Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally applied to modeling the human visual cortex, sparse coding has also been shown to be useful for self-taught learning, in which the goal is to solve a supervised classification task given access to additional unlabeled data drawn from different classes than that in the supervised learning problem. Shift-invariant sparse coding (SISC) is an extension of sparse coding which reconstructs a (usually time-series) input using all of the basis functions in all possible shifts. In this paper, we present an efficient algorithm for learning SISC bases. Our method is based on iteratively solving two large convex optimization problems: The first, which computes the linear coefficients, is an L1-regularized linear least squares problem with potentially hundreds of thousands of variables. Existing methods typically use a heuristic to select a small subset of the variables to optimize, but we present a way to efficiently compute the exact solution. The second, which solves for bases, is a constrained linear least squares problem. By optimizing over complex-valued variables in the Fourier domain, we reduce the coupling between the different variables, allowing the problem to be solved efficiently. We show that SISC's learned high-level representations of speech and music provide useful features for classification tasks within those domains. When applied to classification, under certain conditions the learned features outperform state of the art spectral and cepstral features.

In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings on high dimensional data. The supervised learning problem can be formulated as an energy functional minimization under Tikhonov regularization scheme, where the energy is composed of a squared loss and a total variation smoothing (or Euler's elastica smoothing). Its solution via variational principles leads to an Euler-Lagrange PDE. However, the PDE is always high-dimensional and cannot be directly solved by common methods. Instead, radial basis functions are utilized to approximate the target function, reducing the problem to finding the linear coefficients of basis functions. We apply the proposed methods to supervised learning tasks (including binary classification, multi-class classification, and regression) on benchmark data sets. Extensive experiments have demonstrated promising results of the proposed methods.

Machine learning research is often conducted in vitro, divorced from motivating practical applications. A researcher might develop a new method for the general task of classification, then assess its utility by comparing its performance (such as accuracy or AUC) to that of existing classification models on publicly available datasets. In terms of advancing machine learning as an academic discipline, this approach has thus far proven quite fruitful. However, it is our view that the most interesting open problems in machine learning are those that arise during its application to real-world problems. We illustrate this point by reviewing two of our interdisciplinary collaborations, both of which have posed unique machine learning problems, providing fertile ground for novel research.

We present an objective function for learning with unlabeled data that utilizes auxiliary expectation constraints. We optimize this objective function using a procedure that alternates between information and moment projections. Our method provides an alternate interpretation of the posterior regularization framework (Graca et al., 2008), maintains uncertainty during optimization unlike constraint-driven learning (Chang et al., 2007), and is more efficient than generalized expectation criteria (Mann & McCallum, 2008). Applications of this framework include minimally supervised learning, semisupervised learning, and learning with constraints that are more expressive than the underlying model. In experiments, we demonstrate comparable accuracy to generalized expectation criteria for minimally supervised learning, and use expressive structural constraints to guide semi-supervised learning, providing a 3%-6% improvement over stateof-the-art constraint-driven learning.

In this paper, we study statistical properties of semi-supervised learning, which is considered as an important problem in the community of machine learning. In the standard supervised learning, only the labeled data is observed. The classification and regression problems are formalized as the supervised learning. In semi-supervised learning, unlabeled data is also obtained in addition to labeled data. Hence, exploiting unlabeled data is important to improve the prediction accuracy in semi-supervised learning. This problems is regarded as a semiparametric estimation problem with missing data. Under the the discriminative probabilistic models, it had been considered that the unlabeled data is useless to improve the estimation accuracy. Recently, it was revealed that the weighted estimator using the unlabeled data achieves better prediction accuracy in comparison to the learning method using only labeled data, especially when the discriminative probabilistic model is misspecified. That is, the improvement under the semiparametric model with missing data is possible, when the semiparametric model is misspecified. In this paper, we apply the density-ratio estimator to obtain the weight function in the semi-supervised learning. The benefit of our approach is that the proposed estimator does not require well-specified probabilistic models for the probability of the unlabeled data. Based on the statistical asymptotic theory, we prove that the estimation accuracy of our method outperforms the supervised learning using only labeled data. Some numerical experiments present the usefulness of our methods.

In this paper, we tackle the problem of online semi-supervised learning (SSL). When data arrive in a stream, the dual problems of computation and data storage arise for any SSL method. We propose a fast approximate online SSL algorithm that solves for the harmonic solution on an approximate graph. We show, both empirically and theoretically, that good behavior can be achieved by collapsing nearby points into a set of local "representative points" that minimize distortion. Moreover, we regularize the harmonic solution to achieve better stability properties. We apply our algorithm to face recognition and optical character recognition applications to show that we can take advantage of the manifold structure to outperform the previous methods. Unlike previous heuristic approaches, we show that our method yields provable performance bounds.

We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary symmetric submodular function. Arbitrary non-symmetric submodular functions can be used via symmetrization. Different choices of submodular functions give different versions of the error bound that are appropriate for different kinds of problems. Moreover, the bound is deterministic and holds for adversarially chosen labels. We show exactly minimizing this error bound is NP-complete. However, we also introduce for any submodular function an associated active semi-supervised learning method that approximately minimizes the corresponding error bound. We show that the error bound is tight in the sense that there is no other bound of the same form which is better. Our theoretical results are supported by experiments on real data.

We present a simple, yet effective, approach to Semi-Supervised Learning. Our approach is based on estimating density-based distances (DBD) using a shortest path calculation on a graph. These Graph-DBD estimates can then be used in any distance-based supervised learning method, such as Nearest Neighbor methods and SVMs with RBF kernels. In order to apply the method to very large data sets, we also present a novel algorithm which integrates nearest neighbor computations into the shortest path search and can find exact shortest paths even in extremely large dense graphs. Significant runtime improvement over the commonly used Laplacian regularization method is then shown on a large scale dataset.

This paper presents an approach for learning to translate simple narratives, i.e., texts (sequences of sentences) describing dynamic systems, into coherent sequences of events without the need for labeled training data. Our approach incorporates domain knowledge in the form of preconditions and effects of events, and we show that it outperforms state-of-the-art supervised learning systems on the task of reconstructing RoboCup soccer games from their commentaries.

Despite the recent trend of increasingly large datasets for object detection, there still exist many classes with few training examples. To overcome this lack of training data for certain classes, we propose a novel way of augmenting the training data for each class by borrowing and transforming examples from other classes. Our model learns which training instances from other classes to borrow and how to transform the borrowed examples so that they become more similar to instances from the target class. Our experimental results demonstrate that our new object detector, with borrowed and transformed examples, improves upon the current state-of-the-art detector on the challenging SUN09 object detection dataset.