. This novel result is remarkable in that, while each of the individual kernel plug-in estimators belonging to the ensemble suffer from the curse of dimensionality, by appropriate ensemble averaging we can achieve parametric convergence rates.

The usability of Brain Computer Interfaces (BCI) based on the P300 speller is severely hindered by the need for long training times and many repetitions of the same stimulus. In this contribution we introduce a set of unsupervised hierarchical probabilistic models that tackle both problems simultaneously by incorporating prior knowledge from two sources: information from other training subjects (through transfer learning) and information about the words being spelled (through language models). We show, that due to this prior knowledge, the performance of the unsupervised models parallels and in some cases even surpasses that of supervised models, while eliminating the tedious training session.

In a large visual multi-class detection framework, the timeliness of results can be crucial. Our method for timely multi-class detection aims to give the best possible performance at any single point after a start time; it is terminated at a deadline time. Toward this goal, we formulate a dynamic, closed-loop policy that infers the contents of the image in order to decide which detector to deploy next. In contrast to previous work, our method significantly diverges from the predominant greedy strategies, and is able to learn to take actions with deferred values. We evaluate our method with a novel timeliness measure, computed as the area under an Average Precision vs. Time curve. Experiments are conducted on the eminent PASCAL VOC object detection dataset. If execution is stopped when only half the detectors have been run, our method obtains $66\%$ better AP than a random ordering, and $14\%$ better performance than an intelligent baseline. On the timeliness measure, our method obtains at least $11\%$ better performance. Our code, to be made available upon publication, is easily extensible as it treats detectors and classifiers as black boxes and learns from execution traces using reinforcement learning.

The dominant visual search paradigm for object class detection is sliding windows. Although simple and effective, it is also wasteful, unnatural and rigidly hardwired. We propose strategies to search for objects which intelligently explore the space of windows by making sequential observations at locations decided based on previous observations. Our strategies adapt to the class being searched and to the content of a particular test image. Their driving force is exploiting context as the statistical relation between the appearance of a window and its location relative to the object, as observed in the training set. In addition to being more elegant than sliding windows, we demonstrate experimentally on the PASCAL VOC 2010 dataset that our strategies evaluate two orders of magnitude fewer windows while at the same time achieving higher detection accuracy.