Robust regression and classification are often thought to require non-convex loss functions that prevent scalable, global training. However, such a view neglects the possibility of reformulated training methods that can yield practically solvable alternatives. A natural way to make a loss function more robust to outliers is to truncate loss values that exceed a maximum threshold. We demonstrate that a relaxation of this form of "loss clipping" can be made globally solvable and applicable to any standard loss while guaranteeing robustness against outliers. We present a generic procedure that can be applied to standard loss functions and demonstrate improved robustness in regression and classification problems.

A hallmark of modern machine learning is its ability to deal with high dimensional problems by exploiting structural assumptions that limit the degrees of freedom in the underlying model. A deep understanding of the capabilities and limits of high dimensional learning methods under specific assumptions such as sparsity, group sparsity, and low rank has been attsined. Efforts [1,2] are now underway to distill this valuable experience by proposing general unified frameworks that can achieve the twio goals of summarizing previous analyses and enabling their application to notions of structure hitherto unexplored. Inspired by these developments, we propose and analyze a general computational scheme based on a greedy strategy to solve convex optimization problems that arise when dealing with structurally constrained high-dimensional problems. Our framework not only unifies existing greedy algorithms by recovering them as special cases but also yields novel ones.

Most existing Multiple-Instance Learning (MIL) algorithms assume data instances and/or data bags are independently and identically distributed. But there often exists rich additional dependency/structure information between instances/bags within many applications of MIL. Ignoring this structure information limits the performance of existing MIL algorithms. This paper explores the research problem as multiple instance learning on structured data (MILSD) and formulates a novel framework that considers additional structure information. In particular, an effective and efficient optimization algorithm has been proposed to solve the original non-convex optimization problem by using a combination of Concave-Convex Constraint Programming (CCCP) method and an adapted Cutting Plane method, which deals with two sets of constraints caused by learning on instances within individual bags and learning on structured data. Our method has the nice convergence property, with specified precision on each set of constraints. Experimental results on three different applications, i.e., webpage classification, market targeting, and protein fold identification, clearly demonstrate the advantages of the proposed method over state-of-the-art methods.

Log-linear models are widely used probability models for statistical pattern recognition. Typically, log-linear models are trained according to a convex criterion. In recent years, the interest in log-linear models has greatly increased. The optimization of log-linear model parameters is costly and therefore an important topic, in particular for large-scale applications. Different optimization algorithms have been evaluated empirically in many papers. In this work, we analyze the optimization problem analytically and show that the training of log-linear models can be highly ill-conditioned. We verify our findings on two handwriting tasks. By making use of our convergence analysis, we obtain good results on a large-scale continuous handwriting recognition task with a simple and generic approach.

We propose maximum covariance unfolding (MCU), a manifold learning algorithm for simultaneous dimensionality reduction of data from different input modalities. Given high dimensional inputs from two different but naturally aligned sources, MCU computes a common low dimensional embedding that maximizes the cross-modal (inter-source) correlations while preserving the local (intra-source) distances. In this paper, we explore two applications of MCU. First we use MCU to analyze EEG-fMRI data, where an important goal is to visualize the fMRI voxels that are most strongly correlated with changes in EEG traces. To perform this visualization, we augment MCU with an additional step for metric learning in the high dimensional voxel space. Second, we use MCU to perform cross-modal retrieval of matched image and text samples from Wikipedia. To manage large applications of MCU, we develop a fast implementation based on ideas from spectral graph theory. These ideas transform the original problem for MCU, one of semidefinite programming, into a simpler problem in semidefinite quadratic linear programming.

A majority of approximate dynamic programming approaches to the reinforcement learning problem can be categorized into greedy value function methods and value-based policy gradient methods. The former approach, although fast, is well known to be susceptible to the policy oscillation phenomenon. We take a fresh view to this phenomenon by casting a considerable subset of the former approach as a limiting special case of the latter. We explain the phenomenon in terms of this view and illustrate the underlying mechanism with artificial examples. We also use it to derive the constrained natural actor-critic algorithm that can interpolate between the aforementioned approaches. In addition, it has been suggested in the literature that the oscillation phenomenon might be subtly connected to the grossly suboptimal performance in the Tetris benchmark problem of all attempted approximate dynamic programming methods. We report empirical evidence against such a connection and in favor of an alternative explanation. Finally, we report scores in the Tetris problem that improve on existing dynamic programming based results.

We are motivated by an application to extract a representative subset of machine learning training data and by the poor empirical performance we observe of the popular minimum norm algorithm.

Knowledge-based support vector machines (KBSVMs) incorporate advice from domain experts, which can improve generalization significantly. A major limitation that has not been fully addressed occurs when the expert advice is imperfect, which can lead to poorer models. We propose a model that extends KBSVMs and is able to not only learn from data and advice, but also simultaneously improves the advice. The proposed approach is particularly effective for knowledge discovery in domains with few labeled examples. The proposed model contains bilinear constraints, and is solved using two iterative approaches: successive linear programming and a constrained concave-convex approach. Experimental results demonstrate that these algorithms yield useful refinements to expert advice, as well as improve the performance of the learning algorithm overall.

Most previous research on image categorization has focused on medium-scale data sets, while large-scale image categorization with millions of images from thousands of categories remains a challenge. With the emergence of structured large-scale dataset such as the ImageNet, rich information about the conceptual relationships between images, such as a tree hierarchy among various image categories, become available. As human cognition of complex visual world benefits from underlying semantic relationships between object classes, we believe a machine learning system can and should leverage such information as well for better performance. In this paper, we employ such semantic relatedness among image categories for large-scale image categorization. Specifically, a category hierarchy is utilized to properly define loss function and select common set of features for related categories. An efficient optimization method based on proximal approximation and accelerated parallel gradient method is introduced. Experimental results on a subset of ImageNet containing 1.2 million images from 1000 categories demonstrate the effectiveness and promise of our proposed approach.

We consider a class of sparsity-inducing regularization terms based on submodular functions. While previous work has focused on non-decreasing functions, we explore symmetric submodular functions and their Lovász extensions. We show that the Lovász extension may be seen as the convex envelope of a function that depends on level sets (i.e., the set of indices whose corresponding components of the underlying predictor are greater than a given constant): this leads to a class of convex structured regularization terms that impose prior knowledge on the level sets, and not only on the supports of the underlying predictors. We provide unified optimization algorithms, such as proximal operators, and theoretical guarantees (allowed level sets and recovery conditions). By selecting specific submodular functions, we give a new interpretation to known norms, such as the total variation; we also define new norms, in particular ones that are based on order statistics with application to clustering and outlier detection, and on noisy cuts in graphs with application to change point detection in the presence of outliers.