Max-margin Markov Networks Research Articles

Face Association for Videos Using Conditional Random Fields and Max-Margin Markov Networks.

We address the video-based face association problem, in which one attempts to extract the face tracks of multiple subjects while maintaining label consistency. Traditional tracking algorithms have difficulty in handling this task, especially when challenging nuisance factors like motion blur, low resolution or significant camera motions are present. We demonstrate that contextual features, in addition to face appearance itself, play an important role in this case. We propose principled methods to combine multiple features using Conditional Random Fields and Max-Margin Markov networks to infer labels for the detected faces. Different from many existing approaches, our algorithms work in online mode and hence have a wider range of applications. We address issues such as parameter learning, inference and handling false positves/negatives that arise in the proposed approach. Finally, we evaluate our approach on several public databases.

Tracking Human Pose Using Max-Margin Markov Models.

We present a new method for tracking human pose by employing max-margin Markov models. Representing a human body by part-based models, such as pictorial structure, the problem of pose tracking can be modeled by a discrete Markov random field. Considering max-margin Markov networks provide an efficient way to deal with both structured data and strong generalization guarantees, it is thus natural to learn the model parameters using the max-margin technique. Since tracking human pose needs to couple limbs in adjacent frames, the model will introduce loops and will be intractable for learning and inference. Previous work has resorted to pose estimation methods, which discard temporal information by parsing frames individually. Alternatively, approximate inference strategies have been used, which can overfit to statistics of a particular data set. Thus, the performance and generalization of these methods are limited. In this paper, we approximate the full model by introducing an ensemble of two tree-structured sub-models, Markov networks for spatial parsing and Markov chains for temporal parsing. Both models can be trained jointly using the max-margin technique, and an iterative parsing process is proposed to achieve the ensemble inference. We apply our model on three challengeable data sets, which contains highly varied and articulated poses. Comprehensive experimental results demonstrate the superior performance of our method over the state-of-the-art approaches.

Large Discriminative Structured Set Prediction Modeling With Max-Margin Markov Network for Lossless Image Coding.

Inherent statistical correlation for context-based prediction and structural interdependencies for local coherence is not fully exploited in existing lossless image coding schemes. This paper proposes a novel prediction model where the optimal correlated prediction for a set of pixels is obtained in the sense of the least code length. It not only exploits the spatial statistical correlations for the optimal prediction directly based on 2D contexts, but also formulates the data-driven structural interdependencies to make the prediction error coherent with the underlying probability distribution for coding. Under the joint constraints for local coherence, max-margin Markov networks are incorporated to combine support vector machines structurally to make max-margin estimation for a correlated region. Specifically, it aims to produce multiple predictions in the blocks with the model parameters learned in such a way that the distinction between the actual pixel and all possible estimations is maximized. It is proved that, with the growth of sample size, the prediction error is asymptotically upper bounded by the training error under the decomposable loss function. Incorporated into the lossless image coding framework, the proposed model outperforms most prediction schemes reported.

Structured Set Intra Prediction With Discriminative Learning in a Max-Margin Markov Network for High Efficiency Video Coding.

This paper proposes a novel model on intra coding for High Efficiency Video Coding (HEVC), which simultaneously predicts blocks of pixels with optimal rate distortion. It utilizes the spatial statistical correlation for the optimal prediction based on 2-D contexts, in addition to formulating the data-driven structural interdependences to make the prediction error coherent with the probability distribution, which is desirable for successful transform and coding. The structured set prediction model incorporates a max-margin Markov network (M3N) to regulate and optimize multiple block predictions. The model parameters are learned by discriminating the actual pixel value from other possible estimates to maximize the margin (i.e., decision boundary bandwidth). Compared to existing methods that focus on minimizing prediction error, the M3N-based model adaptively maintains the coherence for a set of predictions. Specifically, the proposed model concurrently optimizes a set of predictions by associating the loss for individual blocks to the joint distribution of succeeding discrete cosine transform coefficients. When the sample size grows, the prediction error is asymptotically upper bounded by the training error under the decomposable loss function. As an internal step, we optimize the underlying Markov network structure to find states that achieve the maximal energy using expectation propagation. For validation, we integrate the proposed model into HEVC for optimal mode selection on rate-distortion optimization. The proposed prediction model obtains up to 2.85% bit rate reduction and achieves better visual quality in comparison to the HEVC intra coding.

Accelerated training of max-margin Markov networks with kernels

Structured output prediction is an important machine learning problem both in theory and practice, and the max-margin Markov network (M3N) is an effective approach. All state-of-the-art algorithms for optimizing M3N objectives take at least O(1/ϵ) number of iterations to find an ϵ accurate solution. Nesterov [1] broke this barrier by proposing an excessive gap reduction technique (EGR) which converges in O(1/ϵ) iterations. However, it is restricted to Euclidean projections which consequently requires an intractable amount of computation for each iteration when applied to solve M3N. In this paper, we show that by extending EGR to Bregman projection, this faster rate of convergence can be retained, and more importantly, the updates can be performed efficiently by exploiting graphical model factorization. Further, we design a kernelized procedure which allows all computations per iteration to be performed at the same cost as the state-of-the-art approaches.

Probabilistic models of vision and max-margin methods

It is attractive to formulate problems in computer vision and related fields in term of probabilistic estimation where the probability models are defined over graphs, such as grammars. The graphical structures, and the state variables defined over them, give a rich knowledge representation which can describe the complex structures of objects and images. The probability distributions defined over the graphs capture the statistical variability of these structures. These probability models can be learnt from training data with limited amounts of supervision. But learning these models suffers from the difficulty of evaluating the normalization constant, or partition function, of the probability distributions which can be extremely computationally demanding. This paper shows that by placing bounds on the normalization constant we can obtain computationally tractable approximations. Surprisingly, for certain choices of loss functions, we obtain many of the standard max-margin criteria used in support vector machines (SVMs) and hence we reduce the learning to standard machine learning methods. We show that many machine learning methods can be obtained in this way as approximations to probabilistic methods including multi-class max-margin, ordinal regression, max-margin Markov networks and parsers, multiple-instance learning, and latent SVM. We illustrate this work by computer vision applications including image labeling, object detection and localization, and motion estimation. We speculate that better results can be obtained by using better bounds and approximations.

Exponentiated Gradient Algorithms for Conditional Random Fields and Max-Margin Markov Networks

Log-linear and maximum-margin models are two commonly-used methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large data sets. This paper describes exponentiated gradient (EG) algorithms for training such models, where EG updates are applied to the convex dual of either the log-linear or max-margin objective function; the dual in both the log-linear and max-margin cases corresponds to minimizing a convex function with simplex constraints. We study both batch and online variants of the algorithm, and provide rates of convergence for both cases. In the max-margin case, O(1/e) EG updates are required to reach a given accuracy e in the dual; in contrast, for log-linear models only O(log(1/e)) updates are required. For both the max-margin and log-linear cases, our bounds suggest that the online EG algorithm requires a factor of n less computation to reach a desired accuracy than the batch EG algorithm, where n is the number of training examples. Our experiments confirm that the online algorithms are much faster than the batch algorithms in practice. We describe how the EG updates factor in a convenient way for structured prediction problems, allowing the algorithms to be efficiently applied to problems such as sequence learning or natural language parsing. We perform extensive evaluation of the algorithms, comparing them to L-BFGS and stochastic gradient descent for log-linear models, and to SVM-Struct for max-margin models. The algorithms are applied to a multi-class problem as well as to a more complex large-scale parsing task. In all these settings, the EG algorithms presented here outperform the other methods.

Structured Max-Margin Learning for Inter-Related Classifier Training and Multilabel Image Annotation

In this paper, a structured max-margin learning algorithm is developed to achieve more effective training of a large number of inter-related classifiers for multilabel image annotation application. To leverage multilabel images for classifier training, each multilabel image is partitioned into a set of image instances (image regions or image patches) and an automatic instance label identification algorithm is developed to assign multiple labels (which are given at the image level) to the most relevant image instances. A K-way min-max cut algorithm is developed for automatic instance clustering and kernel weight determination, where multiple base kernels are seamlessly combined to address the issue of huge intra-concept visual diversity more effectively. Second, a visual concept network is constructed for characterizing the inter-concept visual similarity contexts more precisely in the high-dimensional multimodal feature space. The visual concept network is used to determine the inter-related learning tasks directly in the feature space rather than in the label space because feature space is the common space for classifier training and image classification. Third, a parallel computing platform is developed to achieve more effective learning of a large number of inter-related classifiers over the visual concept network. A structured max-margin learning algorithm is developed by incorporating the visual concept network, max-margin Markov networks and multitask learning to address the issue of huge inter-concept visual similarity more effectively. By leveraging the inter-concept visual similarity contexts for inter-related classifier training, our structured max-margin learning algorithm can significantly enhance the discrimination power of the inter-related classifiers. Our experiments have also obtained very positive results for a large number of object classes and image concepts.