We study the application of a strongly non-linear generative model to image patches. As in standard approaches such as Sparse Coding or Independent Component Analysis, the model assumes a sparse prior with independent hidden variables. However, in the place where standard approaches use the sum to combine basis functions we use the maximum. To derive tractable approximations for parameter estimation we apply a novel approach based on variational Expectation Maximization. The derived learning algorithm can be applied to large-scale problems with hundreds of observed and hidden variables. Furthermore, we can infer all model parameters including observation noise and the degree of sparseness. In applications to image patches we find that Gabor-like basis functions are obtained. Gabor-like functions are thus not a feature exclusive to approaches assuming linear superposition. Quantitatively, the inferred basis functions show a large diversity of shapes with many strongly elongated and many circular symmetric functions. The distribution of basis function shapes reflects properties of simple cell receptive fields that are not reproduced by standard linear approaches. In the study of natural image statistics, the implications of using different superposition assumptions have so far not been investigated systematically because models with strong non-linearities have been found analytically and computationally challenging. The presented algorithm represents the first large-scale application of such an approach.

The design of low-level image features is critical for computer vision algorithms. Orientation histograms, such as those in SIFT [16] and HOG [3], are the most successful and popular features for visual object and scene recognition. We highlight thekernel view of orientation histograms, and show that they are equivalent to a certain type of match kernels over image patches. This novel view allows us to design a family of kernel descriptors which provide a unified and principled frameworkto turn pixel attributes (gradient, color, local binary pattern, etc.) into compact patch-level features. In particular, we introduce three types of match kernels to measure similarities between image patches, and construct compact low-dimensional kernel descriptors from these match kernels using kernel principal componentanalysis (KPCA) [23]. Kernel descriptors are easy to design and can turn any type of pixel attribute into patch-level features. They outperform carefully tuned and sophisticated features including SIFT and deep belief networks.

We introduce a new family of online learning algorithms based upon constraining the velocity flow over a distribution of weight vectors. In particular, we show how to effectively herd a Gaussian weight vector distribution by trading off velocity constraints with a loss function. By uniformly bounding this loss function, we demonstrate how to solve the resulting optimization analytically. We compare the resulting algorithms on a variety of real world datasets, and demonstrate how these algorithms achieve state-of-the-art robust performance, especially with high label noise in the training data.

We present a new way of converting a reversible finite Markov chain into a nonreversible one, with a theoretical guarantee that the asymptotic variance of the MCMC estimator based on the non-reversible chain is reduced. The method is applicable to any reversible chain whose states are not connected through a tree, and can be interpreted graphically as inserting vortices into the state transition graph. Our result confirms that non-reversible chains are fundamentally better than reversible ones in terms of asymptotic performance, and suggests interesting directions for further improving MCMC.

We propose a new supervised learning framework for visual object counting tasks, such as estimating the number of cells in a microscopic image or the number of humans in surveillance video frames. We focus on the practically-attractive case when the training images are annotated with dots (one dot per object). Our goal is to accurately estimate the count. However, we evade the hard task of learning to detect and localize individual object instances. Instead, we cast the problem as that of estimating an image density whose integral over any image region gives the count of objects within that region. Learning to infer such density can be formulated as a minimization of a regularized risk quadratic cost function. We introduce a new loss function, which is well-suited for such learning, and at the same time can be computed efficiently via a maximum subarray algorithm. The learning can then be posed as a convex quadratic program solvable with cutting-plane optimization. The proposed framework is very flexible as it can accept any domain-specific visual features. Once trained, our system provides accurate object counts and requires a very small time overhead over the feature extraction step, making it a good candidate for applications involving real-time processing or dealing with huge amount of visual data.

Dimensionality reduction is often needed in many applications due to the high dimensionality of the data involved. In this paper, we first analyze the scatter measures used in the conventional linear discriminant analysis~(LDA) model and note that the formulation is based on the average-case view. Based on this analysis, we then propose a new dimensionality reduction method called worst-case linear discriminant analysis~(WLDA) by defining new between-class and within-class scatter measures. This new model adopts the worst-case view which arguably is more suitable for applications such as classification. When the number of training data points or the number of features is not very large, we relax the optimization problem involved and formulate it as a metric learning problem. Otherwise, we take a greedy approach by finding one direction of the transformation at a time. Moreover, we also analyze a special case of WLDA to show its relationship with conventional LDA. Experiments conducted on several benchmark datasets demonstrate the effectiveness of WLDA when compared with some related dimensionality reduction methods.

Latent force models encode the interaction between multiple related dynamical systems in the form of a kernel or covariance function. Each variable to be modeled is represented as the output of a differential equation and each differential equation is driven by a weighted sum of latent functions with uncertainty given by a Gaussian process prior. In this paper we consider employing the latent force model framework for the problem of determining robot motor primitives. To deal with discontinuities in the dynamical systems or the latent driving force we introduce an extension of the basic latent force model, that switches between different latent functions and potentially different dynamical systems. This creates a versatile representation for robot movements that can capture discrete changes and non-linearities in the dynamics. We give illustrative examples on both synthetic data and for striking movements recorded using a Barrett WAM robot as haptic input device. Our inspiration is robot motor primitives, but we expect our model to have wide application for dynamical systems including models for human motion capture data and systems biology.

Computing a {\em maximum a posteriori} (MAP) assignment in graphical models is a crucial inference problem for many practical applications. Several provably convergent approaches have been successfully developed using linear programming (LP) relaxation of the MAP problem. We present an alternative approach, which transforms the MAP problem into that of inference in a finite mixture of simple Bayes nets. We then derive the Expectation Maximization (EM) algorithm for this mixture that also monotonically increases a lower bound on the MAP assignment until convergence. The update equations for the EM algorithm are remarkably simple, both conceptually and computationally, and can be implemented using a graph-based message passing paradigm similar to max-product computation. We experiment on the real-world protein design dataset and show that EM's convergence rate is significantly higher than the previous LP relaxation based approach MPLP. EM achieves a solution quality within $95$\% of optimal for most instances and is often an order-of-magnitude faster than MPLP.

The determination of dominant orientation at a given image location is formulated as a decision-theoretic question. This leads to a novel measure for the dominance of a given orientation $\theta$, which is similar to that used by SIFT. It is then shown that the new measure can be computed with a network that implements the sequence of operations of the standard neurophysiological model of V1. The measure can thus be seen as a biologically plausible version of SIFT, and is denoted as bioSIFT. The network units are shown to exhibit trademark properties of V1 neurons, such as cross-orientation suppression, sparseness and independence. The connection between SIFT and biological vision provides a justification for the success of SIFT-like features and reinforces the importance of contrast normalization in computer vision. We illustrate this by replacing the Gabor units of an HMAX network with the new bioSIFT units. This is shown to lead to significant gains for classification tasks, leading to state-of-the-art performance among biologically inspired network models and performance competitive with the best non-biological object recognition systems.

This paper presents an analysis of importance weighting for learning from finite samples and gives a series of theoretical and algorithmic results. We point out simple cases where importance weighting can fail, which suggests the need for an analysis of the properties of this technique. We then give both upper and lower bounds for generalization with bounded importance weights and, more significantly, give learning guarantees for the more common case of unbounded importance weights under the weak assumption that the second moment is bounded, a condition related to the Renyi divergence of the training and test distributions. These results are based on a series of novel and general bounds we derive for unbounded loss functions, which are of independent interest. We use these bounds to guide the definition of an alternative reweighting algorithm and report the results of experiments demonstrating its benefits. Finally, we analyze the properties of normalized importance weights which are also commonly used.