Fair discriminative pedestrian finders are now available. In fact, these pedestrian finders make most errors on pedestrians in configurations that are uncommon in the training data, for example, mounting a bicycle. This is undesirable. However, the human configuration can itself be estimated discriminatively using structure learning. We demonstrate a pedestrian finder which first finds the most likely human pose in the window using a discriminative procedure trained with structure learning on a small dataset. We then present features (local histogram of oriented gradient and local PCA of gradient) based on that configuration to an SVM classifier. We show, using the INRIA Person dataset, that estimates of configuration significantly improve the accuracy of a discriminative pedestrian finder.

This contribution develops a theoretical framework that takes into account the effect of approximate optimization on learning algorithms. The analysis shows distinct tradeoffs for the case of small-scale and large-scale learning problems. Small-scale learning problems are subject to the usual approximation--estimation tradeoff. Large-scale learning problems are subject to a qualitatively different tradeoff involving the computational complexity of the underlying optimization algorithms in non-trivial ways.

Clustering is often formulated as a discrete optimization problem. The objective is to find, among all partitions of the data set, the best one according to some quality measure. However, in the statistical setting where we assume that the finite data set has been sampled from some underlying space, the goal is not to find the best partition of the given sample, but to approximate the true partition of the underlying space.We argue that the discrete optimization approach usually does not achieve this goal. As an alternative, we suggest the paradigm of "nearest neighbor clustering". Instead of selecting the best out of all partitions of the sample, it only considers partitions in some restricted function class. Using tools from statistical learning theory we prove that nearest neighbor clustering is statistically consistent. Moreover,its worst case complexity is polynomial by construction, and it can be implemented with small average case complexity using branch and bound.

We provide a provably efficient algorithm for learning Markov Decision Processes (MDPs) with continuous state and action spaces in the online setting. Specifically, we take a model-based approach and show that a special type of online linear regression allows us to learn MDPs with (possibly kernalized) linearly parameterized dynamics. This result builds on Kearns and Singh's work that provides a provably efficient algorithm for finite state MDPs. Our approach is not restricted to the linear setting, and is applicable to other classes of continuous MDPs.

Markov jump processes play an important role in a large number of application domains. However, realistic systems are analytically intractable and they have traditionally been analysed using simulation based techniques, which do not provide a framework for statistical inference. We propose a mean field approximation to perform posterior inference and parameter estimation. The approximation allows a practical solution to the inference problem, {while still retaining a good degree of accuracy.} We illustrate our approach on two biologically motivated systems.

Assessing similarity between features is a key step in object recognition and scene categorization tasks. We argue that knowledge on the distribution of distances generated by similarity functions is crucial in deciding whether features are similar or not. Intuitively one would expect that similarities between features could arise from any distribution. In this paper, we will derive the contrary, and report the theoretical result that $L_p$-norms --a class of commonly applied distance metrics-- from one feature vector to other vectors are Weibull-distributed if the feature values are correlated and non-identically distributed. Besides these assumptions being realistic for images, we experimentally show them to hold for various popular feature extraction algorithms, for a diverse range of images. This fundamental insight opens new directions in the assessment of feature similarity, with projected improvements in object and scene recognition algorithms. Erratum: The authors of paper have declared that they have become convinced that the reasoning in the reference is too simple as a proof of their claims. As a consequence, they withdraw their theorems.

Maximum entropy analysis of binary variables provides an elegant way for studying therole of pairwise correlations in neural populations. Unfortunately, these approaches suffer from their poor scalability to high dimensions. In sensory coding, however,high-dimensional data is ubiquitous. Here, we introduce a new approach using a near-maximum entropy model, that makes this type of analysis feasiblefor very high-dimensional data--the model parameters can be derived in closed form and sampling is easy. Therefore, our NearMaxEnt approach can serve as a tool for testing predictions from a pairwise maximum entropy model not only for low-dimensional marginals, but also for high dimensional measurements of more than thousand units. We demonstrate its usefulness by studying natural images with dichotomized pixel intensities. Our results indicate that the statistics of such higher-dimensional measurements exhibit additional structure that are not predicted by pairwise correlations, despite the fact that pairwise correlations explain thelower-dimensional marginal statistics surprisingly well up to the limit of dimensionality where estimation of the full joint distribution is feasible.

Learning the common structure shared by a set of supervised tasks is an important practical and theoretical problem. Knowledge of this structure may lead to better generalizationperformance on the tasks and may also facilitate learning new tasks. We propose a framework for solving this problem, which is based on regularization withspectral functions of matrices. This class of regularization problems exhibits appealing computational properties and can be optimized efficiently by an alternating minimization algorithm. In addition, we provide a necessary and sufficient condition for convexity of the regularizer.

The learning of probabilistic models with many hidden variables and nondecomposable dependenciesis an important and challenging problem. In contrast to traditional approaches based on approximate inference in a single intractable model, our approach is to train a set of tractable submodels by encouraging them to agree on the hidden variables. This allows us to capture non-decomposable aspects of the data while still maintaining tractability. We propose an objective function for our approach, derive EMstyle algorithms for parameter estimation, and demonstrate their effectiveness on three challenging real-world learning tasks.

These assumptions are usually encoded in the regulariser or the prior. A generic learning algorithm usually makes rather weak assumptions about the regularities underlying the data.