We propose to solve a label ranking problem as a structured output regression task. We adopt a least square surrogate loss approach that solves a supervised learning problem in two steps: the regression step in a well-chosen feature space and the pre-image step. We use specific feature maps/embeddings for ranking data, which convert any ranking/permutation into a vector representation. These embeddings are all well-tailored for our approach, either by resulting in consistent estimators, or by solving trivially the pre-image problem which is often the bottleneck in structured prediction. We also propose their natural extension to the case of partial rankings and prove their efficiency on real-world datasets.
We present Memory Augmented Policy Optimization (MAPO), a simple and novel way to leverage a memory buffer of promising trajectories to reduce the variance of policy gradient estimate. MAPO is applicable to deterministic environments with discrete actions, such as structured prediction and combinatorial optimization tasks. We express the expected return objective as a weighted sum of two terms: an expectation over the high-reward trajectories inside the memory buffer, and a separate expectation over trajectories outside the buffer. To make an efficient algorithm of MAPO, we propose: (1) memory weight clipping to accelerate and stabilize training; (2) systematic exploration to discover high-reward trajectories; (3) distributed sampling from inside and outside of the memory buffer to scale up training. MAPO improves the sample efficiency and robustness of policy gradient, especially on tasks with sparse rewards. We evaluate MAPO on weakly supervised program synthesis from natural language (semantic parsing). On the WikiTableQuestions benchmark, we improve the state-of-the-art by 2.6%, achieving an accuracy of 46.3%. On the WikiSQL benchmark, MAPO achieves an accuracy of 74.9% with only weak supervision, outperforming several strong baselines with full supervision. Our source code is available at https://github.com/crazydonkey200/neural-symbolic-machines
Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we discuss how structured prediction can be extended to a continuous scenario. Specifically, we study a structured prediction approach to manifold valued regression. We characterize a class of problems for which the considered approach is statistically consistent and study how geometric optimization can be used to compute the corresponding estimator. Promising experimental results on both simulated and real data complete our study.
Conditional random field (CRF) and Structural Support Vector Machine (Structural SVM) are two state-of-the-art methods for structured prediction which captures the interdependencies among output variables. The success of these methods is attributed to the fact that their discriminative models are able to account for overlapping features on the whole input observations. These features are usually generated by applying a given set of templates on labeled data, but improper templates may lead to degraded performance. To alleviate this issue, in this paper, we propose a novel multiple template learning paradigm to learn structured prediction and the importance of each template simultaneously, so that hundreds of arbitrary templates could be added into the learning model without caution. This paradigm can be formulated as a special multiple kernel learning problem with exponential number of constraints. Then we introduce an efficient cutting plane algorithm to solve this problem in the primal, and its convergence is presented. We also evaluate the proposed learning paradigm on two widely-studied structured prediction tasks, \emph{i.e.} sequence labeling and dependency parsing. Extensive experimental results show that the proposed method outperforms CRFs and Structural SVMs due to exploiting the importance of each template. Our complexity analysis and empirical results also show that our proposed method is more efficient than OnlineMKL on very sparse and high-dimensional data. We further extend this paradigm for structured prediction using generalized $p$-block norm regularization with $p>1$, and experiments show competitive performances when $p \in [1,2)$.
We introduce a conceptually novel structured prediction model, GPstruct, which is kernelized, non-parametric and Bayesian, by design. We motivate the model with respect to existing approaches, among others, conditional random fields (CRFs), maximum margin Markov networks (M3N), and structured support vector machines (SVMstruct), which embody only a subset of its properties. We present an inference procedure based on Markov Chain Monte Carlo. The framework can be instantiated for a wide range of structured objects such as linear chains, trees, grids, and other general graphs. As a proof of concept, the model is benchmarked on several natural language processing tasks and a video gesture segmentation task involving a linear chain structure. We show prediction accuracies for GPstruct which are comparable to or exceeding those of CRFs and SVMstruct.
In this paper we derive an efficient algorithm to learn the parameters of structured predictors in general graphical models. This algorithm blends the learning and inference tasks, which results in a significant speedup over traditional approaches, such as conditional random fields and structured support vector machines. For this purpose we utilize the structures of the predictors to describe a low dimensional structured prediction task which encourages local consistencies within the different structures while learning the parameters of the model. Convexity of the learning task provides the means to enforce the consistencies between the different parts. The inference-learning blending algorithm that we propose is guaranteed to converge to the optimum of the low dimensional primal and dual programs. Unlike many of the existing approaches, the inference-learning blending allows us to learn efficiently high-order graphical models, over regions of any size, and very large number of parameters. We demonstrate the effectiveness of our approach, while presenting state-of-the-art results in stereo estimation, semantic segmentation, shape reconstruction, and indoor scene understanding.
Structured prediction is a powerful framework for coping with joint prediction of interacting outputs. A central difficulty in using this framework is that often the correct label dependence structure is unknown. At the same time, we would like to avoid an overly complex structure that will lead to intractable prediction. In this work we address the challenge of learning tree structured predictive models that achieve high accuracy while at the same time facilitate efficient (linear time) inference. We start by proving that this task is in general NP-hard, and then suggest an approximate alternative. Briefly, our CRANK approach relies on a novel Circuit-RANK regularizer that penalizes non-tree structures and that can be optimized using a CCCP procedure. We demonstrate the effectiveness of our approach on several domains and show that, despite the relative simplicity of the structure, prediction accuracy is competitive with a fully connected model that is computationally costly at prediction time.
Graphical models for structured domains are powerful tools, but the computational complexities of combinatorial prediction spaces can force restrictions on models, or require approximate inference in order to be tractable. Instead of working in a combinatorial space, we use hinge-loss Markov random fields (HL-MRFs), an expressive class of graphical models with log-concave density functions over continuous variables, which can represent confidences in discrete predictions. This paper demonstrates that HL-MRFs are general tools for fast and accurate structured prediction. We introduce the first inference algorithm that is both scalable and applicable to the full class of HL-MRFs, and show how to train HL-MRFs with several learning algorithms. Our experiments show that HL-MRFs match or surpass the predictive performance of state-of-the-art methods, including discrete models, in four application domains.
In structured output learning, obtaining labelled data for real-world applications is usually costly, while unlabelled examples are available in abundance. Semi-supervised structured classification has been developed to handle large amounts of unlabelled structured data. In this work, we consider semi-supervised structural SVMs with domain constraints. The optimization problem, which in general is not convex, contains the loss terms associated with the labelled and unlabelled examples along with the domain constraints. We propose a simple optimization approach, which alternates between solving a supervised learning problem and a constraint matching problem. Solving the constraint matching problem is difficult for structured prediction, and we propose an efficient and effective hill-climbing method to solve it. The alternating optimization is carried out within a deterministic annealing framework, which helps in effective constraint matching, and avoiding local minima which are not very useful. The algorithm is simple to implement and achieves comparable generalization performance on benchmark datasets.
Missing value imputation is an important practical problem. There is a large body of work on it, but there does not exist any work that formulates the problem in a structured output setting. Also, most applications have constraints on the imputed data, for example on the distribution associated with each variable. None of the existing imputation methods use these constraints. In this paper we propose a structured output approach for missing value imputation that also incorporates domain constraints. We focus on large margin models, but it is easy to extend the ideas to probabilistic models. We deal with the intractable inference step in learning via a piecewise training technique that is simple, efficient, and effective. Comparison with existing state-of-the-art and baseline imputation methods shows that our method gives significantly improved performance on the Hamming loss measure.
In this paper, we push forward the idea of machine learning systems whose operators can be modified and fine-tuned for each problem. This allows us to propose a learning paradigm where users can write (or adapt) their operators, according to the problem, data representation and the way the information should be navigated. To achieve this goal, data instances, background knowledge, rules, programs and operators are all written in the same functional language, Erlang. Since changing operators affect how the search space needs to be explored, heuristics are learnt as a result of a decision process based on reinforcement learning where each action is defined as a choice of operator and rule. As a result, the architecture can be seen as a 'system for writing machine learning systems' or to explore new operators where the policy reuse (as a kind of transfer learning) is allowed. States and actions are represented in a Q matrix which is actually a table, from which a supervised model is learnt. This makes it possible to have a more flexible mapping between old and new problems, since we work with an abstraction of rules and actions. We include some examples sharing reuse and the application of the system gErl to IQ problems. In order to evaluate gErl, we will test it against some structured problems: a selection of IQ test tasks and some experiments on some structured prediction problems (list patterns).
Structured prediction plays a central role in machine learning applications from computational biology to computer vision. These models require significantly more computation than unstructured models, and, in many applications, algorithms may need to make predictions within a computational budget or in an anytime fashion. In this work we propose an anytime technique for learning structured prediction that, at training time, incorporates both structural elements and feature computation trade-offs that affect test-time inference. We apply our technique to the challenging problem of scene understanding in computer vision and demonstrate efficient and anytime predictions that gradually improve towards state-of-the-art classification performance as the allotted time increases.
We propose a novel hybrid loss for multiclass and structured prediction problems that is a convex combination of a log loss for Conditional Random Fields (CRFs) and a multiclass hinge loss for Support Vector Machines (SVMs). We provide a sufficient condition for when the hybrid loss is Fisher consistent for classification. This condition depends on a measure of dominance between labels--specifically, the gap between the probabilities of the best label and the second best label. We also prove Fisher consistency is necessary for parametric consistency when learning models such as CRFs. We demonstrate empirically that the hybrid loss typically performs least as well as--and often better than--both of its constituent losses on a variety of tasks, such as human action recognition. In doing so we also provide an empirical comparison of the efficacy of probabilistic and margin based approaches to multiclass and structured prediction.
Learning to rank is a supervised learning problem where the output space is the space of rankings but the supervision space is the space of relevance scores. We make theoretical contributions to the learning to rank problem both in the online and batch settings. First, we propose a perceptron-like algorithm for learning a ranking function in an online setting. Our algorithm is an extension of the classic perceptron algorithm for the classification problem. Second, in the setting of batch learning, we introduce a sufficient condition for convex ranking surrogates to ensure a generalization bound that is independent of number of objects per query. Our bound holds when linear ranking functions are used: a common practice in many learning to rank algorithms. En route to developing the online algorithm and generalization bound, we propose a novel family of listwise large margin ranking surrogates. Our novel surrogate family is obtained by modifying a well-known pairwise large margin ranking surrogate and is distinct from the listwise large margin surrogates developed using the structured prediction framework. Using the proposed family, we provide a guaranteed upper bound on the cumulative NDCG (or MAP) induced loss under the perceptron-like algorithm. We also show that the novel surrogates satisfy the generalization bound condition.
Recent work has demonstrated that problems-- particularly imitation learning and structured prediction-- where a learner's predictions influence the input-distribution it is tested on can be naturally addressed by an interactive approach and analyzed using no-regret online learning. These approaches to imitation learning, however, neither require nor benefit from information about the cost of actions. We extend existing results in two directions: first, we develop an interactive imitation learning approach that leverages cost information; second, we extend the technique to address reinforcement learning. The results provide theoretical support to the commonly observed successes of online approximate policy iteration. Our approach suggests a broad new family of algorithms and provides a unifying view of existing techniques for imitation and reinforcement learning.
Structured-output learning is a challenging problem; particularly so because of the difficulty in obtaining large datasets of fully labelled instances for training. In this paper we try to overcome this difficulty by presenting a multi-utility learning framework for structured prediction that can learn from training instances with different forms of supervision. We propose a unified technique for inferring the loss functions most suitable for quantifying the consistency of solutions with the given weak annotation. We demonstrate the effectiveness of our framework on the challenging semantic image segmentation problem for which a wide variety of annotations can be used. For instance, the popular training datasets for semantic segmentation are composed of images with hard-to-generate full pixel labellings, as well as images with easy-to-obtain weak annotations, such as bounding boxes around objects, or image-level labels that specify which object categories are present in an image. Experimental evaluation shows that the use of annotation-specific loss functions dramatically improves segmentation accuracy compared to the baseline system where only one type of weak annotation is used.
In this work, we propose the marginal structured SVM (MSSVM) for structured prediction with hidden variables. MSSVM properly accounts for the uncertainty of hidden variables, and can significantly outperform the previously proposed latent structured SVM (LSSVM; Yu & Joachims (2009)) and other state-of-art methods, especially when that uncertainty is large. Our method also results in a smoother objective function, making gradient-based optimization of MSSVMs converge significantly faster than for LSSVMs. We also show that our method consistently outperforms hidden conditional random fields (HCRFs; Quattoni et al. (2007)) on both simulated and real-world datasets. Furthermore, we propose a unified framework that includes both our and several other existing methods as special cases, and provides insights into the comparison of different models in practice.
In this paper, we propose to learn a Mahalanobis distance to perform alignment of multivariate time series. The learning examples for this task are time series for which the true alignment is known. We cast the alignment problem as a structured prediction task, and propose realistic losses between alignments for which the optimization is tractable. We provide experiments on real data in the audio to audio context, where we show that the learning of a similarity measure leads to improvements in the performance of the alignment task. We also propose to use this metric learning framework to perform feature selection and, from basic audio features, build a combination of these with better performance for the alignment.
Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each depending on two specific labels. Intuitively, the more pairwise terms are used, the better the expected accuracy. However, there is currently no theoretical account of this intuition. This paper takes a significant step in this direction. We formulate the problem as classifying the vertices of a known graph $G=(V,E)$, where the vertices and edges of the graph are labelled and correlate semi-randomly with the ground truth. We show that the prospects for achieving low expected Hamming error depend on the structure of the graph $G$ in interesting ways. For example, if $G$ is a very poor expander, like a path, then large expected Hamming error is inevitable. Our main positive result shows that, for a wide class of graphs including 2D grid graphs common in machine vision applications, there is a polynomial-time algorithm with small and information-theoretically near-optimal expected error. Our results provide a first step toward a theoretical justification for the empirical success of the efficient approximate inference algorithms that are used for structured prediction in models where exact inference is intractable.
To cope with the high level of ambiguity faced in domains such as Computer Vision or Natural Language processing, robust prediction methods often search for a diverse set of high-quality candidate solutions or proposals. In structured prediction problems, this becomes a daunting task, as the solution space (image labelings, sentence parses, etc.) is exponentially large. We study greedy algorithms for finding a diverse subset of solutions in structured-output spaces by drawing new connections between submodular functions over combinatorial item sets and High-Order Potentials (HOPs) studied for graphical models. Specifically, we show via examples that when marginal gains of submodular diversity functions allow structured representations, this enables efficient (sub-linear time) approximate maximization by reducing the greedy augmentation step to inference in a factor graph with appropriately constructed HOPs. We discuss benefits, tradeoffs, and show that our constructions lead to significantly better proposals.